Demand for the Company’s Products Probability of this Demand Occurring Rate of Return if this Demand Occurs Weak 0.1 (30%) Below average 0.1 (14) Average 0.3 11 Above average 0.3 20 Strong 0.2 45 1.0 Assume the risk-free rate is 2%. Calculate the stock’s expected return, standard deviation, coefficient of variation, and Sharpe ratio.
Question
Demand for the Company’s Products Probability of this Demand Occurring Rate of Return if this Demand Occurs Weak 0.1 (30%) Below average 0.1 (14) Average 0.3 11 Above average 0.3 20 Strong 0.2 45 1.0 Assume the risk-free rate is 2%. Calculate the stock’s expected return, standard deviation, coefficient of variation, and Sharpe ratio.
Solution
To calculate the expected return, standard deviation, coefficient of variation, and Sharpe ratio, follow these steps:
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Expected Return: Multiply the rate of return of each demand scenario by its probability of occurrence, then sum these values.
Expected Return = (0.1*-30%) + (0.1*-14%) + (0.311%) + (0.320%) + (0.2*45%) = -3% -1.4% + 3.3% + 6% + 9% = 13.9%
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Standard Deviation: First, calculate the variance. Subtract the expected return from the return of each scenario, square the result, multiply by the probability of the scenario, then sum these values. The standard deviation is the square root of the variance.
Variance = 0.1*(-30%-13.9%)^2 + 0.1*(-14%-13.9%)^2 + 0.3*(11%-13.9%)^2 + 0.3*(20%-13.9%)^2 + 0.2*(45%-13.9%)^2
Standard Deviation = sqrt(Variance)
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Coefficient of Variation: This is the standard deviation divided by the expected return.
Coefficient of Variation = Standard Deviation / Expected Return
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Sharpe Ratio: Subtract the risk-free rate from the expected return, then divide by the standard deviation.
Sharpe Ratio = (Expected Return - Risk-Free Rate) / Standard Deviation
Please note that the expected return calculation assumes that the negative returns for "weak" and "below average" demand are losses, and are therefore entered as negative values. If these are actually positive returns of 30% and 14%, respectively, then the signs should be changed to positive in the calculations.
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