Question

Consider the following two investments. One is a risk-free investment with a $100 return. The other investment pays $2,000 20% of the time and a $375 loss the rest of the time. Based on this information, answer the following:

(i) Compute the expected returns and standard deviations on these two investments individually. (ii) Compute the value at risk for each investment.

(iii) Which investment will risk-averse investors prefer, if either? Which investment will risk- neutral investors prefer, if either?

Answer 1

i) Compute the expected returns and standard deviations on these two investments individually

Answer = The expected rate of return is $100 for the risk-free investment. The risk-free investment has a standard deviation of zero because the return is certain. For the risky investment:

Expected return = 0.2($2000) + 0.8(-$375) = $100

Standard Deviation = 0.2*(2000-100)²+ 0.8*(-375-100)²= 902500 = 950

(ii) Compute the value at risk for each investment.

Answer =The value at risk for the risk-free investment is $100 because it pays a certain return. The value of risk for the risky investment is -$375, this is the maximum amount the investor can lose.

(iii) Which investment will risk-averse investors prefer, if either? Which investment will risk- neutral investors prefer, if either?

Answer = The risk-averse investor will prefer the risk-free investment. The risk-neutral investor will not have a preference between the two investments because they pay the same expected return.