Question

The CFA Institute prescribes the following utility function: U = E[r] - 0.5*A*σ². The major convenience of using this function is related to the ....

Answer 1

It shall be noted that the CFA Institute prescribes the following utility function: U = E[r] - 0.5*A*σ².

Where,

U = utility

E(r) = portfolio expected return

A = risk aversion coefficient

σ² = portfolio variance

The risk aversion coefficient, A, is positive for risk-averse investors (any increase in risk reduces utility), it is 0 for risk-neutral investors (changes in risk do not affect utility) and negative for risk-seeking investors (additional risk increases utility).

The risk-aversion for different investors as depicted using the given utility function is:

One can now overlay an investor’s indifference curve with the capital allocation line (green line) to determine the investor’s optimal portfolio.

Thus, the major convenience of using this function is related to the determination of risk aversion and selection of an optimal portfolio, given an investor’s utility (or risk aversion) and the capital allocation line.