(a) A stock has the following predicted returns under the following economic conditions:
Economic Condition Probability Return (K)
Recession 0.30 50
Stable economy 0.3 100
Moderate growth 0.3 120
Boom 0.10 200
Step by step Compute the following
(i) Expected monetary value.
(ii) Standard deviation.
(iii)Coefficient of variation.
(iv)Return-to-risk ratio.
(i) Expected monetary value (EMV)
EMV = Σ(Probability * Return) = (0.3 * 50) + (0.3 * 100) + (0.3 * 120) + (0.1 * 200)
EMV = 15 + 30 + 36 + 20 = 101
(ii) Standard deviation
First, calculate the variance.
Variance = Σ(Probability * (Return - Expected Return)^2)
Variance = (0.3 * (50 - 101)^2) + (0.3 * (100 - 101)^2) + (0.3 * (120 - 101)^2) + (0.1 * (200 - 101)^2)
Variance = (0.3 * 4225) + (0.3 * 1) + (0.3 * 361) + (0.1 * 7921)
Variance = 1267.5 + 0.3 + 108.3 + 792.1 = 2168.2
Standard deviation = √(Variance)
Standard deviation = √2168.2 = 46.56
(iii) Coefficient of variation
Coefficient of variation = (Standard deviation / Expected monetary value) * 100
Coefficient of variation = (46.56 / 101) * 100 = 46%
(iv) Return-to-risk ratio
Return-to-risk ratio = Expected monetary value / Standard deviation
Return-to-risk ratio = 101 / 46.56 = 2.17
Therefore, the expected monetary value is 101, the standard deviation is 46.56, the coefficient of variation is 46%, and the return-to-risk ratio is 2.17.