Question

9. Assume that you expect to hold a $20,000 investment for one year. It is forecasted to have a year end value of $21,000 with a 30% probability; a year end value of $24,000 with a 45% probability; and a year end value of $30,000 with a 25% probability. What is the standard deviation of the holding period return for this investment? A) 12.1% B) 14.4% C) 16.86% D) 33.5% Answer: C

Please help me understand how the answer is C showing work using formulas or financial calculator. Thanks.

Answer 1

Investment Amount = $20000

Given, R₁ = 21000 for P₁ = 0.30
R₂ = 24000 for P₂ = 0.45
R₃ = 30000 for P₃ = 0.25

Holding Period Return = H = (Year End Value - Investment Amount)/Investment Amount

H₁ = (21000 - 20000)/20000 = 0.05
H₂ = (24000 - 20000)/20000 = 0.20
H₃ = (30000 - 20000)/20000 = 0.50

Average Return ER = ΣP_iH_i = 0.30*0.05 + 0.45*0.20 + 0.25*0.50 = 0.23

Standard Deviation = sqrt [ ΣP_i(H_i - ER)² ]

= sqrt [0.30(0.05 - 0.23)² + 0.45(0.20 - 0.23)² + 0.25(0.50 - 0.23)² ]

= 0.1684 or 16.84%

Hence, correct option is (c) 16.86%