Question

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 (38%)
Below average 0.1 (14)   
Average 0.3 13   
Above average 0.3 31   
Strong 0.2 63   
1.0

Assume the risk-free rate is 4%. 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

The statistical return information of the portfolio is being calculated as follows

Risk Free

4%

Demand

Probability

Rate %

Weak

0.1

-38

Bel Avg

0.1

-14

Avg

0.3

13

Ab Avg

0.3

31

Strong

0.2

63

For the

Expected Return we have

Er= (Prob1 (Er1)+ Prob 2x Er2….. )

= (0.1*-38) + (.1*-14) …… (0.2*63)

= 20.6 %

Standard Deviation

Is calculated based on probanlistic return

= ((P1 (return 1- exp return)^2 + p2( return 2- exp return)^2 ……..) ^ 0.5

= 0.1 ( -38-20.60)^2 + 0.1(-14 – 20.6)^2 ……. )^0.5

= 29.54%

Coefficient of variation

CV= Std dev / Mean = 29.537 / 20.6 = 1.43

Sharpe ratio = Rp – Rf / Std dev

Where Rp is exp return of portfolio

Rf = risk free rate of 4%

Sharpe ratio = 20.60- 4 / 29.537

= 0.56

Risk Free

4%

Demand

Probability

Rate %

Deviation from mean square

ProbxRate%

Prob*Dev from mean sw

Weak

0.1

-38

3433.96

-3.8

343.396

Bel Avg

0.1

-14

1197.16

-1.4

119.716

Avg

0.3

13

57.76

3.9

17.328

Ab Avg

0.3

31

108.16

9.3

32.448

Strong

0.2

63

1797.76

12.6

359.552

Return of portfolio

20.60

Std dev

29.54

Coefficient of Var

1.43

Sharpe

0.56

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