Last week, a reader brought up an interesting point with respect to investment decisions:
"I disagree with the idea that an investment that has a non-trivial probability of a large loss is necessarily a bad one. I would claim that the key metric is the investment's Expected Value (EV)."
Intuitively, this makes sense. But I would argue that EV should not be the metric by which investors make their decisions.
The most obvious reason expected value should not be used to make investment decisions is that a few poor results (i.e. low probability, but high loss-entailing) could cripple a portfolio. But the reader understands this point, stating: "I agree that it's a mistake to have a *concentrated* position (e.g., 10% of the portfolio) in a stock like this one, but if the EV is high, then having a basket of, say, 1% positions like this may make a lot of sense."
The problem with this approach does not just have to do with diversification, however. The problem is that it's impossible to accurately determine EV. One of the recurring themes of value investing is that the future is impossible to predict consistently. As such, trying to come up with accurate expected values is riddled with traps.
One smart person's EV for a company will differ greatly from another smart person's (...as long as they are thinking independently. If they are not, the groupthink-like EV they come up with together is likely to be even more useless.) Furthermore, even the same person's estimation of EV is likely to change with his moods and the times. For example, the same investor would likely have had very different opinions of a company's expected earnings had he been deliberating during 2005-2007 as compared to 2008-2009. As such, even in a diversified portfolio, you may be doing no better than throwing darts at a board if you're investing based on the assumption that you can determine an expected value.
This is especially true if a company does not have a stable operating history. A company with no revenue and no earnings, for example, that has pinned all its hopes on a new wonder drug that requires a ton of cash burn has such a high range of possible outcomes that it is impossible to come with a credible EV with any degree of accuracy.
Warren Buffett's first rule of investing is: Don't lose money. This is in direct contradiction to "invest for expected value", because a high expected value can still be derived from a set of scenarios with a high frequency of losses. Expected values are too tough to figure out accurately. Protecting the downside is far more profitable.