Question

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:

Answer 1

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

Thanks . Please Upvote if you like