University:
University of Texas at Austin
Course:
ACC 311 | Fundamentals of Financial Accounting
Academic year:

2023
Views:

466

Pages:

3
Author:

Vina J.

Measures of Financial Risk So far, our analysis of risk has been based on discrete returns. We have noted that in practice such returns will normally be continuous - discrete analysis is at best an approximation. An alternative approach is to use a measure of spread of the continuous distribution as a proxy for risk. In finance, the standard deviation or variance is often taken as such a measure of risk where returns are continuous. A distribution with a higher standard deviation is assumed to be more risky than one with a lower standard deviation. This idea is expressed by the mean variance rule, which states that, first, where two distributions have an equal mean the distribution with the lower variance is to be preferred for all risk-averse individuals; second, an option with a higher expected return and a lower variance is to be preferred; third, a risk return trade-off has to be established where one option has a higher expected value and a higher variance. These preferences are illustrated in Figure. Investment A is inferior to all points in the north-west quadrant (B,C,D), and superior to all those in the south-east quadrant (E,F,G), the points lying in the remaining two quadrants (HI) being determined by risk return trade-off. This is the basis for deriving the efficient set in portfolio analysis. Where distributions are normal, mean and variance may be used as the basis for selecting investments, as the returns are completely described by the mean and variance Haley and Schall (1973), p. 97). Thus, the returns of the investments in Figure 3.19 are assumed to appear as in Figure 3.20. There are two further important assumptions. First, if investments are combined, it is assumed that their combined distribution will also be normal, i.e. they are jointly normal. Secondly, the returns represent the total returns to the owner (or manager acting as agent). In practice distributions are unlikely to be periectly normal and may well be markedly non-normal. In such circum-stances, it would be wrong to apply the mean variance rule. To illustrate the error that can result, suppose that a manager must choose between the two investments in Table, he might make the following remarks: "The attraction of investment A is that it offers a guaranteed level of business with a small promise of high returns. As for investment B, I would expect to have a higher return but there isn't the same guaranteed level, and the returns may be worryingly low'. \ In this case, the standard deviations are identical, therefore, the mean variance rule would select B as it has the higher expected return. However, B is not stochastically dominant over A (it has a lower bottom value). If, for instance, the manager has a utility curve characterized by U = log(x), then he or she will be indifferent between the two investments and a curve such as U = log(x-9.5) would imply preference for A over B despite the lower mean. Selection, as the dominance rules suggest, is dependent upon the degree of risk-aversion, a result not indicated by the mean variance rules.