In: Finance

# A stock's returns have the following distribution: Demand for the Company's Products Probability of This Demand...

A stock's returns have the following distribution:

 Demand for the Company's Products Probability of This Demand Occurring Rate of Return If This Demand Occurs Weak 0.1 (36%) Below average 0.1 (15) Average 0.3 16 Above average 0.3 21 Strong 0.2 56 1.0

Assume the risk-free rate is 3%. Calculate the stock's expected return, standard deviation, coefficient of variation, and Sharpe ratio. Do not round intermediate calculations. Round your answers to two decimal places.

Stock's expected return:   %

Standard deviation:   %

Coefficient of variation:

Sharpe ratio:

## Solutions

##### Expert Solution

a) Expected Return- It refers to the sum of the average return of each stock multiplied by its weight or probability.

E(R) = P1 * R1 + P2 * R2 +.......Pn * Rn

where, P1 ,P2 ...Pn = Probabilty of return

R1 ,R2 ...Rn  = Return expectation

Here, E(R) = (0.1* -36%) + (0.1 * -15%) + (0.3 * 16%) + (0.3 * 21%) + (0.2 * 56%)

= -0.036 - 0.015 + 0.048 + 0.063 + 0.112 = 0.172 or 17.2%

b) Standard Deviation- It is a measure of volatility or risk. It is the squareroot of the variance.

p = [P1 * (R1- E(R))2 + P2* (R2- E(R))2 + ......... Pn * Rn - E(R))2]

p =  (0.1 * (-0.36-0.172)2) + (0.1 * (-0.15-0.172)2) + (0.3 * (0.16-0.172)2) + (0.3 * (0.21-0.172)2 ) + (0.2 * (0.56-0.172)2)

p=   (0.0283 + 0.0103684 + 0.0000432 + 0.0004332 + 0.0301)

p= (0.0692448)

p= 0.2631 or 26.31%

c) Coefficient of variation - It is the ratio of standard deviation to the mean (expected return)

COV = SD/ expected return

COV = 26.3%/ 17.2% = 1.52

d) Sharpe ratio - The ratio is the average return earned in excess of the risk-free rate per unit of volatility or total risk

Sharpe ratio = Rp - Rf / p

where, Rp - Return on portfolio

Rf - Risk free rate

p - Standard deviation of portfolio

Sharpe ratio = Rp - Rf / p

= (0.172 - 0.03) / 0.263

= 0.53

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