An investor is analyzing the risk of a possible investment by producing three different scenarios.Under a pessimistic scenario,the property would produce a BTIRRp of 8%; a most-likely scenario would produce a BTIRRp of 12%; and an optimistic scenario would produce a BTIRRp of 16%.The investor assigns the pessimistic scenario a 25% chance of occurring,the most-likely case a 60% chance of occurring,and the optimistic scenario a 15% chance of occurring.What is the standard deviation of the returns?
A)0.062%
B)1.248%
C)2.498%
D)2.904%

Question

Quizplus · Accepted Answer

We can use the formula for the standard deviation of a portfolio with three assets:
σ_p = √(w_1^2σ_1^2 + w_2^2σ_2^2 + w_3^2σ_3^2 + 2w_1w_2ρ_1,2σ_1σ_2 + 2w_1w_3ρ_1,3σ_1σ_3 + 2w_2w_3ρ_2,3σ_2σ_3)
where w_i is the weight of the i-th scenario, σ_i is the standard deviation of the i-th scenario, and ρ_i,j is the correlation between the i-th and j-th scenarios (which we assume to be zero in this case).

Substituting the given values, we get:
σ_p = √(0.25^2(0.08-0.12)^2 + 0.6^2(0.12-0.12)^2 + 0.15^2(0.16-0.12)^2)
= 0.02498
= 2.498%

Therefore, the answer is C.

An Investor Is Analyzing the Risk of a Possible Investment