Frequancy versus Magnitude
The frequency of correctness does not matter; it is the magnitude of correctness that matters. Say that you own four stocks, and that three of the stocks go down a bit but the fourth rises substantially. The portfolio will perform well even as the majority of the stocks decline. Building a portfolio that can deliver superior performance requires that you evaluate each investment using expected value analysis.
Expected value is difficult because it runs against human nature in a very fundamental way.
People are a lot happier when they are right frequently. What’s interesting is that being right frequently is not necessarily consistent with an investment portfolio that outperforms its benchmark The percentage of stocks that go up in a portfolio does not determine its performance, it is the dollar change in the portfolio. A few stocks going up or down dramatically will often have a much greater impact on portfolio performance than the batting average.
Bulls, Bears and Odds In his wonderful book, Fooled by Randomness, Nassim Taleb relates an anecdote that beautifully drives home the expected value message. In a meeting with his fellow traders, a colleague asked Taleb about his view of the market. He responded that he thought there was a high probability that the market would go up slightly over the next week. Pressed further, he assigned a 70% probability to the up move. Someone in the meeting then noted that Taleb was short a large quantity of S&P 500 futures—a bet that the market would go down—seemingly in contrast to his “bullish” outlook. Taleb then explained his position in expected value terms. He clarified his thought process with the following table:
| Event | Probability | Outcome | Expected value |
|---|---|---|---|
| Market goes up | 70% | +1% | +0.7% |
| Market goes down | 30% | -10% | -3.0% |
| Total | 100% | -2.3% | |
| In this case, the most probable outcome is that the market goes up. But the expected value is negative, because the 4 outcomes are asymmetric. Now think about it in terms of stocks. Stocks are sometimes priced for perfection. Even if the company makes or slightly exceeds its numbers the majority of the time (frequency), the price doesn’t rise much. | |||
| But if the company misses its numbers, the downside to the shares is dramatic. The satisfactory result has a high frequency, but the expected value is negative. | |||
| Now consider the downtrodden stock. The majority of the time it disappoints, nudging the stock somewhat lower. But a positive result leads to a sharp upside move. Here, the probability favors a poor result, but the expected value is favorable. |
Investors must constantly look past frequencies and consider expected value. As it turns out, this is how the best performers think in all probabilistic fields. Yet in many ways it is unnatural: investors want their stocks to go up, not down. Indeed, the main practical result of prospect theory is that investors tend to sell their winners too early (satisfying the desire to be right) and hold their losers too long (in the hope that they don’t have to take a loss). We now turn to three leading practitioners in separate probabilistic fields: investing, pari-mutuel betting, and black jack.
Naturally, coming up with likely outcomes and appropriate probabilities is not an easy task. But the discipline of the process compels an investor to think through how various changes in expectations for value triggers—sales, costs, and investments—affect shareholder value, as well as the likelihood of various outcomes. Such an exercise also helps overcome the risk aversion pitfall.
