Wednesday, August 10, 2011

Investing For Expected Value?

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 ( 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.


Anonymous said...

It is probably better to think in terms of expected growth rather than expected value when it comes to investing.

Anonymous said...


Thanks for replying to my comment. I happen to believe this is an extremely important topic. I could fill many pages with my thoughts, but given the limitations of this forum I'll try to be brief.

1) Whitney Tilson agrees with me on this point, so at least I'm not alone! :-) If you haven't seen this already, take a look at this excerpt from one of his investor letters:

2) Thinking about an investment in terms of EV certainly isn't the best analytical technique in all cases. Far from it. It's best used in special situations that have discrete outcomes whose probabilities can be estimated by someone knowledgeable in the field. A great recent example would be GCVRZ, which is a "contingent value right". Here's an example of how to value a security like this:

3) Knowing how to size bets like these is crucial. I think a solid understanding of the "Kelly Criterion" is necessary. Are you familiar with that concept? Wikipedia has an ok introduction:

4) As with any investment methodology, the EV method should only be used within one's "circle of competence". In other words, if you don't know how to estimate the relevant probabilities conservatively, don't make the investment. When in doubt, use a large margin of safety on the probabilities and outcomes.

- aagold

Anonymous said...

"3) Knowing how to size bets like these is crucial. I think a solid understanding of the "Kelly Criterion" is necessary. Are you familiar with that concept? Wikipedia has an ok introduction"

I alluded to this in my previous comment. The Kelly Criterion sizes bets to maximize expected growth. This will eliminate placing bets on situations Saj was referring to: "a high expected value can still be derived from a set of scenarios with a high frequency of losses."

If anyone is interested in the Kelly Criterion, I highly recommend reading the book Fortune's Formula, where it is used in both blackjack and investing.

Anonymous said...


Yes, I agree that "Fortune's Formula" is a great book to read on this topic. That's where I was first introduced to it. Your first comment was a bit too brief for me to figure out that's what you meant by "expected growth". But now that I know what you meant, then yes I agree with you.

I partially agree with what you said about the Kelly Criterion precluding an investment with a high probability of loss, even if it has a high EV. However, the analysis is more complex than that. The impact of diversification, for example, is very important.

Let's say I have a basket of 10 *statistically independent* investments, each of which has a 50% chance of total loss. What's the probability of a total loss on the whole basket? Less than 0.1%. In a case like this, the key factor ends up being the EV of each one of the investments considered separately. In other words, if the price one pays for each investment in the basket is low enough to provide a very high expected rate of return, and the investments are independent, then the basket becomes a *very* attractive investment.

Now obviously in the real world no investments are truly independent of all others in a basket, but the basic idea is sound and it can be extended to the more realistic case where there's some correlation between investments.

- aagold

Saj Karsan said...

Hi aagold,

I definitely don't think you're the only one, I would say most investors would shoot for EV. I would agree with you that it can be useful when applied very selectively. I just reject the notion that the odds and results can be accurately calculated most of the time, making it difficult to apply Kelly C (which I covered in this book review)

Anonymous said...


Buffet did similar style investment..Check Annual Meeting Transcript (not sure abt the year)

Bufffet: Pepsi is running a contest in which one person will have a 1-in-1,000 chance of winning $1 billion -- a present value of $250 million [since the billion is paid out over time]. [If the person wins,] we will pay it. We are willing to assume that for a payment, and very few people would be. We would be willing to assume a $2.5 billion payout (but not $25 billion) if we got paid more than proportionally more.
Munger: If you're risking a $250 million payout and you have $60 billion of capital, it's not crazy. But I think it's crazy to do it based on someone else's circumstances or abilities.


Anonymous said...


Yes, that's a good point. The insurance business is a great of example of when to use EV as an analytical technique.

So actually, I'm pretty confident that Buffett would endorse this way of thinking about investing. Especially in a case such as the example I described in a previous comment (10 independent bets in a "basket", each of which has a 50% probability of total loss but an attractive EV).

- aagold