Market Price of Risk and Positive Expected Returns
Summary
The document explains why a nonzero market price of risk can coexist with positive expected returns on risky investments. If investors were risk neutral, they would focus on expected return and increased demand could push asset prices until expected returns matched the risk-free rate.
The answers emphasize that real investors are generally risk averse, so they may require compensation for bearing market risk and do not all bid risky assets up until that premium disappears. The risk premium therefore need not fall to zero simply because investors seek positive expected returns; the expected return compensates for exposure to risk. The discussion is qualitative, using stocks and investor reactions to losses as illustrations. It does not quantify the premium or establish that every risky strategy has a positive realized return; the claim concerns expected compensation under the stated market assumptions.
Key ideas
- A nonzero market price of risk corresponds to compensation investors expect for bearing market risk.
- Risk-neutral investors could bid risky assets up until their expected return matched the risk-free rate.
- Risk aversion helps explain why risky assets may continue to offer a positive expected premium.
- Expected positive return does not guarantee positive realized performance for every investment or period.
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Full text
# Does MPR imply strategies with positive average return? # Does MPR imply strategies with positive average return? Doesn't the existence of Market Price of Risk make investment strategies relying on the average outcome of a risky investment attractive as compared to the expected value of it (computed under the risk free measure)? I understand there is some heterogeneity going on but, wouldn't the demand for such a strategy anyway decrease the MPR until making it zero, so that the average payoff of the security matches the risk-free computed value? ## Answer by Alex C (score 0, accepted) https://quant.stackexchange.com/a/35747 It depends what kind of people inhabit your world (or your model). If people are risk neutral, then indeed they will look only at expected return. They will rush into stocks and raise their price until the return is equal to the risk free rate. The risk premium on stocks will drop to zero. But there is a lot of evidence that this is not how real human beings behave. They really are risk averse and they will not all decide to buy stocks. Historically the risk premium on stocks does not seem to be dropping to zero but remains positive. And in my experience those who are initially enthusiastic about being in stocks moderate their opinion considerably when the first recession hits and they personally experience just how unpleasant it is to lose money. (In fact some give up on stocks altogether). ## Answer by Chris Taylor (score 1) https://quant.stackexchange.com/a/35745 Yes, the existence of non-zero market price of risk implies the existence of strategies with a positive expected return. The expected return is the compensation demanded for bearing market risk. The demand for positive expected return strategies doesn't decrease the market price of risk to zero (equivalently, it doesn't decrease the expected return of risky strategies to zero). Why would it? Why would you buy stocks if the expected return was the same as holding cash?
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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.