Assorted tips on personal finance

By Brian Tomasik

First published: . Last nontrivial update: .

Summary

This page compiles various ideas for personal-finance practices that can save money and allow you to donate more to important causes. It's focused on the USA, and some of the ideas may not apply in other countries. There are already many resources for general advice on managing your money well, and this piece is not intended as a substitute. If you're a newcomer, probably it's best to read the more standard advice.

For further reading, see Ben Kuhn's "Giving away money: a guide."

This piece was originally written in the present tense, but some of these statements no longer apply to me now that I'm not any longer earning to give. Read this piece knowing that many parts were written in 2012.

Update in 2018: The Tax Cuts and Jobs Act of 2017 "increases the allowable deduction for cash donations made to public charities from 50 percent of Adjusted Gross Income (AGI) to 60 percent of AGI" (Miller 2018). I've therefore updated my article to say "60%" where it formerly said "50%" in various places.

Note: Since writing this piece, I've come to learn that many of the ideas about investing presented here are naive and underinformed. When it comes to a complicated topic like this, you really need to be an expert to get things right. So you may want to ignore my investing advice or at least take it with many grains of salt. Unfortunately I don't have the time or expertise to correct all the mistakes. One point that I often failed to appreciate in the past was that unless you're literally risk-neutral (which you shouldn't be even if you're investing for altruistic reasons), you should care about reducing the variance of your portfolio, because lower variance of your portfolio means you can get higher expected returns via leverage for the same amount of risk.

Originally I titled this piece "Advanced tips on personal finance", because some of the ideas discussed here are obscure. However, I changed the word "Advanced" to "Assorted" to avoid giving the impression that I'm an expert regarding this topic. This piece just represents some personal notes I've accumulated over time, focused on optimizing my own individual financial situations.

Contents

Introduction

Money is the unit of caring, and even small amounts of money can prevent tremendous quantities of suffering. Therefore, it's worthwhile for us to learn some basics about personal finance (to the point of diminishing returns from reading more).

General points

First things first

Before worrying about personal-finance and tax optimizations, focus on the big picture. What career will have the highest impact? If you want to earn money to donate, where can you earn the most, taking into account your skills, working hours, lifestyle sustainability, etc.? Do you want to shoot for a startup? You can make the biggest impact to your wealth by thinking about these areas.

Spend time learning the basics of personal finance

Get an intro book or three on the subject, or browse various articles you can find online. Don't worry so much about news, but try to focus on more timeless information, e.g., from Wikipedia or other standard websites.

Investing

Brokerage and checking accounts

I have a brokerage account for trading stocks. With the same company, I also have a donor-advised fund (DAF, see further discussion below) that allows me to get tax deductions for giving now without committing to a specific 501(c)(3). (Before putting a lot of money irrevocably into a DAF, make sure that you can donate to your charity of choice through it. But in practice, you should be able to donate to almost all standard US 501(c)(3)'s without a problem.)

The rest of my bills I pay from the checking account of a local credit union. I keep in the checking account only as much as I need to pay expenses in the next month, because the interest rate on the account is near 0%.

When I earn a paycheck every half-month, I deposit some amount into my checking account. The remainder is direct-deposited to my brokerage account, from which point I either buy a new, random stock or else donate the cash to my DAF.

Buying stocks

It's best to buy stocks during normal trading hours on weekdays, since after-hours trading may involve larger bid-ask spreads and other problems.

Stocks historically have had higher expected returns than bonds. For more evidence on this point, see the discussion about the "equity premium puzzle." Even if you don't believe the equity premium is large, it seems harder to argue that it's not at least positive (see a summary table of risk-premium estimates from various studies on p. 3 of "Rethinking the Equity Risk Premium: An Overview and Some New Ideas"). And since altruists should generally be less risk-averse than egoists, it seems better to invest exclusively in equity, not in fixed-income securities, most of the time.

Some paragraphs of this piece that I wrote in earlier years took the incorrect stance that if you're close to risk-neutral, then you shouldn't care that much about the variance of your investments. I think this is true if you're literally 100% risk-neutral, but if you have even a little bit of risk aversion, as you almost certainly should even if you plan to donate all your wealth, then variance does matter. That's because if portfolio B has the same expected return but lower variance than portfolio A, then you can leverage B until it has the same variance as A, and B will then have higher expected return than A.

Efficient-market hypothesis?

I generally don't worry about the apparent quality of the stock that I buy; I pick something basically at random, perhaps with some bias toward high-beta stocks, though the existence of an advantage for stocks with greater systemic risk has been disputed. There may or may not also be a persistent premium for small-cap stocks. (Update from 2020: This paragraph is old. Now I tend to buy index ETFs or value ETFs. I buy diversified ETFs rather than random stocks mainly for convenience and also for somewhat better diversification, including easier international diversification.)

When you're competing against dozens of hedge funds and investment banks with sub-second trading systems and hordes of experts who spend 60 hours a week researching companies, I don't think you should expect to gain much advantage by making a trade based on a 30-minute-old story you read in the news, or even based on your pet theory of the economy's future. We can debate how efficient the markets actually are, but in any case, it seems unlikely that you could achieve a systematic edge over millions of other investors in your position without doing significant amounts of work. I've heard there are some small opportunities to gain advantage with thinly traded securities if you put in enough effort. The argument goes that hedge funds tend to ignore such opportunities because the potential profits aren't huge. Taking advantage of small market inefficiencies would be like a mouse eating the crumbs from a human's loaf of bread (with hedge funds eating the loaves of bread). I expect it would take at least a few hours per week to take advantage of such opportunities, and I'm not sure how big the potential gains are over regular buy-and-hold investing. I'd like to explore this further, but a priori the task seems unlikely to be easy, since otherwise more people would do it.

While picking individual winning stocks seems dubious, I'm more open to the possibility that systemic trends can be predicted to above-chance accuracy, such as that stock returns as a whole will be lower over the coming 10-20 years based on CAPE. Ideas like this grate against my intuition, because it seems like such trends should be well known until they stop being true. For instance, if people see that the US stock market is overpriced, they should switch to foreign stocks or bonds until prices drop enough that price-to-earnings ratios no longer indicate overpricing. Yet bubbles do happen, and it doesn't seem like they can be completely explained away by hindsight bias. One reasonable-sounding explanation for the failure of efficiency in the case of bubbles is the following: Investment managers are rewarded based on relative rather than absolute performance, so there's incentive to get on the same bandwagon. If you duck out of a bubble while your peers continue to ride it upward, you get hurt. In contrast, if you're part of a bubble when it pops, you're not worse off than anyone else. It seems like this argument shouldn't apply to wealthy individuals like Warren Buffett who aren't compensated based on relative performance, but maybe these people don't own enough of the market to prevent bubbles from developing.

Lower dividends are better?

Another criterion for stock selection may be low dividend yield. The reason is that "non-qualified" dividends are taxed at ordinary income-tax rates (e.g., 28%) on the year of the dividend, whereas capital gains are taxed at lower rates (e.g., 15% as of 2013) and not until you sell the stock. Moreover, if you donate the stock, you never pay capital-gains tax at all but actually can save money from higher capital gains. Actually, many dividends are "qualified" and so are taxed at capital-gains rates, but it's still undesirable that you have to pay these taxes earlier rather than when you dispose of the stock, or not at all if you donate it.

Michael Dickens disagrees with my advice here because "stocks with a high dividend yield historically outperform stocks with low dividend yield, even without considering the value of the dividend. So you're better off buying stocks that pay high dividends." Dickens is citing the extensive literature on the "value premium", discussed in the next subsection.

Value premium

This paper explains:

Companies with a high book-to-market ratio (BEME), referred to as “value firms”, have a higher return than companies with a low book-to-market ratio, or “growth firms”. This “value premium” was first identified by Graham and Dodd (1934) and its interpretation has inspired heated debate. Some authors have warned that this finding may result from sample selection biases or data-snooping. Its apparent persistence, however, both out of sample and after correction for selection biases, has lead to a near consensus on its authenticity.

There's disagreement about the explanation of the value premium. This paper says:

while a number of studies have argued that the superior returns produced by the book-to-market strategy compensate for risk (see, e.g., Fama and French, 1992; Vassalou, 2001; Doukas, Kim and Pantzalis, 2002), others (see, e.g., La Porta et al., 1997; Griffin and Lemmon, 2002; Ali, Hwang and Trombley, 2002) have asserted that there is little evidence to support this risk explanation and offer a mispricing story instead.

This piece summarizes five main explanations for the appearance of a value premium.

I might actually feel more comfortable about the value premium if the efficient-market explanation is correct, because then the value premium would just be a risk premium, similar to the premium for holding stocks rather than bonds. For those who are closer to risk-neutral than most people, this is fine. In contrast, if the value premium relies on human irrationality, it may vanish or reverse in the future. As this page notes:

A key question with any documented return premium is whether it will persist into the future. If a return premium is clearly risk-based like the market factor, then there is no reason to believe it will not persist if financial markets are competitive (making return and risk related). The value premium may be risk-based, behavioral or, more likely, some combination of risk and behavior. But behaviors can persist too. We are more confident in the persistence of the market premium than the value premium.

This post opines:

Does it make sense that the value premium should shrink going forward when compared to past levels?

Certainly. Investors have known about value investing for decades, but the rise of smart beta products and the increased collective knowledge base of the investing community would suggest that the 3+% annual premium should be a thing of the past.

Does that mean the value premium will completely disappear in the future?

No one knows the answer to this question.

I'm still confused and insufficiently educated about this topic, but the empirical case for a value premium seems pretty strong. And even if the value premium fails to materialize going forward, it seems unlikely that value investing will be significantly harmful relative to investing in index funds or growth stocks, except maybe due to taxes and/or fund expense ratios.

This article says:

the fundamental [i.e., value-investing] index fund is less tax efficient, since the rebalancing results in realized capital gains that have to be distributed to the underlying investors. It also incurs more transaction costs and expenses.

In backdating tests, fundamental index funds that base stocks[']’ weights on book values, cash flows, sales or dividends produced higher long-run average returns, often on the order of 2% per year. In practice, when compared to traditional index funds, fundamental-based index funds are essentially value-tilted portfolios. So, you should not be surprised to see higher gross returns on fundamental indexes. However, these higher gross returns do not take into consideration higher mutual fund expense ratios, higher transaction costs, or higher tax bills associated with these more active indexing strategies.

The article doesn't say whether these additional costs outweigh the 2% annual return premium.

Capital gains

As discussed in later sections, donating appreciated assets is a good way to eliminate capital gains. You can use your current-year income to pay for costs of living, since not all of it can be deducted by charitable donations and thus you have to pay income tax on some of it regardless of how it's used. By using current-year income to pay your bills, you avoid selling assets with capital gains and thereby paying more tax. Alternatively, if you have assets with capital losses, you should sell those to get a deduction.

If you absolutely must incur capital gains by selling rather than donating appreciated assets, try to postpone the capital gains as long as possible. The idea is that you'll end up paying the same nominal amount in capital-gains tax regardless of when you cash out, but if you wait, the cost will have lower present value. For example, suppose you buy stock for $1000. You wait five years, and by this time it's worth $1500. If you sold it now, you'd pay capital-gains tax on the $500 appreciation. But you don't do that, and you instead wait another five years. Now it's worth $2000. You sell it. You pay capital-gains tax on the $500 from the first five years and the $500 from the second five years. But the $500 payment for the first five years has been delayed, so its present value is less than it would have been had you paid the same amount five years ago.

What about mutual funds?

Index funds with low expense ratios can be a good option. I personally prefer to buy stocks instead because there are complications you have to remember to avoid paying double taxes on mutual funds, and I would rather not have to think about that. (Non-Vanguard ETFs can also avoid those tax complications.)

As far as fees, it's possible to find index funds with expense ratios below ~0.2% per year. That's for mutual funds. For stocks purchased directly: When I make a trade through my broker, I pay an ~$8 flat fee, and to buy ~$2K worth of stock, this implies a fee of ~0.4%. But mutual-fund fees accumulate every year, while this stock-trading fee is a one-time cost, so after a few years, it's cheaper to buy the stock directly. If you also sell the stock, you might need to wait longer for this break-even point to happen, since there would be another ~$8 fee to sell it, but this isn't the case if you donate the stock. In general, it's best to hold a stock as long as possible before selling in order to push the capital-gains taxes as far into the future as possible. Paying tax on the same amount of capital gains is better more years into the future because of the time value of money now vs. later.

As with stocks, it's better to pick mutual funds with lower distributions (which are similar to dividend yields). Fortunately, distributions from index funds tend to be low because of minimal turnover in the underlying basket of stocks. So index funds are a win-win: Low expense ratios and low distributions at the same time. ETFs, like stocks, don't incur capital-gains tax until they're sold, so index ETFs could be an alternative to index mutual funds.

My DAF only allows for investing in mutual funds rather than stocks, but this isn't so bad because the income-tax-deduction benefits of the DAF far outweigh the possibly higher expenses that mutual funds involve, and the tax-reporting complications of mutual funds don't apply here because the funds in the DAF aren't taxed. By the same token, dividend yields aren't a concern for mutual funds in a DAF. Finally, consistent with the point about equity vs. fixed income above, I pick mutual funds that are 100% equity.

Holding individual stocks rather than a single mutual fund can be advantageous from a tax perspective, because

For more on the tradeoff between individual stocks vs. mutual funds, see "Passively managing individual stocks" at Bogleheads® wiki.

Donating stocks

I donate to charity by depositing stocks into my DAF that have high long-term capital gains (held >1 year). See "Advice for Donors with Capital Gains" for details. If you have stocks bought through an ESPP, you may need to wait up to 2 years before these are considered "long-term" for purposes of (a) securing lower capital-gains tax rates when selling or (b) deducting the fair-market value instead of the cost basis when donating.

I modify my W4 to have a larger-than-usual number of allowances to account for the fact that I'll be getting a big tax deduction by donating to my DAF. This means I pay less in taxes now rather than getting a refund next year, since a refund is an interest-free loan to the government.

Inconveniences of owning stocks directly

Owning stocks directly involves some extra burden in dealing with special events that arise, like tender offers and subscription rights (discussed below). If you don't act on notifications of these events, you may lose thousands of dollars. If you tend to miss emails a lot, this could be a significant argument against buying individual stocks.

The corporate actions discussed below tend to happen mainly for smaller companies, so one way to avoid them is to buy large-cap stocks. However, if there really is a persistent small-cap premium, then buying large caps may imply slightly lower expected returns.

Tender offers

One annoying aspect of owning stocks directly is that every so often, you'll get a letter about a "tender offer" to buy your shares for a fixed price prior to a merger. This has happened to me five times in ~4.5 years of owning ~15 stocks at any given time.

It seems you should either accept the offer or dispose of the shares before expiration. In a Yahoo Answers discussion, one reply warns of what happens if you don't dispose of the shares:

Take the recent example of Pipex. Another company took over the bulk of Pipex and in payment made a tender offer of 10-11p for 58% of shareholdings. If you didn[']t tender then you retained all of your shares, which dropped to a[ ]couple of pence, I think.

Another adds:

Often there is a secondary tender offer if the deal goes through. If you miss that, you may end up with something that is very hard to trade (not listed on exchanges).

You can typically call your broker and ask to accept the offer. Note that a tender offer triggers short- or long-term capital gains just as if you sold the security in any other way. If it's a capital gain, you might consider selling some other stocks at capital losses during the same year to cancel out the gain and thereby avoid capital-gains taxes for the year.

The stock price often converges to the tender-offer price, and in that case you can also just donate the stock, which avoids capital-gains implications.

Note that "mini-tender offers" are much less well regulated than tender offers, and general advice is to avoid taking them.

Subscription rights

In addition to tender offers, I once also got an offer for subscription rights, which allow you to buy additional shares at a lower-than-market price to counteract the effects of dilution when new shares are offered. You should probably either take the offer (with maximal over-subscription when available) or sell it. Selling should generally give you a fair price (including value for the possibility of over-subscription? one person disputes this) without your needing a lot of cash to buy additional shares. There may be differential tax treatment between these two choices. In my case, I sold my rights even though I paid a higher capital-gains rate by doing so. Why? Because in order to exercise the offer I would have needed to invest $50-100K to buy new shares, and holding that much in one volatile company was more risk than I was willing to take.

Schedule K-1

One stock that I used to own required me to fill out Schedule K-1 on my taxes. It took maybe an extra 1.5 hours for me to read the form and make sure I entered the data properly in TurboTax. But worse than that, the form wasn't mailed to me until March, whereas I had already submitted my taxes in February. This meant I had to submit a tax correction, which required another few hours of work.

Robo advisors

In 2015 I learned about some "robo-advisors" like Betterment and Wealthfront. I haven't looked into them in detail, but based on reading a few articles, my impression is that they're a good alternative to buying individual stocks for people who don't already have experience buying individual stocks.

Robo-advisors are claimed to offer a few benefits over index mutual funds:

  1. Automatic portfolio rebalancing
  2. Individualized asset allocation based on individual risk preferences
  3. Automatic tax-loss harvesting.

From my perspective, #1 and #2 are both unnecessary, but #3 is quite useful and maybe worth the cost on its own. Here's some further explanation:

  1. Rebalancing: Rebalancing can reduce risk if you initially chose a low-volatility asset allocation. As an easy way to see this, imagine that you initially bought 50% of ETF #1 and 50% of ETF #2. Then ETF #1 increases 1000000%. Now you essentially have only ETF #1, which means your risk is equal to that of ETF #1. I personally don't care enough about risk among asset classes to bother rebalancing, though. Some claim that rebalancing also improves expected returns. For instance, this post on Betterment claims that rebalancing "amounts to systematically buying low and selling high, which improves your returns slightly over the years". It cites a previous blog post, which gives the following explanation:

    The book explains that due to various market manias, occasionally one of these asset classes will start to inflate into a bubble, even while others will drop in price. To take advantage of this, you sell the funds that have appreciated, and use the proceeds to buy the assets that have gone on sale. Once per year, you simply make the appropriate mix of sales and purchases to set all of your allocations back to 25%, and you have effectively done a “buy low, sell high” move without even knowing what companies you own.

    This makes sense if you want to reduce risk, but I'm doubtful whether it improves expected returns if the market is efficient. If the market is inefficient and actually does have predictable bubbles, then sure, rebalancing to get out of bubbles would help. But it's a huge stretch to claim that there are ex ante predictable bubbles that are not taken advantage of by thousands of the smartest traders in the world. (Note: I haven't studied this topic in depth, so maybe there's some counterintuitive math to justify the claim that rebalancing improves expected returns even for a risk-neutral investor.) Moreover, rebalancing incurs capital-gains taxes, since you're selling the securities that had the biggest gains. It also entails some transactions costs (bid/ask spreads, trading fees, etc.).

  2. Individualized advice: In my opinion, most altruists not near retirement should invest in mostly equity, because risk is not a big deal. If the stock market tanks, you just lose out on some potential donations and divert more of your income to personal savings. So just buying equity index funds or equity index ETFs is sufficient. If you want further investment advice, there are plenty of free services online that will suggest an asset allocation between an equity fund and a fixed-income fund.
  3. Tax-loss harvesting: This is the feature that may make robo-advisors worth their fees. If you only own one index fund or index ETF, you may not have a chance to take advantage of tax-loss harvesting because your asset might never decline below its purchase price. You're more likely to be able to harvest if you own multiple securities. But owning many securities is more hassle, especially if you count occasional tender offers, subscription rights, and other annoyances discussed above. So robo accounts allow for harvesting without manual effort. That said, you could pretty easily replicate a robo-advised account in your own brokerage account buy buying, say, 10 ETFs in various industries/markets and manually selling those that have losses. This would take very little time. Manual control of harvesting may also be advantageous in certain cases. For instance, in 2014, I had such low income that I would have preferred to not harvest losses that year, in order to save my losses for a future year when I would actually pay income tax. But these optimizations are minor and may not be worth their mental cost if you're not used to manual harvesting already. (Manual loss harvesting is like manual memory management in C++. It can help give small performance gains relative to automatic garbage collection but also requires more effort.)

A main reason I won't switch to a robo-advised account is that I already know how to manage stocks/ETFs manually and so would get little gain from switching, while incurring costs of learning the new platform. But if I were just starting out and didn't plan to learn about personal finance much, I might use a robo account.

Here are some additional possible downsides of robo accounts:

Comparing annual fees among strategies

The following table compares different investment options for a hypothetical altruist with a $500K investment account. Suppose she's in the 28% income bracket, but because she also donates, say, half of her income, her actual marginal tax rate is 28%/2 = 14%. If she buys stocks or ETFs, she does so 12 times per year, with a fee of $8 for each transaction. I assume her time is worth $50/hour. Other inputs used in the calculation below, such as the dividend yield of an index ETF, are based on actual funds I looked at.

Strategy Annual costs of various kinds Total annual cost
Buy individual stocks with low dividend yields (mostly small/medium-sized) ($8 * 12 fees to buy stocks) + (0.14 income tax rate * ~0.8% dividend yield on stocks * $500K) + ($50/hour * 10 hours burden to take care of tender offers, etc.) + (~5% chance of missing a stock's tender offer or something and thereby losing ~$5K) $1406
Buy individual stocks with bigger dividend yields (mostly large cap) ($8 * 12 fees to buy stocks) + (0.14 income tax rate * ~2% dividend yield on stocks * $500K) + $0 of work with tender offers on the assumption that big companies don't have them $1496
Buy a single low-dividend index ETF ($8 * 12 fees to buy ETF) + (0.14 income tax rate * 0.86% dividend yield on ETF * $500K) + (0.09% expense ratio * $500K) + (say ~80% chance there aren't losses to harvest * $3000 loss deduction limit * 0.14 income tax rate) + (?? capital-gains tax from stock turnover) $1484 + ??
Buy many low-dividend index ETFs ($8 * 12 fees to buy ETFs) + (0.14 income tax rate * ~1% average dividend yield on ETFs * $500K) + (~0.15% expense ratio * $500K) + (say ~60% chance there aren't losses to harvest * $3000 loss deduction limit * 0.14 income tax rate) + (?? capital-gains tax from stock turnover) $1798 + ??
Betterment (?no? fees to buy ETFs) + (0.14 income tax rate * ~2.10% average dividend yield on stocks * $500K in stocks) + (0.15% Betterment fee + 0.15% expense ratio on ETFs) * $500K + (?? capital-gains tax from stock turnover) $2970 + ??

Pricing in the dividend tax penalty?

One complication with the above table is that it assumed that taxes on dividends are only a cost. But in theory, the so-called "dividend tax penalty" should be partly priced in to the security.

In particular, imagine that all investors paid taxes on dividends at the same marginal rate as you. Then securities that paid more dividends would incur greater costs, so investors would demand that those securities provide higher returns before investing in them. In other words, in this world, higher returns would offset tax costs, so the dividend taxes could be omitted from the calculations. This reasoning seems to be recognized in the academic literature, e.g.: "Is a dividend tax penalty incorporated into the return on a firm's common stock?"

In practice, not all investors pay taxes on dividends, such as 401k investors. And those who trade frequently pay short-term tax rates on capital gains, in which case dividends incur no more tax penalty than a comparable amount of capital gain. So in fact, not all investors incur extra tax costs from dividends. It's not obvious to me how to determine the actual return premium of high-dividend stocks over low-dividend stocks when some investors pay extra taxes on dividends and others don't. For the sake of simplicity, we could assume that the return premium compensates for half of the cost of dividend taxes to a typical taxed investor. A typical taxed investor pays ~30% income taxes on dividends but only ~15% taxes on capital gains, so if a stock gives returns via capital gains rather than dividends, a typical taxed investor saves ~15% of the return amount. Assuming the return premium compensates for only half of this, we should expect a return premium of ~7.5%. In this case, we should reduce the dividend tax cost by ~7.5% times the dividend amount in order to represent the increased return of the stock from the dividend-tax premium. (Of course, if dividend-paying stocks did have return premiums, we should expect to see non-taxed investors buy lots of them and taxed investors buy few of them, which would eliminate the premium....)

This is all very speculative, but if we do make an adjustment for a dividend premium, then large-cap stocks would look slightly more promising than they did before though still less promising than small caps, ignoring the hassle of owning small caps.

Pricing in higher expense ratios?

Typically foreign ETFs have higher expense ratios than domestic, but plausibly foreign ETFs also have compensatingly larger expected returns? This isn't clear, since maybe US investors only hold foreign ETFs for diversification reasons rather than expected returns. But insofar as you care about diversification, holding many types of ETFs may be worth it in your situation too despite slightly higher expense ratios.

Small-cap premium?

One other factor to consider is whether small-cap stocks have higher expected returns than large-cap. Normally I'm very skeptical of hypothesizing differences in expected returns among types of stocks, but small-cap stocks have historically performed better, and perhaps greater systemic risk plays some role in explaining this. Other explanations seem plausible as well. For instance: "early on, small cap stocks had bigger premiums and were more expensive to buy and sell, but isn't easily captured in historical analysis, and in reality likely skewed total return for investors."

In expectation, say small caps have ~0.2% higher annual returns than large caps. If that's true, then small-cap strategies in the above table will tend to dominate large-cap strategies or full-index strategies. Personally, in 2015, I'm inclining toward trying out buying a few small-cap growth index ETFs with low expense ratios and dividend yields. Originally I was going to use Vanguard ETFs, but apparently they're less tax-advantaged than other ETFs, so I'll probably choose a different company. However, I'm not sure ETFs are worth their cost relative to just picking individual stocks.

Lending Club?

Lending Club is another interesting investment option. I haven't explored it fully, but I currently lean toward thinking it's probably not as good as equity, especially in the case of altruistic investing. I might change my mind, though.

The average actual returns (net of fees and defaults) for Lending Club investors are at best ~9%. Daniel Odio and his wife "created a fairly aggressive portfolio that is projecting a 10.15% annual return." Moreover, interest is treated as ordinary income, so if you're in the 25% bracket, the returns are more like ~7%. In contrast, if you donate appreciated securities, you pay 0% in taxes on the capital gain, so the pre-tax return on equity equals the post-tax return.

Historically equity has returned more than 7%/year, so one would expect stock investing to do better than Lending Club. Of course, there are biases in historical market-return estimates suggesting that actual returns to equity should be lower in the future than in the past. But a similar comment could be made about Lending Club, since maybe part of why it has been so successful is that so far it's returns have been good. (I don't know how much this is the case in practice.)

Another minor reason against Lending Club is that it's new and could go bankrupt. The company has a contingency plan for this: "an arrangement with a large established debt collection firm (Portfolio Financial Servicing Co) that would step in should Lending Club step off." Still, the risk seems slightly higher than for regular investing—maybe equivalent to, say, an extra 0.2-0.4% cost per year or something.

For these reasons, I don't plan to use Lending Club now, but if the company becomes more mainstream and continues its current returns for many years into the future, I'd give it another look.

If you're pessimistic about US stocks because of their high CAPE as of ~2015 and if you don't want to pursue foreign ETFs, Lending Club might look more appealing in the short term. However, in my case, most of my savings are locked in to equities in the sense that I don't want to sell the stocks and thereby incur capital gains, which I would have to do in order to move the money to Lending Club. (If I keep the stocks in equities until I donate them, I won't have to pay any capital-gains tax.) A guaranteed 15% penalty on my equity via capital-gains tax seems worse than possible future stock-market downward corrections due to presently excessive CAPE.

Employer matching

I take full advantage of the ESPP that my company offers. Because I don't care too much about risk, it doesn't bother me to hold a lot of stock in one company. That said, it's also relatively costless to reduce this risk. After the 2-year time limit mentioned above on ESPP-stock disposition passes, I can donate appreciated ESPP stock instead of donating newly earned income; this still gives the same income-tax deduction as donating newly earned income but reduces my stake in a single company. (Update: Donating ESPP stocks can be a tax headache if you do your own taxes.)

In addition, my employer matches every $1 I put in my 401k with an additional $0.50 contribution up to 6% of pay. I max out this matching because the free money is too good to pass up. Whether to contribute more than the maximum that will be matched and all the way up to the IRS limit ($18,000 per year in 2015) of what's tax-deferred is debatable:

In a later section of this piece, I discuss 401k tradeoffs in more detail. A summary is that if you expect to retire early or transition from a high-earning job to a low-income job, then contributing to a 401k could be a good idea in order to avoid capital-gains taxes and reduce your income while you're in a higher marginal bracket. If you expect to earn a lot and donate a lot indefinitely, then contributing more than what your employer will match to a 401k is a less obvious tradeoff between possibly modest financial gains vs. flexibility to use the money sooner.

Note that your employer may max out its match on a per-pay-period basis rather than a per-year basis. This means you may not be able to frontload 401k contributions all to early months, because your employer wouldn't match any more than normal in the early months but would stop matching in the later months when you made no further contributions, which would reduce your total match amount.

ESPP is a tax headache

While participating in an ESPP does give you a decent amount of free money, doing taxes on ESPP shares can be quite complicated (Lawrence 2010). I would therefore only be inclined to participate in an ESPP program if I expect savings of at least several thousand dollars. If I planned to be with a company for only like one year, then perhaps it wouldn't be worth the hassle of taking part in the ESPP.

The first time I sold ESPP shares, it took me several days to really understand how ESPP taxes work, find all the required input numbers, and figure out how to properly input everything into TurboTax. Now that I know the process, doing ESPP taxes in subsequent years is less of a struggle, but it's still complicated and time-consuming. If you have someone else prepare your taxes for you, this may be less of a problem. However, even if someone else does your taxes, you still need to make sure you hold on to each year's Form 3922 that you got from your employer until you sell the stocks, which could be many years later. Or if you lose those forms, you'll need to deduce the equivalent numbers from other records, such as those your broker may have.

You might hope to avoid this hassle by donating rather than selling ESPP shares, but you can't, because as user Carl notes in a comment on Maher (2013): "you may owe income tax when you dispose of espp shares through a charitable gift. This is a disposition, and any income tax owed on the disposition is owed." So you still have to do all the complex tax calculations even if you donate your shares. Indeed, doing taxes for donated ESPP shares may be even harder, because I think TurboTax doesn't have a standardized walkthrough for the donation scenario, while it does for the scenario of selling ESPP shares.

I don't know why ESPP tax rules were made so complicated. The process could have been vastly simplified if the so-called "compensation income" portion were reported by your employer on your W-2 in the year the stock was bought (while you're still at that employer), rather than waiting until the year the stock is sold (by which time you may no longer get a W-2 from that employer). And because you'd be immediately paying the compensation income, the cost basis could be adjusted to its correct value by your broker right away. At that point the ESPP shares would be just like ordinary shares, and the special tax paperwork would be unnecessary. Alas, this is not how things work.

Donations

Employer matching

I also take full advantage of my employer's "matching contributions" program, which doubles the value of my donation to any 501(c)(3) public charity in the US up to $15K per year. At most companies the match amount is smaller, but in some cases it can be quite large, implying above-average incentive for altruists to work at employees of that type.

Tax deductions

I do my own taxes using TurboTax, and one reason is that I like to learn how taxes are computed in order to organically find out about opportunities for deductions and other tax optimizations. (The other reason is that I'm a geek.)

Take a look at Wikipedia's list of itemized deductions to get a quick sense of what things might be relevant, and if you have any of those, put records of them in a place where they won't get lost. I track my charitable donations using ItsDeductible, which can be automatically imported into TurboTax.

Get started on your taxes early in case complications arise that take more time than you expected, as well as to get your refund earlier. (That said, if you expect to owe money on your tax return, it makes sense to wait as long as possible.)

Marginal tax rate is roughly halved when you donate a lot

Suppose you're in the 28% tax bracket. You earn an extra $10K. This means you pay an extra $10K * .28 = $2.8K, right? Maybe, but if you're donating up to the charitable-contributions limit of 60% of your adjusted gross income (AGI), then a $10K increase in income means a $6K increase in your charitable limit. This means you can deduct $6K more and hence only pay 28% taxes on the remaining $4K. In effect, your marginal tax rate is a bit less than half of what it appears. This is only true if you actually remember to donate more because your AGI is higher or if you donate enough to guarantee that you'll still be donating at least 60% of AGI even with small increases in income.

Bunching donations

If you don't donate huge amounts and don't have a reason to donate every single year (such as because of non-trivial employer matching donations), then it may make sense to donate a lot in one year and none in other years. This means you can take the standard deduction in the non-donation years while itemizing deductions in the donation year. This is better than never getting to take the standard deduction or, if you donate very little per year, always taking the standard deduction and not getting any lowering of your taxes from your donations. (This is a standard idea that's called "bunching" donations.)

A donor-advised fund helps with this strategy because then you can still distribute money to charities regularly every year (which is better for the stability of the charities' funding) while having an irregular pattern of donations for tax purposes. Employer matching donations will probably be based on distributions from your donor-advised fund rather than contributions to it, so you might also be able to pull off this strategy even if you take advantage of donation matching.

Why doesn't this strategy work even if you do donate huge amounts? Because if you donate enough, then you'll hit the 60%-of-AGI donation limit when grouping donations together. Donations should be spread out over each year to keep from bumping up against this limit. In theory you can transfer deductions from donations in excess of 60% of AGI forward to future years if you hit the 60% cap in one year, but then I think you'd still be itemizing deductions in those future years rather than taking the standard deduction, which defeats the purpose of this irregular-donation strategy. See Adcock (2018) for more details on donation bunching in the face of the 60% limit.

Countries without a charity-deduction limit

Some countries appear not to limit tax deductions for charitable giving. In this discussion, people report that the UK and Australia don't limit tax benefits from donating, with some caveats.

Other things being equal, you might save a bit on taxes by moving to countries without deductibility limits. For example, suppose you earn $200K. In the US, you could deduct only $120K of that for charity donations, and you'd pay ~$14K of taxes on the other $80K. If instead you could deduct, say, $175K of donations, you'd pay almost no tax.

However, other things may not be equal. For instance, if you work in software, my impression is that pay is better in the US. The following table gives average annual salaries on Glassdoor (average over all cities in the country) for the first four big software companies that I decided to look up, with foreign currencies converted to US$ using June 2015 exchange rates:

Company and job title US UK Australia
Microsoft senior software development engineer US$137K US$104K US$128K
Google senior software engineer US$162K US$123K US$102K
Oracle principal consultant US$106K US$85K US$83K
IBM managing consultant US$128K US$101K US$134K

The trend isn't uniform, but often, the salary boost from working in the US more than offsets not being able to deduct income beyond 60% of AGI. Of course, this depends a lot on the industry in which you work; maybe some industries pay better in UK/Australia.

Other potential arguments against moving outside the US:

Miscellaneous

Cafeteria plans

Your employer may have a so-called cafeteria plan that allows for choosing between (a) some benefits defrayed with pre-tax dollars vs. (b) being paid extra post-tax salary. Typically I choose (b) because the benefits aren't useful for me, with certain exceptions. I'm not sure what to do in the case of life insurance. In general I assume that buying (non-health) insurance means a net loss in expected value, i.e., expected benefits are less than premiums in order for the insurance company to make a profit. But if premiums can be paid without taxes, does that make insurance a net expected financial gain?

Credit card

I use a credit card with a 1% cash back that also includes 5% cash back on selected categories each quarter of the year. I use this to pay all bills that can be paid with a credit card, both because of the cash back and because this gives me a one-month interest-free loan on paying those bills. Since groceries are my biggest expense that I pay with a credit card, I'm planning eventually to switch to an AmEx card with 3-6% cash back on groceries.

About half of my credit-card expenditures go toward groceries, and groceries are one of the special cash-back categories during one quarter of the year. So on average, my cash back is 1% for every purchase plus an additional 4% for about (1/4)*(1/2) of purchases, or ~1.5%. In addition, the interest-free loan on purchases lasts between 1 and 2 months (say 6 weeks on average). Assuming, e.g., an 8% discount rate and simple interest, delaying repayment for 6 weeks is worth (6/52)*(8%) = 0.9% returns. So overall, purchases with my credit card save ~1.5 + ~0.9 = ~2.4% over purchases with cash or a debit card. If I spend, say, $8,000 per year on purchases, I save ~$190 per year through cash back and delayed repayment.

It's good practice to monitor your credit card's activity about once a month to make sure you don't see unauthorized purchases. As of 2020, I've had a credit card misused on two separate occasions, during ~15 years of using credit cards. Because I monitor my credit-card account regularly, I caught the fraudulent purchases within a week or so. Typically the credit-card company waives the costs of all unauthorized transactions, but it's still better to nip them in the bud. Many people I know have had credit cards stolen at least once, so it's reasonably likely to happen to you some day.

American Express (Amex) credit cards may offer higher cash back (I've seen 2%), but Amex is also not accepted by as many small businesses as Mastercard and Visa. This means that if you get an Amex card, you might also need an ancillary card if you expect to shop with merchants that don't accept Amex. The extra hassle of keeping track of two credit cards may or may not be worth the extra cash back from using Amex. In my case I think the hassle is not worth it.

Saving on spending

A penny saved is a penny earned[*], so I also think about ways to spend less. When I first wrote this section in 2012, I lived within walking distance of my workplace, so I didn't own a car and didn't have to buy gas or vehicle insurance. I bought big bags of beans from Safeway to help reduce food expenses. I bought all of my clothes at Goodwill except socks and underwear. My main expenditures consisted of (in descending order) rent, food, Internet, electricity, water/sewer, and occasionally other random purchases, like sneakers or my computer monitor or my treadmill. Since then my job and residence have changed, but my frugality efforts have remained similar.

[*] Correction: Because of income tax, a penny saved is more than a penny earned, unless you can fully deduct the earned pennies.

Will and beneficiaries

I found a lawyer to write me a simple will that leaves all of my assets to charity. This is important because by default, if I were to die, my assets would go to my family. Even at my age, the average male probability of death is about 0.15% per year. Maybe your probability of death is much lower if you live in a safe place and don't have a mental illness. Suppose your annual probability of death is 0.05%. If you have, say, $100K in assets, a will provides an expected $50 of value per year, assuming your family wouldn't spend the money in useful ways were they to inherit it.

To create the will, I looked around for local lawyers, wrote to one of them with my requirements, and set up a meeting to sign the paperwork. In total, it cost $425. I then sent copies of my will to my family and a friend, and I kept a copy for myself that I store in a known location. During the same visit, the lawyer provided me with documents for durable power of attorney, durable power for health purposes, and a health-care directive.

My 401k account, brokerage account, and employer-sponsored life insurance have beneficiary designations, and these need to be updated as well. I was able to designate my DAF as the beneficiary for my brokerage account. My DAF, in turn, has a section where I can designate the default charities to which the money would go if I didn't donate it all on my own.

My 401k account can't designate the DAF, so I'm looking into how to set the beneficiary to be a specific charity instead.

Special topic: Advice for donors with capital gains

Introduction and caveats

This section gives some suggestions about optimal donations with respect to capital gains. I've only studied the USA, so this may not be useful for those in other countries. Also, my view of the landscape of tax ideas has been narrowly restricted to my particular financial situation, so I can't say much about people in other circumstances. Keep in mind that I'm not a tax expert. Most of what I've written is from memory or logical reasoning, so I haven't always cited sources, but you can find a lot of this basic info by searching around the web.

Negative capital-gains tax

Normally when you have stocks, mutual funds, or other property that has appreciated in value, this is bad news for you from a tax standpoint because you have to pay capital-gains tax. Short-term capital gains (which happen when you sell property for more than you bought it after holding it for <1 year) are taxed as ordinary income (so, if you're in the 25% marginal bracket, you'll pay 25%), and long-term capital-gains (held >1 year) are taxed at 15% for most middle/high earners. Either way, you pay some amount.

The situation changes when you're donating to charity. Common tax advice is that if you have capital gains, you should donate those properties rather than donate cash, because not only do you not have to pay any capital-gains tax, but if you have long-term capital gains, then your charitable tax deduction is equal to the fair-market value of the donated securities at the time of transfer, rather than the cost basis.

Example: Ordinarily, if you have long-term capital gains of $1000, you pay $1000 * 15% = $150 in capital-gains tax. But if you donate the stock to charity, then your tax deduction is $1000 bigger due to the capital gains. If you're in the 25% bracket, that means you save $250. The bigger the capital gains, the less you pay in taxes.

There's one caveat to keep in mind, which I quote from the article "Avoid Capital Gains Tax Donating the Property to a Charity": "The deduction of charitable contributions of an individual is generally limited to 50 percent [update: due to the Tax Cuts and Jobs Act of 2017, this is now 60%] of the taxpayer's adjusted gross income (AGI). However, for the contributions of long-term capital gain property, the limit is 30 percent of the AGI of the taxpayer unless the taxpayer chooses to deduct only the adjusted basis of the property instead of its fair market value."

Should you use negative capital gains to make money?

Suppose you have $1000 that you're planning to give to a donor-advised fund (DAF). "However," you think, "in view of negative capital-gains taxes, I could instead use this strategy: Invest the $1000 for a year, get a capital gain of, say, 8%, and then donate the $1080 next year to the DAF. This way, I'll be able to deduct an extra $80 from my taxes."

Yes, I think this would work. Of course, you might get a capital loss instead, but if so, you can deduct that as well (see below for more on capital losses). However, keep in mind the time value of money: A tax deduction this tax year is worth more than the same deduction next tax year. If you donate this year, you'll deduct $1000 for this tax year. If you wait, you'll deduct (in expectation) $1080 next year. But since we're assuming the discount rate is 8%, $1080/1.08 = $1000, so the present value of next year's deduction is only $1000. Another way to see this is to note that if you donate $1000 this year, it should grow to an expected $1080 in the tax-free DAF by next year.

So there's an elegant symmetry between the options, and in this simplified model, you should be indifferent between them. However, there are several caveats:

But if you already have gains, make sure to harvest them

In the previous section, I analyzed the choice of whether to invest new money into a stock for the purpose of reaping negative capital-gains tax and suggested that it's not worth it. However, if you already have a stock that has positive capital-gains, then you should consider waiting for it to be held at least a year and then donate it.

Say it's a stock held less than a year with a $1000 cost basis that has already appreciated 10% to $1100. If you donate it now, you do avert income tax on the short-term capital gains from selling it, but you don't deduct any income tax beyond the $1000 cost basis. If you wait a year with an 8% average return, the stock will appreciate to around $1188, which you can then deduct next year. That has a present value this year of $1188/1.08 = $1100, which is more than the $1000 cost basis.

In contrast, if you have a stock that has so far 0% appreciation, then if you donate now, you get the cost basis of $1000 tax deduction, and if you wait a year, you get on average $1000 * 1.08 = $1080 long-term capital-gains deduction, which translates to $1000 in present value. It's as though you have just cash in this case.

What if you have to donate now?

This situation happened to me last year. I had to donate $12K each year in order to take full advantage of a yearly employer-matching opportunity. I had several stocks, but few had long-term capital gains. Among those that had short-term capital gains, some had essentially no appreciation over cost basis, while others had lots of appreciation. Obviously I donated the stocks with long-term capital gains, but that didn't reach the $12K total. So for the short-term stocks, which were the best to donate at that time?

Interestingly, the answer depends on your expectations for future donations. If you plan never to donate again, then you should give the stocks with highest short-term capital gains, because that way you avoid paying the most tax when you sell the remaining ones.

But if you plan to give more later, then you should donate the stocks with the lowest short-term capital gains. Donating these is essentially like donating cash, and it doesn't really matter that you can only deduct the cost basis due to their being held less than a year because the fair-market value is pretty close to the cost basis. But the stocks that already have some appreciation would be wasted if donated right now because you can get a bigger deduction from those gains next year.

Capital losses and harvesting

What if the stock goes down in value? Capital losses are deductible up to $3K per year whether you itemize or not, and if you have more than that, you can carry them forward to future years.

This leads to the idea of "tax loss harvesting": If you have capital-loss securities, then sell them before the end of the year to incur the capital loss and lower your income taxes. Since in an efficient market, you're indifferent between selling a stock or holding it at any time, there's no harm to selling. When you do, you should wait 30 days until the "wash sale period" is over and then buy something new with the funds. (You can buy something new sooner as long as it's not "substantially similar" to the old one, but I prefer to wait to make sure I don't mess it up.)

Actually, there's one benefit to holding onto a stock with capital losses instead of selling it. If it does go up later, then because it started with a higher cost basis, you'll have a smaller capital gain. That said, for people who donate large amounts to charity, capital gains can be a good thing because of negative capital gains tax.

Harvest regularly

If you plan to donate most of your stocks eventually, it's important to harvest capital losses regularly. This is because if you wait too long, what was a loss may become a gain again, since on average, stocks go up more than they go down. For example, even if your stock currently has, say, a -$1000 loss, that loss is more likely to disappear than it is to become -$2000. Moreover, even if stocks do go down further, you could always sell at the -$1000 loss and then sell again when the new stock has declined a further -$1000. If there were no transactions costs, it would be optimal to sell whenever any stock had any loss, in order to accumulate as many losses as possible. In practice this isn't true because buying and selling stocks incurs a brokerage fee and causes slightly more hassle, both when selling/buying and when filling out taxes. Also, if you've already harvested huge capital losses, the value of harvesting more may be lower than it seems because you can only deduct $3K of them per year. Finally, remember that frequent loss harvesting only makes sense for those who will donate appreciated stocks to charity, since otherwise, the losses you harvest now will turn into bigger capital gains that you have to pay for later.

Say there's an $8 fee to buy and sell a stock. Say that the overhead of buying and selling incurs an extra ~$14 in terms of your time. Then it costs $30 to harvest a given loss. If you're in the 25% tax bracket, the benefit of harvesting a given loss is .25*(loss amount) if you don't have a surfeit of losses already. Naively, this might lead one to think that harvesting whenever a loss exceeds -$120 is optimal. But if you had waited until the loss was, say, -$500, you could have harvested the whole loss all at once with less transaction costs. Determining the optimal frequency with which to harvest losses is a hard problem. If you have so many stocks that you're pretty much guaranteed to get more than $3K in losses every year, then you could just harvest, say, once per year and not worry about further optimization.

Deduction limitations

Income-tax deductions from charitable donations are limited to 60% of AGI (30% for long-term capital-gains donations, and 30% for private foundations), although donations in excess of this can be carried forward to future tax returns for up to 5 years.

Fortunately, charitable contributions still reduce taxable income even if you pay the Alternative Minimum Tax (AMT). This benefit isn't true for many other types of deductions.

Keeping track of donations

To reduce the burden of recording my donations in a place where I might lose them, I use ItsDeductible. I enter the information when I donate, and then when I prepare my taxes with TurboTax, I can import the data directly from ItsDeductible without re-typing it. There are probably similar services for other tax-software packages, but I haven't checked.

Special topic: Should you use a donor-advised fund (DAF)?

There's a good argument to be had over whether altruists should donate or invest under various circumstances: If you know what types of projects are most cost-effective, then donating now captures social returns on investment due to snowballing of the changes you bring about. On the other hand, if you're gathering lots of new information that drastically changes your assessments of the relative cost-effectiveness of various projects, it's probably better to hang on to the money for a few years.

One argument in favor of donating now is that it allows you to take advantage of tax deductions. Since there's a limit on the tax deductibility of donations to private foundations of 30% of AGI and to public charities of 60% of AGI, it may not be the best idea to hoard up one's wealth for many years and donate it all at once—there's a tax benefit to donating smaller chunks over time. That said, charitable carryover deductions mean that if you donate more than the limit in one year, you can carry over the excess for up to 5 subsequent years. In addition, you might overcome the difficulty of not knowing right now which causes are most cost-effective by donating not to a particular charity but to a donor-advised fund, which would allow you to choose the recipient later on.

In the remainder of this section, I raise some points to consider when deciding whether to donate to such a vehicle for the tax benefit or whether to hold onto one's wealth privately.

Reasons to favor donating to a fund

  1. The tax benefit is the main one. If your marginal income-tax rate is, say, 25%, then avoiding taxes on your donation multiplies the amount of donation you can eventually make by 4/3 (since you can donate 100% instead of 75% of income that you don't need for living expenses). If your marginal tax rate is 33%, it multiplies the amount of your donation by 3/2.b
  2. There's a chance that you'll become more selfish with age and decide not to donate the income after all. You might also tend to spend slightly more than necessary on personal purchases if you have lots of money sitting around in your private possession. Even if you think this is unlikely, remember that dispositions change a lot over time.
  3. DAFs make it much easier to donate appreciated stocks, which is more tax-advantageous than selling stocks and donating the cash. You can donate appreciated stocks directly to a charity too, but this is a hassle because you need to ask someone at the charity for the charity's brokerage-account information. In contrast, donating stocks to your DAF can be as easy as a few clicks on your own computer. Even if I plan to donate to a charity right away, I still donate through my DAF because donating stocks is so much easier that way.
  4. Having money ready to be donated might buy you more influence when approaching charities and encouraging them to favor more cost-effective projects, because they know you're serious about eventually giving away large amounts (possibly to them).

Reasons favoring owning the wealth privately

  1. Donor-advised funds restrict your donations to US 501(c)(3) organizations if you're in the US. (The same is not necessarily true in other countries—e.g., in the UK, trusts can donate to foreign organizations.) That said, some foreign charities can get donations as grants from US charities, in which case you can donate to a US charity and request a grant to the foreign charity. And if you plan to donate large amounts, it might become cost-effective for a foreign charity to set up a US fiscal sponsor just for you (though I don't know if this runs afoul of the "public support test"?). There's also the option of trading donations with someone in another country, i.e., you donate to the foreign donor's favorite US charity via your DAF, and the foreign donor gives to your favorite charity.
  2. You may legitimately come across uses for the money that are better than donating to a charity. For instance, you might decide to found a startup and want to use your own private wealth to get it off the ground without depending as much on external investors. Or you might decide that your time is better spent doing research or activism than making money to pay others, in which case your wealth would be best spent paying for your living expenses while you do those other projects, assuming you can't get paid by an existing charity to do that work. (In effect, you would in that case be donating to a charity whose purpose was to have you do your important work, only without the bureaucracy of 501(c)(3) status.)
  3. Along similar lines, there might be small, informal projects that would be cost-effective to fund. For instance, you might want to pay a researcher a few thousand dollars to look into a question on your behalf. Or you might want to fund some off-the-wall project for which no public charity exists. That said, if you have a good network of friends at charities, you might be able to arrange to earmark donations to existing charities to do the projects you want done.
  4. Foundation donations can't go toward political lobbying, so if you ultimately decided that such an approach was most-cost effective, you'd be out of luck.
  5. Donor-advised funds often have minimum-distribution requirements (say, giving an average of 5% of the value per year averaged over a few years), which means you still have to donate a little bit now, but this isn't a big deal.

All told, I think the arguments in favor of a DAF generally outweigh those against, except in special circumstances. Because there's a limit of 60% of AGI for donation deductions, even if you do want to donate significant amounts toward non-tax-deductible projects, you may be able to do that out of the 40% of your income that can't be deducted anyway. I think the main realistic case where you wouldn't want to donate to a DAF is if you're planning to retire from earning within a few years and won't be paid by anyone else beyond that point.

If you want to donate to cause XYZ, would it be possible to, if necessary, start your own charity for cause XYZ and then have your DAF donate to that charity? (Are there legal restrictions against funding "your own" charity?) I called my donor-advised fund to ask whether you're allowed to donate to your own charity. Here "your own" could mean (a) one that you founded, (b) one for which you sit on the Board of Directors, or (c) one from which you receive a salary. I was told donating to your own charity is in fact allowed as long as (1) it's a 501(c)(3) charity that passes the public-support test, and (2) you don't receive a personal benefit from the donation. (2) requires that the donation doesn't go toward your salary. Therefore, it seems you can't just donate to yourself to pay your own costs of living while working at your charity. But you certainly can donate to charities that you founded and on which you sit on the Board of Directors. Indeed, Board members are often an important source of donations to a charity.

Special topic: 0% capital-gains rate during a sabbatical year

WARNING: Don't attempt this technique unless you know what you're doing. Making a mistake could cost far more than what you would save by succeeding.

In 2014, the long-term capital-gains tax rate is 15% for people in the 25% income bracket but 0% for those in the 15% income bracket or below.

This suggests the following idea: If, for another reason, it makes sense for you to take at least a year off from your job (e.g., as a sabbatical to do direct altruism work, to go back to school, etc.), then you could consider selling some of your long-term capital gains during that year and then buying back new stocks or mutual funds at a higher cost basis. This way you avoid ever having to pay tax on the accumulated capital gains even if you later return to a higher-paying job.

If you have, say, $25K in accumulated capital gains, then not paying 15% tax is worth $3,750. If you wouldn't have paid this tax amount until many years down the road, then the savings should be time discounted, in which case the actual savings could be several times smaller. The main cost is a tiny bit of effort for you to sell the securities and buy them back, plus some trading fees (but these are probably at most ~$100-$400). Obviously, the savings aren't enough that this should tip your decision about whether to take a year off from work, but if you happen to be doing that anyway, you might avail yourself of the opportunity.

Note that you probably shouldn't sell your short-term capital gains, because those are taxed as ordinary income. If you're in the 15% bracket during the year off, you'd pay 15% on them, which is the same amount you'd have to pay in capital gains if you were earning more, but you have to pay it sooner, which is bad from a time-value-of-money standpoint. If you're in the 10% income bracket during the year off, it could be good to sell the short-term securities, but (a) if you stay in the 10% income bracket next year too, you should wait until next year and sell them as long-term gains, and (b) if you plan to hold onto the stocks for a least ~5 years, paying 15% capital-gains tax later isn't as bad as paying 10% now.

Finally, keep in mind that stocks donated to registered charities don't incur capital-gains tax anyway, so concerns about avoiding capital-gains tax only matter if you plan to use the money for non-deductible projects.

There are several big risks with this strategy:

  1. Selling too much could be devastating. Capital gains still count as income, so if you realize too many in one year, you push yourself into a higher income bracket. Say you were earning $15K in regular income and tried to avoid capital gains on $25K of securities by selling them. Ignoring adjustments, you'd have a total income of $40K, which would push you into the 25% tax bracket if you're single. But people in the 25% bracket pay 15% capital-gains tax, so your strategy has been foiled. In the worst case, if you tried to sell, say, $100K of appreciated securities, you would end up paying most(?)/all(?) of the capital-gains taxes you were trying to avoid and would do so sooner than if you waited.
  2. Consider state and local income taxes. Selling during a sabbatical year doesn't work in states like New York that tax all income, whether capital gains or not. It would work in states like Washington that have no state income taxes. Watch out for local income taxes too.
  3. Wasting capital losses. You may have in the past harvested a nice crop of capital losses that you're using to get a $3K/year income deduction. But since capital losses first offset capital gains and only then contribute to the $3K/year deduction, if you have lots of capital gains, you might waste your whole batch of capital losses, so you won't be able to deduct them in the future. At that point, you'd need to harvest new capital losses if you still have any left or forgo the $3K/year deduction.

Another possible problem that I haven't explored: Say you're earning $5K of regular income and sell $10K of appreciated securities. Ignoring income adjustments like the standard deduction for the sake of simplicity, this puts you in the 15% income bracket. Is the $5K of regular income now taxed at 15% or still at 10%?

Mostly of academic interest: Using a 401k to avoid capital-gains tax by withdrawing early?

Summary

If you expect to retire early or transition from a high-earning job to a low-income job, then contributing to a 401k could be a good idea in order to avoid capital-gains taxes and reduce your income while you're in a higher marginal bracket. If you expect to earn a lot and donate a lot indefinitely, then the decision of whether to contribute more than what your employer matches is less clear. The magnitude of the importance of this argument is limited, especially if you don't earn much.

Caveats

The following section is speculation about a topic on which I'm not an expert, so don't treat what I say as established wisdom.

Why 401k?

I won't explain the full details of a 401k plan here because it's well-enough documented on Wikipedia and elsewhere. As I understand it, the advantage of a 401k is that you can avoid capital-gains tax on the income that your investments earn, so that when you withdraw the money after age 59.5, you only have to pay the original income tax, not additional capital-gains tax.

To explain more precisely: Say you have X dollars of income now. Let your current income-tax rate be t0. For example, t0 = 0.25 means you're in the 25% bracket. If you take the X dollars as income now and pay tax on it, you have (1-t0)X left over to invest. With that money, you buy a stock with an annual geometric-average return of r (e.g., r = 0.08) over N years (e.g., N = 20). After N years, your investment is worth (1-t0)X(1+r)N. However, before you can use the money to defray your costs of living, you need to pay capital-gains tax. Say your capital-gains rate is cN = 0.15 (that is, 15%) at year N. Then you have to pay cN(1-t0)X[(1+r)N-1] of capital-gains tax, and the amount you have left over is

(1-t0)X(1+r)N - cN(1-t0)X[(1+r)N-1] = (1-cN)(1-t0)X(1+r)N + cN(1-t0)X.   (equation 1)

In contrast, say you instead put your X dollars of income into a tax-deferred 401k. Let N be big enough that you can withdraw at age 59.5 without penalties. All X dollars of your contribution grow tax-free, so after N years, the fund has X(1+r)N dollars. When you take the money out, you have to pay income tax at some rate tN. The amount you have left is

(1-tN)X(1+r)N.   (equation 2)

Let's take the ratio of equation 1 to equation 2:

[ (1-cN)(1-t0)X(1+r)N + cN(1-t0)X ] / [ (1-tN)X(1+r)N ].

For simplicity, say t0 = tN. Then we have

1 - cN + cN/(1+r)N.

If N = 0, you have no capital gains, so this equals 1. If N > 0, this ratio is always less than 1, which means you save on capital-gains taxes by using the 401k. When N is large, the capital gains on your investment swamp the principal, and the ratio becomes about 1-cN, which says that you pay cN of capital-gains taxes if you invest without the 401k but don't pay them if you use the 401k.

Why not 401k?

Until now, I personally have contributed only 6% of my yearly income to my 401k. The reason I contributed at all was that my employer matches every $1 I donate with an additional $0.50 free, but only up to 6% of contributions on my part. However, I could in fact contribute $17.5K before hitting deferral limits. So why didn't I?

Money in your 401k is locked until you turn 59.5, so I figured that if I contributed more, I would be preventing myself from having the option to use that money for important projects in the shorter term. If the returns on animal-suffering meme-spreading are higher than those on mutual funds, then it would be a shame to lock away the money for all those years just to save 15% on capital-gains taxes. Indeed, in the next 34 years before I turn 59.5, the world may look very different. Maybe financial institutions as we know them won't exist any longer. I would put the chance of this around 15% or maybe higher.

Withdrawal penalties

However, one thing that I neglected is that money in a 401k isn't totally locked. You can make early withdrawals if you're willing to pay a 10% fee on top of income taxes from the distributions. If that's all you have to pay, and you don't have to pay anything else for capital gains, then it seems it could actually be more advantageous to withdraw early from a 401k than to invest on your own.

Here's the intuition. If you withdraw early, you pay 10% of everything that you put in: principal and capital gains. If you instead invest on your own, you pay 15% but only on the capital gains. After a long enough time, when the capital gains swamp the principal, it'll be advantageous to use the 401k approach (up to your annual tax-deferral limit).

In particular, let p = 0.1 be the penalty for withdrawing early. Say you withdraw at year M. I think(?) the 10% penalty is paid separately on the pre-tax amount you withdraw from the 401k, so equation (2) becomes

(1-tM-p)X(1+r)M.   (equation 3)

At what year M does it become advantageous to use the 401k strategy? Set equation 3 equal to equation 1.

(1-tM-p)X(1+r)M = (1-cM)(1-t0)X(1+r)M + cM(1-t0)X
(1-tM-p) = (1-cM)(1-t0) + cM(1-t0)/(1+r)M.

Say r = 0.08, t0 = 0.25, tM = 0.25, cM = 0.18, and p = 0.1; this gives M = 17.5. So if you plan to need living expenses 17.5 or more years down the road, it appears advantageous to put money into the 401k and then break out. (Note: Currently the capital-gains rate is 0.15, not 0.18, but I wrote this section back when it was expected to be 0.18 and didn't want to repeat the calculations.)

How the tradeoff varies with M

The algebra is getting messy, so I put together an Excel workbook to compute the ratio of wealth using the no-401k strategy to that using the 401k strategy as a function of M = years from now. Below are sample snapshots for different r.


What if you have significantly lower income later?

Say you will in the future have a lower-earning job such that your marginal tax bracket will drop to 15% (tM = 0.15 even though t0 = 0.25 still). In this case, it's always advantageous to use the 401k strategy, because even though you pay a 10% penalty, 15% + 10% = 25%, so you pay no more than you would have otherwise. This ignores the savings due to not paying capital-gains tax, so if we include those savings, the benefit is even higher. At the 15% marginal income-tax bracket, your capital-gains rate would be 8% for five-year capital gains starting in 2013. (Actually, this is not true: Congress instead set the capital-gains rate to 0% for the 15% income bracket. However, I didn't recompute the figure with this new information.) Even with that low capital-gains rate, you get the results shown below.

What if you plan to keep earning a lot indefinitely?

If you plan to keep earning a lot indefinitely, then additional 401k contributions are less important, because you can keep using your current income to fund your costs of living (no need to dip into the 401k early and incur the additional penalty), and you can donate all of your investments to avoid capital-gains taxes entirely (i.e., cM = 0). That said, you probably will retire before you die, and unless you have massive savings accumulated already, your income during retirement may be less than that during working years, so you might save some on taxes by deferring your income through a 401k. How this benefit contrasts with the lost freedom of being able to use money flexibly by keeping it out of a 401k needs to be assessed case by case.

What about a Roth 401k?

In general, a Roth 401k has advantages and disadvantages versus a regular 401k depending on your situation. If you plan to retire early, a Roth 401k can be inferior to a regular 401k, because with a Roth 401k, you'd pay your marginal tax rate while earning (25%, 28%, or more), while with a regular 401k, you'd pay your marginal tax rate when not earning (10% or 15%).

That said, in the unlikely event that the tax-rate differential between earning now vs. retirement is less than 10%, and if you expect to need to withdraw money after you stop working, it may make sense to use a Roth 401k because doing so allows you to withdraw your original contributions without penalty, while your capital gains remain tax-free. Essentially, the Roth 401k is a way to avoid capital-gains taxes on a subset of your earnings, while keeping the earnings flexible for use prior to retirement. However, keep in mind that making Roth 401k contributions comes at the expense of not being able to make similar regular 401k contributions.

Another argument for the Roth approach is if you expect taxes to increase substantially in the future, or if you're highly risk-averse with respect to the tax rate. I'm personally doubtful that the low-bracket tax rates would increase from their current ~10-15% to something above 25%, since it seems that most tax hikes would probably be applied to higher tax brackets. The lowest US tax bracket has been at or below 15% since 1965, and the highest it ever reached was 23% in 1944-45, during which time the highest bracket was 94%!

Could you also use IRAs for this purpose?

Short answer: Only if your income is low enough to use a tax-deductible IRA. If you earn too much, you can't deduct contributions to a traditional IRA. Even if traditional IRA deductions would save you money, the annual IRA contribution limit is only $5,500 (worth 0.25 * $5500 = $1375 if you're in the 25% bracket, minus the taxes you pay on withdrawal), so the hassle of setting one up is probably not worth it unless you plan to use it for many years.

Why not also use a non-deductible IRA? It still exempts you from capital gains, right? Yes, but the problem is those capital gains get converted to income when you withdraw. This is worth it in a deductible IRA or tax-deferred 401k because you never paid income tax before you put the money in, but with an after-tax IRA, you pay income tax both before putting the money in and after taking it out, which is worse than just paying income tax before putting the money into an investment fund and then paying capital-gains tax on its returns.

The disadvantage of a non-deductible IRA is confirmed by other sources. Here's one:

Dispel yourself of the notion of capital gains in an IRA; there is no such thing. IRAs have earnings whether they come from dividends, interest or asset appreciation. Withdrawals or conversions from an IRA result in ordinary income no matter what underlying asset generated the growth.

[...]

If you had purchased the securities that are currently in the nondeductible IRA outright, your maximum tax after more than one year would be the 15 percent capital gains rate. For this reason, many people do not care to use a nondeductible IRA to invest in securities, as it converts capital gain into ordinary income, which can be taxed by as much as 35 percent.

Another source: "Upon distribution, a non-deductible Traditional IRA converts capital gains, which are taxed favourably, into higher taxed ordinary income."

A third source:

With stocks, though, the benefits over time are much less. While stocks in a regular taxable account qualify for lower tax rates on gains, all IRA withdrawals—even from nondeductible IRAs—are taxed at your regular rate. With maximum tax rates at 35% versus 15% for capital gains and dividends, that's a huge difference that can wipe out your gains.

Long-term capital-gains rates are always strictly less than income-tax rates, so it's probably best to stay away from a non-deductible IRA.

What about Roth/backdoor IRAs?

The Roth IRA limits are higher than for traditional IRAs, and if you earn too much for the limits, you can get a Roth IRA anyway by a backdoor method. Since you don't pay taxes on qualified distributions from the Roth IRA, there's no problem of paying income tax rates on capital gains. You do pay high taxes on the income while you're earning it, but that would be true anyway for income you can't deduct, and at least the Roth IRA lets you avoid capital-gains taxes when that money is invested.

The main problems with a Roth IRA are

  1. hassle to set up and maintain it
  2. restriction of your ability to spend the money before retirement.

It may also be unnecessary because

  1. you don't pay capital-gains tax when donating appreciated securities to 501(c)(3)'s, so the only capital gains of concern are those on income that you plan to spend on yourself, but your annual 401k contributions may be sufficient to carry you through retirement
  2. you may have some capital losses among your investments, which can be cashed in without capital-gains tax.

But in particular cases, contributing to a Roth IRA above 401k contributions might be useful, such as if an altruist will only be earning significant income for a few years of her life. In fact, even if she's no longer earning now, she could still donate small chunks to a Roth IRA to prevent further capital-gains accumulation on that wealth, if she doesn't plan to donate that particular wealth.

It's not worth it to frontload 401k contributions early in the year

In 2013, I came up with an idea. Since savings in a 401k avoid capital-gains tax, if I did all my 401k contributions up to the $17.5K limit at the beginning of the year, all of those contributions would earn investment returns for the whole year, on none of which would I pay capital-gains tax. If instead the 401k contributions were spaced throughout the year as is normal practice, there will be slightly fewer expected investment returns, since the contributions near the end of the year wouldn't have much time to accumulate returns. Therefore, I thought I could save a tiny amount of capital-gains tax in retirement by frontloading my 401k contributions to the beginning of the year.

This plan turned out to be a bad idea. The reason is that my employer's 401k matching contribution was capped at 3% per pay period. If I contributed up to my 401k limit within the first few months of the year, I wouldn't make any more 401k contributions that year, in which case my employer's match wouldn't happen either. The match only worked for a pay period if I was making my own contributions in that specific pay period. I confirmed this with my company. Therefore, it's necessary to space out 401k contributions rather than frontloading them. In theory you could frontload a little bit while leaving enough slack to continue making contributions all year, but this seems burdensome and potentially error-prone, and the savings that would come from frontloading aren't very big, as I discuss in the next paragraphs.

Here's a quick-and-dirty upper bound on the hypothetical value of frontloading all 401k contributions to the beginning of the year. Assume a constant, non-varying nominal annual rate of return on investments of 8%. The 401k limit in 2015 is $18K. If you contributed the whole $18K on 1 January, you would earn $1440 in returns by 31 Dec. and would avoid capital-gains tax on all of this. If instead you contributed the $18K evenly throughout the year, your investment returns would be only half this amount: $720. Frontloading thus implies an extra $720 of returns that escape capital-gains tax. If you would have a low enough income during retirement, you wouldn't pay capital gains on this extra money, implying no savings. But if you had a high income during retirement, you might pay 15% capital-gains tax. Hence, the possible savings would be $720 * .15 = $108, expressed roughly as present-value dollars. (The actual savings after year N would be $720 * 1.08N-1, but to make this a present value, it should be discounted by 1.08N.) Note that these are savings before withdrawal from the 401k. If you'd pay, say, 25% income tax on the 401k withdrawal, the actual savings would be $108 * (1-.25) = $81. This upper bound on savings per year due to frontloading isn't huge and doesn't seem worth the risk of losing employer match by forgetting to toggle 401k contribution amounts during the year each year.

Following is a more careful analysis of the situation to verify the intuition behind the above calculation. The current year is 0, and you retire at year N. Your marginal income-tax bracket now is t0 and in retirement will be tN. The capital-gains rate will be c in your retirement. Let r be the unvarying nominal annual rate of return on investments. Suppose you earn $1 on 1 Jan. and $1 on 31 Dec., with a 401k contribution limit of $1. (I'm normalizing to $1 to make the algebra cleaner.) Your two options are

  1. Contribute $1 to the 401k on 1 Jan. and invest the $1 on 31 Dec. into a regular stock not exempt from capital-gains tax.
  2. Invest in a regular stock with the $1 from 1 Jan. and contribute the $1 on 31 Dec. to the 401k.

In case 1, your returns at year N are as follows: (1+r)N from the 401k investment, on which you pay tax of tN for withdrawal, plus (1-t0)(1+r)N-1 from the after-tax stock investment, on which you pay capital-gains tax in the amount of c(1-t0) [(1+r)N-1 - 1]. The total value at year N is thus

(1-tN)(1+r)N + (1-t0)(1+r)N-1 - c(1-t0) [(1+r)N-1 - 1].

In case 2, your returns at year N are similar but flipped:

(1-tN)(1+r)N-1 + (1-t0)(1+r)N - c(1-t0) [(1+r)N - 1].

Case 1 minus case 2 equals

(1-tN)(1+r)N + (1-t0)(1+r)N-1 - c(1-t0) [(1+r)N-1 - 1] - { (1-tN)(1+r)N-1 + (1-t0)(1+r)N - c(1-t0) [(1+r)N - 1] }
= (1-tN)(1+r)N-1[(1+r) - 1] + (1-t0)(1+r)N-1[1-(1+r)] - c(1-t0) (1+r)N-1 [1-(1+r)]
= (1-tN)(1+r)N-1[r] + (1-t0)(1+r)N-1[-r] - c(1-t0) (1+r)N-1 [-r].

Since this is a value to be realized in year N, the present value is 1/(1+r)N times that amount. I'll make the simplifying approximation that (1+r)N-1/(1+r)N = 1. The present value of the difference between case 1 and case 2 is then

r(1-tN) - r(1-t0) + rc(1-t0)
= r - rtN - r + rt0 + rc(1-t0)
= r[t0 - tN + c(1 - t0)].

(Note: I'm puzzled why the c(1-t0) part of this expression isn't c(1-tN), since it seems like the interpretation of the (1-t) factor is that you pay taxes on withdrawing the funds during retirement, at which point your tax rate is tN. I wonder if I made a mistake or if my equation actually reveals a deeper insight that not understanding.)

Finally, recall that we used a $1 401k limit instead of an $18K limit, so the actual savings are $18K times that expression.

Plugging in c = .15, r = .08, and t0 = tN = .25, we get $18K * .08 [.25 - .25 + .15 * (1-.25)] = $162. And finally, the value of "frontloading" versus "constant 401k contributions throughout the year" is half of the difference of case 1 and case 2 above, because in case 2 above, all of the 401k contributions came at the end of the year. So the actual value is $162/2 = $81, in agreement with the intuitive calculation from before.

If your tax rate would be lower during retirement, the above value would be slightly higher. Suppose that t0 = .25 but tN = .15. Then the savings are $18K * .08 * [.25 - .15 + .15 (1-.25)] / 2 = $153, which still isn't huge.

Also note that this calculation significantly overstates the upside potential of frontloading because in practice you have to space out most of your 401k contributions throughout the year. If you can only frontload, say, 1/3 of the total, the value would be more like $81/3 or $153/3 per year, which I think is not enough to justify the risk and hassle.

Mostly of academic interest: How often should you buy a new stock?

Summary

Depending on your income, expected rate of return, and purchase transactions fees, it makes sense to buy a new stock about every half month or every month, assuming you manually buy stocks as your vehicle for continuous investment.

Problem

Say you earn $800 post-tax per week, and you want to invest those earnings by buying some random stock. Suppose you think the stock will earn a nominal rate of 7% per year in expectation, and for convenience, let's use simple interest, which is approximately correct on short time scales. When you buy a stock, there's a fixed transactions fee of $8 per purchase. How many weeks should you wait before you buy a stock in order to optimally trade off the cost of missed investment income against the transaction cost of buying a new stock?

Notation

To generalize, let's say your wage is w = $800, and that you earn n = 52 wages in a year. You expect an annual return of r = 0.07 with simple interest. When buying stocks, the transaction fee is c = $8.

Cost formula

Every wage period when you don't use w dollars to buy stock, you lose out on expected investment income of wr/n, since r/n is the expected interest rate for one wage period.

If you wait two wage periods to buy a stock, w dollars lie idle for one week, and w dollars are used immediately. The only lost income is from the first wage period in the amount of wr/n.

If you wait three wage periods, w dollars lie idle for two weeks, w dollars lie idle for one week, and w dollars are used immediately. The lost income is then (wr/n)(2) + (wr/n)(1).

If you wait k wage periods, the lost income is (wr/n)(k-1) + (wr/n)(k-2) + ... (wr/n)(1) = (wr/n)[k(k-1)/2] using the formula for triangular numbers.

Say you follow this pattern of waiting k wage periods for a long time T, where T is sufficiently big that we can assume it's a multiple of k and ignore the irregularities at the end of the time period. You would then buy stocks T/k times.

The purchase cost of the stocks would be c(T/k). The lost income would be (wr/n)[k(k-1)/2](T/k). The total cost is

c(T/k) + (wr/n)[k(k-1)/2](T/k),

which is what we want to minimize.

Minimizing the cost

T factors out of the cost, so it suffices to minimize

F(k) := c/k + (wr/n)[k(k-1)/2](1/k) = c/k + (wr)(k-1)/(2n).

While k can only take on discrete values, we can pretend for the moment that this function is continuous so that we can differentiate and set equal to 0:

dF/dk = -c/k2 + wr/(2n) = 0
wr/(2n) = c/k2
k2 = 2cn/(wr)
k = sqrt(2cn/(wr)).

Note that the second derivative with respect to k is d2F/dk2 = 2c/k3 > 0, so this is indeed a minimum point.

Plugging in values

Using the figures in the original problem, the continuous solution is k = sqrt(2 * 8 * 52 / (800 * 0.07)) = 3.85. Using Excel, I found the actual values of the cost at each k from 1 to 5:

F(1) = 8

F(2) = 4.5

F(3) = 3.7

F(4) = 3.6

F(5) = 3.8 .

So k=4 is indeed the minimum. In other words, using these figures, you should buy a new stock about once a month.

Alternate values

Suppose instead you're paid twice a month (n = 24), with w = $2000 per pay period and an assumed rate of return of r = 0.10. Then the optimal continuous value of k = 1.4, which means it's better to buy a stock every pay period than to hold on for a second pay period.

Related problems

These situations of accumulating benefits for an action that has fixed cost crop up a lot. For example: How often should you cut your hair? I like to have short hair because it reduces shower time and saves on hot-water bills, but getting a haircut also costs money and time in itself. Every day that you have hair longer than it needs to be, you lose a small amount of money, say L(d), when it's been d days since your last hair cut. L(0) = 0, and then L(d) grows as d grows. The accumulated cost after waiting k days will be ∑i=1k L(i). The minimization will be the same as before, with the [k(k-1)/2] part replaced by this summation.

Regarding haircuts: In 2014, I realized that I could cut my own hair (perhaps with help from a friend) rather than going to a shop. I did this by buying a razor of a similar type as what's used by a barber. The best seller on Amazon was "Conair 22 Piece Cord/Cordless Rechargeable Haircut Kit", which was a steal for only ~$18. It works amazingly well, though I do need someone to snip a few hairs in the back of my head that I can't see myself.

Acknowledgments

Thanks to Denis Drescher, Michael Dickens, and others for comments on this piece.

Footnotes

  1. A friend gave me this excellent feedback:

    In the "Should you use negative capital gains to make money?" section, you mention the symmetry between two situations: donate now, or donate in 1 year. You use a pre-tax discount rate to show that they're equivalent. But what you have at the end of a year is not quite the same between the two situations:

    If you give $1000 now, you save $250. You buy $250 worth of stock, and in 1 year you have $270 in stock, and your basis is $250. If you give $1080 next year, you save $270. You can buy $270 in stock, and your basis is $270.

    So if you need to save money for a non-deductible purpose, I think there's an advantage to donating later, and you'd use an after-tax discount rate to compare the present values.

    Here's my answer: Yes, that is a great point. I thought about that as well, realizing that—as you said—the "discount rate" after adjusting for taxes isn't quite the same as the rate of return on the security, because the discount rate should be lower due to capital-gains taxes. That's why I cheated in the example by assuming that "you have $1000 that you're planning to give to a donor-advised fund (DAF)." That way, you wouldn't pay capital-gains tax on the security you buy with the $250 of saved income tax, so the security's cost basis is irrelevant.

    The other complication I didn't consider was that tax years are discrete, but returns from investment are (approximately) continuous. Say it's early 2012 and you follow the strategy of buying the stock. You can hold it until late 2013 and get more than a year of capital gains on it (almost 2 years). However, the tax savings still come just one year later: as part of your refund in 2014, instead of in 2013 (or as reductions in withholding in 2013 instead of 2012). So I suppose one could follow the buy-stocks strategy early in the year and then switch to donating directly at the end of the year.

    In fact, based on this observation, I came up with the following plan for how to donate throughout the year:

    1. With income from early/middle of the year, buy new, low-dividend stocks.
    2. With income from the end of the year, donate cash from new salary income directly to my donor-advised fund (DAF), in the amount of ~20% of my AGI. Only 30% of AGI can be deducted in the form of long-term capital gains at fair-market value, so this extra 20% takes me up to the 50% combined AGI limit on charitable deductions.
    3. Near the end of the year, donate stocks with high capital gains to my DAF, in the amount of ~30% of my AGI.

    It's better to donate stocks with capital gains than to donate a new paycheck, because donating the stocks clears out the old, accumulated capital gains. Example: Say you bought a stock for $1000 that has now grown to $1200. If you donate $1200 of new salary, you get $1200 in deduction, but you still have a stock with cost basis $1000 for which you might need to pay capital gains tax later on. If, instead, you donate the stock and then buy a new stock for $1200, you have a stock with $1200 cost basis, and you still get a $1200 deduction. It's better to have a higher cost basis in case you ever need to sell rather than donate the stock in the future. Therefore, the second strategy is better. One quibble with this argument is that buying a new stock costs a few dollars for the stock trading fee, but compared against the possibility of paying 15% * ($1200 - $1000) in capital-gains taxes, this fee seems relatively unimportant.

    Unfortunately, you can only donate capital-gain stocks up to 30% of AGI or else you have to deduct only their cost basis rather than their fair market value (FMV). Probably it's better to wait until another year when you can deduct the FMV. So the remainder of the donations I make before hitting the 50%-of-AGI income-deductibility limit I do through out-of-paycheck contributions.

    The reason to wait until the end of the year for the capital-gains donations is that you can get more capital gains during the year and hence more deductible donation value at the end. As discussed above, this is true because the IRS doesn't give you more credit for donating early; it only cares that you've donated by the end of the year. So the same amount of money can yield a bigger deduction for you if you wait, even though the amount the DAF receives is expected to be the same. Another benefit of waiting until the end of the year is that you might decide to donate to a project that you can't support through your DAF, and waiting keeps options open. On the other hand, waiting also leaves around more spend-able money in your own hands, which may or may not be an appreciable risk.

    I don't know if there's a good reason to prefer buying stocks early and donating paycheck money later vs. the other way around. Any stocks you buy early in the year can't be donated later in the year because you won't have held them for at least a year. If you buy stock first, you'll be expected to have slightly more stock with some extra capital gains. If you donate first, the DAF will be expected to have slightly more money from its investment returns. The problem of which to put first based on your eventual plans is too hard for me to figure out right now.

      (back)

  2. Note, however, that it doesn't make sense to donate more than the maximum amount (60% of AGI) to a DAF because the DAF typically charges a small annual administrative fee (maybe 0.5%-1%), and the tax consequences are roughly the same between
    1. donating income beyond the 60%-of-AGI limit now to a fund that grows without capital-gains taxes vs.
    2. buying your own stocks with income beyond the 60%-of-AGI limit and donating these stocks later once they've appreciated.

    Indeed, with option #2, you can carry forward the deduction potential of your appreciated securities for more than 5 years and without being penalized by the time value of money for deductions that have to wait to be applied. That said, the annual DAF fee should not discourage you from donating deductible income. For instance, if you're in the 25% bracket, donating $1000 a year early saves $250 in taxes, which can then earn 5% * $250 = $12.50 at a ~5% expected nominal rate of return in the DAF, while the extra $1000 incurs only $5-10 extra in administration fees in the same year.  (back)