Compute the expected return, standard deviation, and value at risk for each of the following investments:Investment (A): Pays $800 three-fourths of the time and a $1,200 loss otherwise.Investment (B): Pays $1,000 loss half of the time and a $1,600 gain otherwise.State which investment will be preferred by each of the following investors, and explain why.(i) a risk-neutral investor(ii) an investor who seeks to avoid the worst-case scenario.(iii) a risk-averse investor.

Question

What will be an ideal response?

Answer 1

Investment (A)
Expected return = 0.25(-$1,200) + 0.75($800) = $300
Standard Deviation = 
 =  = 866
Value at Risk = -$1,200
Investment (B) 
Expected return = 0.5(-$1,000) + 0.5($2,000) = $500
Standard Deviation = 
 =  = 1,300
Value at Risk = -$1,000
(i) The risk-neutral investor is indifferent between these two investments because they pay the same expected return.
(ii) The investor who seeks to avoid the worst-case scenario will choose Investment (B) because it has the lower value at risk.
(iii) The risk-averse investor will prefer Investment (A) because it has a lower standard deviation. This suggests that there is less uncertainty about the expected return relative to Investment (B).