Question

All the steps required, pleas!

U E (r) - Ao2, what is the significance of A?

Answer 1

The given equation tries to quantify the utility of a given investment opportunity, that has an expected return of E(r) and a variance (risk) of $\sigma ^2$ , for an investor who has a risk aversion coefficient of A.

The idea is that every investor is different and they all have very different tolerances towards risk. This means that whether an investment opportunity is good or not is highly subjective and depends on a particular investor's individual preferences. Someone who is highly risk averse (higher A) would not consider equity as a viable investment compared to someone who has a greater risk appetite (lower A). So, to include this subjectivity to figure out whether an investment is viable or not for a particular investor, A is introduced into the above equation. A magnifies the risk of a security by how risk averse a particular investor is. It usually ranges from 1 to 10.

For example, if an investor has a risk aversion of 5, expected return on an investment is 10% and its standard deviation is 16%, then the utility is:

U = 0.10 - 0.5*5*0.16^2 = 0.036 or 3.6%

If risk free rate was less than 3.6% then this investment presents a viable opportunity for this investor. But if A was higher than 5, meaning the investor was more conservative then the situation would be different.