Six Reasons to Not Take Returns at Face Value

We all know that past returns are not indicative of future results. But past returns may not be indicative of true past results, either.

Come again? Surely nothing's more straightforward than a return calculation. Well, the more time you spend analyzing returns, the more wrinkles you find. There are dozens of reasons that a stock or fund return might be misleading or not reflect true changes in investor wealth. Some of these effects are small--small enough that you can live a long and peaceful investing life and never think twice about them. Some can be quite large, however.

In the spirit that the informed investor is a better investor, let's walk through six oddities, which I summarize in this table.

Deciphering Return Oddities
Return Oddity	Description
1. Trades moving prices	A buy/sell order can move a stock price.
2. Dollar-weighted versus time-weighted returns	Published returns don't reflect what average investors experienced.
3. Nonsynchronous trading	Not all stock prices are up-to-date.
4. Short-term return reversals	Stocks tend to snap back over very short time intervals
5. T+1 accounting	Mutual funds don't use current holding data to calculate NAV.
6. Leaning for the tape	Academics think some funds juice returns at quarter-end.

1. A stock begins the year at $20 per share. It ends the year at $25. The annual return of the stock is therefore 25%. Would I really have earned a 25% return on the stock if I had bought at the start of the year and sold at the end?
That's what the math says, but the 25% is a hypothetical return--there's no guarantee you could have earned it. If you're trading a small number of shares, meaning your trade represents only a small fraction of the shares traded on any given day, yes, your return would probably have been 25%. You could have bought at $20 and sold at $25. If, however, you're a big-time money manager, or if few shares of the stock change hands on a daily basis, you may not have been able to buy at $20 or sell at $25.

To see why, let's begin with the $20 price quote. This means that at the beginning of the year, two parties exchanged the stock at $20. A price quote is simply a record of a historical transaction--it's the price at which the last transaction occurred. There's no guarantee that the next transaction will occur at $20. If you place a small buy order--100 shares, say, for a stock that trades 100,000 shares in a typical day--chances are, some seller will be willing to part with the stock at or very near the last transaction price.

But let's say the order was for 100,000 shares. Perhaps one seller is willing to sell you 10,000 shares for $20.05. Another seller will part with 5,000 shares at $20.10. Another will sell 7,000 at $20.20. And so on. Your ultimate price may be well above $20, and it will depend on how quickly you want to buy (the less patient you are, the costlier the trade) and how much depth there is to the market. The same analysis applies when you go to sell the shares at year-end.

It's akin to Heisenberg's uncertainty principles in physics. If you touch the stock, you change what the return would have been. Such transaction costs are very real, and they are a key reason why investors should always question the results of paper portfolios or back-testing, particularly if the proposed investment strategy involves buying illiquid stocks. For a good discussion of these issues, I'd recommend David Leinweber's paper Using Information from Trading and Portfolio Management: Ten Years Later.

2. A mutual fund has a five-year annualized return of 30%. Are the fund's shareholders, as a group, a lot richer today?
Maybe, maybe not. When you look at the published return of a stock or mutual fund, you see the time-weighted return, which is the return investors would have received had they bought and held over the entire time period. Few investors actually do this. Instead, many buy in when the price is high and sell when the price is low. If you measure the returns that mutual fund investors actually earned in a fund--using so-called dollar-weighted returns--they're almost always lower than the time-weighted returns.

There's also a difference between time- and dollar-weighted returns when it comes to stocks, although there's an important difference. For any single stock investor, the dollar-weighted return will depend on the timing of purchases and sales, just as with a mutual fund. For investors in the aggregate, though, one person's well-timed trade is someone else's poorly timed trade, so the winners cancel out the losers. What drives a wedge between aggregate dollar-weighted returns and published returns are stock issuances and other changes to firms' capital accounts, and the academic evidence suggests that companies (and their investment banks) are good at selling high. In a 2004 paper, Ilia Dichev finds dollar-weighted returns to be 1.3% lower than time-weighted returns for stocks on the New York Stock Exchange and more than 5% lower for Nasdaq stocks.

3. The market was down 5% today, but my stock was flat. Why is that?
Chances are, your stock bucked the trend for a good reason related to the fundamentals of the company. But there's also a chance the price of your stock is stale. Remember that price quotes are records of historical transactions. If your stock didn't trade toward the close of the day, the last quoted transaction could be old. Academics call this nonsynchronous trading. The price quotes of some stocks reflect up-to-date market information, but some may not.

Nonsynchronous trading is behind the stale-price arbitrage that hedge funds have used to milk mutual fund investors out of money. Let's say an investor buys mutual fund shares on Tuesday at that day's ending net asset value (NAV) for the fund, which might be $10. If the fund holds a lot of stocks that haven't traded in a while--like Asian stocks, for which the markets closed much earlier, or illiquid stocks in the U.S. market--the NAV could be based partly on stale prices. If the U.S. market rose sharply on Tuesday, it's a good bet that Asian markets and illiquid U.S. stocks will rise on Wednesday. Buy the mutual fund, short an index to reduce market risk, and you've got yourself a good chance of a small positive return.

Do it enough times in any given year and the compound returns can become quite large. Academics actually calculated how much an investor could earn by following this strategy before Eliot Spitzer's mutual fund probe made stale-price arbitrage (or "market-timing") front-page news. The paper is "Predictable Changes in NAV: The wildcard option in transacting mutual fund shares" by Chalmers, Edelen, and Kadlec.

This article is continued here.