Akamai has an Employee Stock Purchase Plan, which I’ve tried very hard not to think of as magical free money. But I think it basically is. It works like this: you set aside some fraction of your after-tax paycheck, and every six months the company uses that money to buy the company’s own stock for you. There are some limits on how the ESPP can be structured: the company can give you the stock at a discount, but the discount can’t be any more than 15% off the fair market value (FMV); you can’t get more than \$25,000 in stock (at FMV) per year; and Akamai (in keeping, apparently, with general practice) imposes a further limit, such that you can contribute at most 15% of your eligible compensation.

To see how great the return on this is, consider first a simplified form of an ESPP. You put some money in, then wait six months; the company buys the stock, and you sell it immediately. They gave it to you at a 15% discount, i.e., 85 cents on the dollar. So basically you take your 85 cents, turn around, and sell it for a dollar. That’s a 17.6% return (1/.85 ~ 1.176) in six months. To turn that into an annual rate, square it. That makes it a 38% annual return.

Introducing some more realism into the computation makes it even better, because your money isn’t actually locked up for six months. In practice, you’re putting away a little of your money with every paycheck. So the money that you put in at the start of the ESPP period is locked up for six months, but the money you put in just before the end of the period is locked up for no time at all. The average dollar is locked up for three months. So in exchange for three months when you can’t touch the average dollar, that dollar turns into \$1.176. Annualized, that’s a 91.5% return.

Doing this in full rigor means accurately counting how long each dollar is locked up. A dollar deposited at the start is locked up for 6 months; a dollar deposited two weeks later is locked up for six months minus two weeks; and so forth. It looks like this:

End of pay period 0: You have \$0 in the bank.

End of pay period 1: You deposit \$1. Now you have \$1.

End of pay period 2: You deposit \$1, and you earn a rate r on the money that’s already in the bank. So now you have 1 + (1 + r) dollars in the bank.

End of pay period 3: You deposit \$1. The 1 + (1 + r) dollars already in there earn rate r, meaning that they grow to (1 + (1 + r))(1 + r) = (1 + r) + (1 + r)2. In total you have 1 + (1 + r) + (1 + r)2.

In general, at the end of period n, you have 1 + (1 + r)2 + (1 + r)3 + … + (1 + r)n-1 in the bank. That simplifies nicely: at the end of period n, you have (1 – (1 + r)n)/(1 – (1 + r)), or (1/r) (-1 + (1 + r)n) dollars in the bank.

At the end of the n-th period, you get back (1/.85)n dollars for the n dollars that you put in. So what does r have to be so that you end up with n/.85 dollars when period n is over? You need to solve (1/r) (-1 + (1 + r)n) – n/.85 = 0 for r. Use your favorite root-finding method. I get r=0.02662976. That’s the per-period interest rate. (It’s also known as the Internal Rate of Return (IRR).) In our case it’s a 6-month ESPP period, with money contributed every two weeks, so there are about n=13 periods. So the return on your money is ~1.026613 in six months, or 1.026626 in a year. That comes out to about a 98% return. Which is, to my mind, insane.

The full story would be both somewhat better and somewhat worse than that. Somewhat better, in that the terms of our ESPP are even more generous: when it comes time to buy the stock, Akamai buys it for you at the six-months-ago price, or the today price, whichever is lower. So imagine you have \$12,500 in the ESPP account, that the stock is worth \$60 today, and that it was worth \$40 six months ago. You get shares valued at \$40 apiece, minus the 15% discount. So the company buys shares at .85*\$40=\$34. It can buy at most \$12,500 in shares (at FMV), so it can buy floor(12500/40)=312 shares. Cool. Now you have 312 shares, which you can turn around and sell for \$60, for a total of \$18,720. That is, you put in \$12,500, and you got out \$18,720. Magic \$6,220 profit.

The “somewhat worse” part is that you pay taxes on two pieces of that. First, you pay taxes on the discount that they gave you (since it’s basically like salary). Second, if you hold the stock for any period of time and pick up a capital gain, you pay tax on that; if you held the stock for less than a year, that’s short-term capital gains (taxed at your regular marginal rate), whereas if you hold for a year or more you pay long-term cap gains (15%, I believe).

I’ve not refined my return calculation to incorporate the tax piece, but I doubt it changes the story substantially. First, it’s hard for me to imagine that the taxes lower the rate of return from 98% down to, say, 15%. Second, any other investment (a house, stocks, bonds, a savings account) would also require you to consider taxes. And since the question isn’t “Is an ESPP good?” but rather “Is an ESPP better than the alternatives?”, I suspect that taxes would affect all alternatives equally. It strikes me that ESPP must win in a rout here — which would explain why the amount you can put in the ESPP is strictly limited; otherwise it really would be an infinite magical money-pumping machine.

So far as I understand the conceptual basis for a lot of theorems in finance, one of the ideas seems to be reasonably straightforward: if some type of investment — domestic equities, foreign equities, bonds, housing, whatever — were systematically higher-yielding than some other type of investment, then everyone would just invest in the higher-yielding category and wipe out the difference in yield. So in the long run, you’d expect yields across asset classes to equilibrate.

Yes, this is based on assumptions, which might well be false. But let’s assume that it’s roughly true. Then the usual argument says that you can’t beat the market, and you’ll never do better than to diversify your portfolio. But note carefully what “diversify” means here. It *doesn’t* just mean “invest in all 500 stocks in the S&P 500”. There’s a whole lot more market out there! That is, there are a lot more asset classes than just large industrial stocks of the sort that the S&P traffics in. Even within the class of U.S. stocks, there are larger indexes like the Wilshire 5000. Or there’s the set of stocks tracked by the Vanguard Total Stock Market Index Fund. And then there are foreign stocks. And then government bonds. And municipal bonds. And corporate bonds.

But there’s *still* a lot more market out there. Some asset classes are harder to invest in than others, like houses. Wouldn’t it be cool if you could buy housing across many worldwide markets? It’s a little weird to imagine exactly how that would work, though large property owners do own a shocking amount of property across many cities. So in our imagined perfectly diversified portfolio, we’d have a bunch of housing. And we’d also have a lot of unlisted stocks. And we’d have some private equity. And we’d own some mines. Because again, the principle behind the diversification is that if everyone already knew that some asset class yielded outsized returns, they’d already be investing in it. The only way to beat the market in such a case is to know something that others don’t — to avoid some asset class that you know yields lower returns than the rest of the world thinks it does, or to invest in an asset class that others are systematically avoiding. In principle, I can’t see any reason why your buddy Doug’s new venture doesn’t count as an asset class for the purposes of this argument.

So here’s my question: how do I, J. Random Small Investor, get my portfolio fully diversified across all possible asset classes? One of Piketty’s observations in his masterwork is that the wealthy are able to obtain systematically above-market returns, in no small part because they can invest in asset classes that you and I don’t have access to. And in one example he gives — the Harvard endowment — it helps that the Harvard Corporation spends \$100 million every year to manage \$30 billion in assets. You and I could probably also do very well as investors if we spent all day every day managing our investments, and if we had a staff to do it, and if we had enough money to play with that we could offset some losing bets with more winning bets.

But that argument isn’t convincing to me, because we *do* have that ability; this is why we hire mutual funds. Apparently the Vanguard Total Stock Market Index Fund has \$190 billion in assets. Granted, that particular fund won’t be investing in obscure corners of the asset universe, but why doesn’t Vanguard set up a fund that’s truly diverse across all asset classes, draw many billions of dollars from investors like me, and earn the same returns as the Harvard endowment or Bill Gates?

One possible answer is that regulation forbids them from investing in risky asset classes (like hedge funds or complicated swaps) if non-rich guys like me are on the other end of the trade. Is there some other reason I’m missing why wealthy people *must* earn higher returns than mutual funds do?