### Thursday, December 16, 2004

## Agreeing to disagree

In the long run, value triumphs everything else. But as Keynes said, in the long-run, we’re all dead. The inevitable truth is that markets can remain irrational much longer than most investors can remain solvent. But how do you make money when you know you’re right, but the market doesn’t agree with you? That’s a question I’ve pondered for quite some time now. I have a variety of views on this issue, to which I will return in future posts. But for now, let me ask a simple question: can “rational” investors ever be in a position where they find it sensible to buy shares of a company whose stock is trading above its ‘intrinsic value’, knowing full well that the expected return to holding the stock ‘for the long-run’ is negative?

Let me be more concrete: consider a biotech company that is in the early stages of bringing a drug to market. EVERYONE agrees that if the drug is a success, the share price should be worth $10. Similarly, everyone agrees that if the drug is a failure, the shares will be worthless. Moreover, everyone agrees that there is a 50 percent of success, and a 50 percent chance of complete failure, with nothing in between. What should be the price of the stock? For convenience, let’s assume that that the time periods involved are sufficiently short so that we can ignore the opportunity cost of holding money that earns no interest, and that investors hold the stock as part of a well diversified portfolio (which weans out idiosyncratic risks). [p.s. none of the results listed below will change if we relax these assumptions].

If investors are rational, the price of the will be $5, right? In general, the answer is yes, since there is a 50 percent chance that the stock will end up being worth $10, and a fifty percent chance that the stock will be worth nothing.

However, let me add in an additional wrinkle. Suppose that before the final verdict on the drug is announced, the company will release a “preclinical study” assessing the drug’s efficacy. Now suppose that there are two groups of investors. The first group, (let’s call them Group E ... the ‘Earlies’) believes that the results of this preclinical study will determine beyond a shadow of a doubt whether the drug is a success or failure. However, the second group (let’s call them Group F ... ‘the Finals’) believes that the results of the preclinical study are totally meaningless because they are too premature, and that only the final results should count.

Now I know that these are pretty extreme positions. But let’s stay with my thought experiment and ask the following question: what will the price of shares now be? The answer, as I will now explain, is $7.5. In other words, both group of investors will be willing to buy the shares at $7.5, even though both groups agree that the stock’s expected value in the long-run is $5.

How so you ask? Well, work backwards. Suppose you are a member of Group F. Since you consider the preclinical test to be irrelevant, you will be prepared to pay at least $5 regardless of the outcome of the test. Now, suppose you are a member of Group E. If you buy the stock and the results of the preclinical trials are unfavorable, you know you will be able to sell your shares to members of group F for $5. On the other hand, if the test is favorable, you know the price will jump to $10 since you and other members of Group E will regard the favorable results as conclusive evidence of the drug’s efficacy. Thus, for someone in Group E, the downside to buying the stock before the preclinical results are released is only $5, but the upside is $10. Hence, people in Group E will be prepared to pay $7.5 for each share.

Similarly, people in Group F know that if the preclinical trial is favorable, they will sell all their shares to Group E at $10 per share. If the preclinical trial is unfavorable, they will happily buy all the shares from Group E at $5 per share. Hence, members of Group F will also be willing to buy the shares at $7.5. Let’s summarize the key results:

• All investors agree that the intrinsic value of the stock in the “long-run” (after the final results are released) will be either $10 or nothing, which implies an expected value of $5.

• Nevertheless, all investors are happy to buy the shares at $7.50, which represents a 50 percent premium to the stock’s expected intrinsic value.

• The stock’s expected return in the short-run (between now and when the preclinical trial results are released) is zero. But in the long-run, the expected return is negative 33 percent.

• None of these results listed above depend on “who is right” (though obviously, if this scenario were repeated many times, the actual profits accruing to each group would depend who’s view is correct. But of course in that case, the members of the group with the incorrect view would eventually lose all their money and/or investors would move from one group or the other when the truth became known).

• Moreover, it is not even clear if one group is more sensible than the other (though clearly for the purpose of fleshing out my conclusions, I assumed that both groups are rather irrational in having such stark views about the relevance or irrelevant of the preclinical trial).

• My conclusion would break down if short-selling were allowed (I leave it as an exercise for you to figure out why!). In practise, however, this is not an important consideration since short-selling is not very common, as reflected by the fact that even at the height of the NASDAQ bubble, fewer than ½ percent of NASDAQ shares were sold-short).

Let me be more concrete: consider a biotech company that is in the early stages of bringing a drug to market. EVERYONE agrees that if the drug is a success, the share price should be worth $10. Similarly, everyone agrees that if the drug is a failure, the shares will be worthless. Moreover, everyone agrees that there is a 50 percent of success, and a 50 percent chance of complete failure, with nothing in between. What should be the price of the stock? For convenience, let’s assume that that the time periods involved are sufficiently short so that we can ignore the opportunity cost of holding money that earns no interest, and that investors hold the stock as part of a well diversified portfolio (which weans out idiosyncratic risks). [p.s. none of the results listed below will change if we relax these assumptions].

If investors are rational, the price of the will be $5, right? In general, the answer is yes, since there is a 50 percent chance that the stock will end up being worth $10, and a fifty percent chance that the stock will be worth nothing.

However, let me add in an additional wrinkle. Suppose that before the final verdict on the drug is announced, the company will release a “preclinical study” assessing the drug’s efficacy. Now suppose that there are two groups of investors. The first group, (let’s call them Group E ... the ‘Earlies’) believes that the results of this preclinical study will determine beyond a shadow of a doubt whether the drug is a success or failure. However, the second group (let’s call them Group F ... ‘the Finals’) believes that the results of the preclinical study are totally meaningless because they are too premature, and that only the final results should count.

Now I know that these are pretty extreme positions. But let’s stay with my thought experiment and ask the following question: what will the price of shares now be? The answer, as I will now explain, is $7.5. In other words, both group of investors will be willing to buy the shares at $7.5, even though both groups agree that the stock’s expected value in the long-run is $5.

How so you ask? Well, work backwards. Suppose you are a member of Group F. Since you consider the preclinical test to be irrelevant, you will be prepared to pay at least $5 regardless of the outcome of the test. Now, suppose you are a member of Group E. If you buy the stock and the results of the preclinical trials are unfavorable, you know you will be able to sell your shares to members of group F for $5. On the other hand, if the test is favorable, you know the price will jump to $10 since you and other members of Group E will regard the favorable results as conclusive evidence of the drug’s efficacy. Thus, for someone in Group E, the downside to buying the stock before the preclinical results are released is only $5, but the upside is $10. Hence, people in Group E will be prepared to pay $7.5 for each share.

Similarly, people in Group F know that if the preclinical trial is favorable, they will sell all their shares to Group E at $10 per share. If the preclinical trial is unfavorable, they will happily buy all the shares from Group E at $5 per share. Hence, members of Group F will also be willing to buy the shares at $7.5. Let’s summarize the key results:

• All investors agree that the intrinsic value of the stock in the “long-run” (after the final results are released) will be either $10 or nothing, which implies an expected value of $5.

• Nevertheless, all investors are happy to buy the shares at $7.50, which represents a 50 percent premium to the stock’s expected intrinsic value.

• The stock’s expected return in the short-run (between now and when the preclinical trial results are released) is zero. But in the long-run, the expected return is negative 33 percent.

• None of these results listed above depend on “who is right” (though obviously, if this scenario were repeated many times, the actual profits accruing to each group would depend who’s view is correct. But of course in that case, the members of the group with the incorrect view would eventually lose all their money and/or investors would move from one group or the other when the truth became known).

• Moreover, it is not even clear if one group is more sensible than the other (though clearly for the purpose of fleshing out my conclusions, I assumed that both groups are rather irrational in having such stark views about the relevance or irrelevant of the preclinical trial).

• My conclusion would break down if short-selling were allowed (I leave it as an exercise for you to figure out why!). In practise, however, this is not an important consideration since short-selling is not very common, as reflected by the fact that even at the height of the NASDAQ bubble, fewer than ½ percent of NASDAQ shares were sold-short).