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 (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


Related Solutions

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 (26%) Below average 0.2 (14)    Average 0.3 10   Above average 0.3 21   Strong 0.1 73   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...
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 (48%) Below average 0.1 (15)    Average 0.3 11    Above average 0.3 40    Strong 0.2 65    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...
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 -46% Below average 0.1 -13 Average 0.4 14    Above average 0.3 34    Strong 0.1 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...
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 (28%) Below average 0.1 (11)    Average 0.4 10    Above average 0.3 35    Strong 0.1 61    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...
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...
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 (32%) Below average 0.3 (14)    Average 0.4 11   Above average 0.1 36   Strong 0.1 55   1.0 Assume the risk-free rate is 2%. 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...
eBook Problem Walk-Through A stock's returns have the following distribution: Demand for the Company's Products Probability...
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 (42%) Below average 0.2 (10)    Average 0.3 13    Above average 0.3 21    Strong 0.1 51    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...
eBook Problem Walk-Through A stock's returns have the following distribution: Demand for the Company's Products Probability...
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...
Rand Inc. and McNally Corp. have the following probability distribution of returns: Probability Rand Returns McNally...
Rand Inc. and McNally Corp. have the following probability distribution of returns: Probability Rand Returns McNally Returns 0.3 15% 12% 0.4 9 5 0.3 18 20 a) Calculate the expected rates of return for the two stocks. b) Calculate the standard deviation of returns for the two stocks. c) Calculate the expected return and standard deviation on a portfolio P made up of 75% invested in McNally stock and the remaining invested in Rand stock.
Expected Returns: Discrete Distribution The market and Stock J have the following probability distributions: Probability rM...
Expected Returns: Discrete Distribution The market and Stock J have the following probability distributions: Probability rM rJ 0.3 12% 21% 0.4 10 4 0.3 17 12 a.Calculate the expected rate of return for the market. Round your answer to two decimal places. % b. Calculate the expected rate of return for Stock J. Round your answer to two decimal places. % c. Calculate the standard deviation for the market. Round your answer to two decimal places. % d. Calculate the...
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT