Question

(a) Explain precisely how stand-alone risk is measured in finance.

(b)   Find the expected return and coefficient of variation given the following information about an asset:

Return possibilities               Probabilities

.10                                       .05

.20                                       .90

.30                                       .05

Answer 1

Explain precisely how stand-alone risk is measured in finance.

It's important to understand the meaning of the word "risk" before we handle this question. A risk is a probability of unfavorable outcome. A risk is deviation from normal. A risk is deviation from expected behavior.

Stand alone risk refers to the risk associated with one single asset or one single unit of company or one operation of a company. Stand alone risks of a security is measured in finance by two methods:

1. Standard deviation of the returns of the security and / or
2. Coefficient of variation: Coefficient of variation (“CV”) is the ratio of standard deviation with the expected return (mean). It’s a measure of risk per unit of return. The ratio may not make sense in isolation but definitely acts as a relative measure of risk.Lower the CV, more attractive will be the project to an investor.

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If P_i = probability of occurrence of state "i" and R_i is the return in state "i" then,

Expected return E(R) = sum of probability weighted return of different possibilities

= 0.05 x 0.10 + 0.9 x 0.2 + 0.05 x 0.3 =  0.20 = 20%

Variance of the return

= 0.05 x (0.10 - 0.20)² + 0.90 x (0.20 - 0.20)² + 0.05 x (0.30 - 0.20)² = 0.001

Hence, standard deviation, =  0.03162

Coefficient of variation = / E(R) =  0.03162 / 0.20 =  0.15811 = 15.81%