1. Returns and Risk
Estimate and compare the returns and variability (i.e. annual standard deviation over the past five years) of Reynolds and Hasbro with that of the S&P 500 Index. Which stock appears to be riskiest?
S&P 500 Annualized Expected Return: 6.8920% S&P 500 SD (Annualized): 12.477%
Reynolds Annualized Expected Return: 22.4980% Reynolds SD (Annualized): 32.446%
Hasbro Annualized Expected Return: 14.2060% Hasbro SD (Annualized): 28.114%
Reynolds appears to be the riskiest stock since it has the highest standard deviation. The fact that Reynolds also has the highest annualized expected return supports this calculation since risk and return should be directly correlated.
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That is why as the risk of a stock in a portfolio increases, the expected return of that portfolio increases.
To support this concept, we used the 3-month Treasury bill to estimate the risk-free interest rate in the market. Estimated Risk-free interest rate = .023%
Expected Return (Reynolds and S&P 500) = .023% + .7356 (6.8920% - .023%) = 5.0754%
Expected Return (Hasbro and S&P 500) = .023% + 1.41979 (6.8920% - .023%) = 9.7756% The above CAPM calculations demonstrate that riskier stocks (compared to the market), or those with a higher beta, also yield a higher expected return.
5. In what stock(s) (if any) should Sharpe invest?
In order to determine which stock/s Shape should invest in, we would have to understand her risk aversion. Reynolds creates a more diversified portfolio, making it a safer investment that also yields a lower return. On the other hand, a portfolio with Hasbro is a riskier portfolio, but it also yields a higher return.
Nevertheless, it seems that the difference in yield between Reynolds (5.0754%) and Hasbro (9.7756%) which is 4.7002%, is a lot more significant than the difference in their standard deviations, or riskiness, which is only .0061%.
In order to make a more objective decision about which decision is a better investment, it would be useful to calculate the Sharpe Ratio, which measures risk-adjusted performance.
Sharpe Ratio = (Expected Portfolio Return –