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Homework ex. 7.9


J'ai un petit doute sur l'exercice 7.9. Je voulais savoir si lorsque la variance était plus grand que le retour attendu, cela implique que l'investissement est fortement déconseillé au risque de perdre de l'argent.


Bonne journée

Posted by Peter Bossaerts on Tuesday 23 October 2007 at 19:53
Good question. Here is the right way to think about it.
1. The volatility (return standard deviation) of individual securities is irrelevant, whether it is above the average return or not. What matters for individual securities is beta. Intuition: you will never want to buy one single security; you buy a portfolio because of its diversification effect. An individual security adds to the volatility of the portfolio through its beta (covariance with return on portfolio as a whole, scaled by portfolio variance).
2. For portfolios, volatility matters. Now, you wonder whether the expected return should be at least as large as the volatility (standard deviation). That would mean a "Sharpe ratio" (mean return in excess of risk free rate divided by volatility) of 1. As a matter of fact, this is rare out there. On an annual basis, stock portfolios like the SP500 earn a Sharpe ratio of about 0.5. Which effectively means that there is a high probability of getting a negative return... But that's what the market can bear. In other words, risk aversion is not so high out there that investors require a much lower probability of negative return...
3. Also, as a matter of fact, many economists think that a Sharpe ratio of 0.5 is still too high. That is, it reflects very high risk aversion. This is known as the "equity premium puzzle."
Take care,
Posted by Peter Bossaerts on Tuesday 23 October 2007 at 19:55