Читать книгу Alternative Investments - Black Keith H. - Страница 13

Consider the following two investment choices available to an asset owner:

investment A will increase by 10 % or decrease by 8 % over the next year, with equal probabilities.

Investment B will increase by 12 % or decrease by 10 % over the next year, with equal probabilities.

The expected return on both investments is 1 % (found as the probability weighted average of their potential returns); however, their volatilities will be different (see Equation 4.9 of CAIA Level I).

Investment A: Standard deviation =

Investment B: Standard deviation =

If an asset owner expresses a preference for investment A over investment B, then we can claim that the asset owner is risk averse. Although it is rather obvious to see why a risk-averse asset owner would prefer A to B, it will not be easy to determine whether a risk-averse investor would prefer C to D from the following example:

Investment C will increase by 10 % or decrease by 8 % over the next year, with equal probabilities.

Investment D will increase by 12 % or decrease by 9 % over the next year, with equal probabilities.

In this case, compared to investment C, investment D has a higher expected return (1.5 % to 1 %) and a higher standard deviation (10.5 % to 9 %). Depending on their aversion to risk, some asset owners may prefer C to D, and others, D to C.