Question

Security E(r) Standard Deviation

W 8% 12%

X 12% 12%

Y 12% 20%

Z 14% 20%

Which of the above is not true for all risk averse investors?

a. X is preferred to W

b. Y is preferred to W

c. X is preferred to Y

d. Z is preferred to Y

e. Cannot tell with information given.

Answer 1

Answer :-

The Option C is the answer.

The standard deviation of the return is a metric used to measure risk.The higher the value of standard deviation the higher the volatility of return. The risk averse investor will prefer lower standard deviation for a given level of risk.

In Option c which states that X is preferred to Y is not correct as the return is same = 12% but the standard deviation is more for Y (20%) than X (12%) which the risk averse will not prefer.

For Option a is X is preferred to W is preferable as the return of X (12%) is more than W ( 8%) for a same level of standard deviation ( 12%), so it can be preferred.

For Option b is Y is preferred to W is preferable as the return of Y (12%) is more than W ( 8%) for a given standard deviation of Y (20 %) which is higher than W (12%). As the investor is compensated higher return for higher risk, so it can be preferred.

For Option d is Z is preferred to Y is preferable as the return of Z (14%) is more than Y ( 12 %) for a same level of standard deviation ( 20 %) ie. risk, so it can be preferred.