Question

eBook Problem Walk-Through 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 (48%) Below average 0.1 (13)    Average 0.4 18    Above average 0.3 22    Strong 0.1 54    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:

Answer 1

Demand of company's product	Probability	Returns (%)
Weak	0.10	-48%
Below Average	0.10	-13%
Average	0.40	18%
Above Average	0.30	22%
Strong	0.10	54%
Calculation of Expected Return of Stock
Demand of company's product	Probability (a)	Returns (%) (b)	a X b
Weak	0.10	-48%	-4.80%
Below Average	0.10	-13%	-1.30%
Average	0.40	18%	7.20%
Above Average	0.30	22%	6.60%
Strong	0.10	54%	5.40%
Expected Return	13.10%
Expected Return = sum of (a X b)
Expected Return of Stock = 13.10%
Calculation of Standard Deviation Stock
Demand of company's product	Probability (a)	Returns (%) (b)	Expected Return % (c )	{Square of (b-c)}*a
Weak	0.10	-48%	13.10%	3.73321%
Below Average	0.10	-13%	13.10%	0.68121%
Average	0.40	18%	13.10%	0.09604%
Above Average	0.30	22%	13.10%	0.23763%
Strong	0.10	54%	13.10%	1.67281%
Sum	6.42090%
Standard Deviation = square root of [sum of {Square of (b-c)}*a]
Standard Deviation = square root of 6.42090%
Standard Deviation of Stock = 25.34%
Calculation of Coefficient of variation
Coefficient of variation= Standard Deviation / Expected Return
Coefficient of variation= 25.34% / 13.10%
Coefficient of variation= 1.94
Calculation of Sharpe Ratio
Sharpe Ratio= ( Rp-Rf)/ Standard deviation of fund
Where
Rp= Return on fund
Rf= Risk Free Return
Rf= 3%
Standard Deviation= 25.34%
Rp= 13.10%
Sharpe Ratio= ( Rp-Rf)/ Standard deviation of fund
Sharpe Ratio= ( 25.34% - 3%)/ 25.34%
Sharpe Ratio= 22.34% / 25.34%
Sharpe Ratio= 0.88