1. (Expected Rate of Return and Risk) B. J. Orange Enterprises is evaluating a s
ID: 2662963 • Letter: 1
Question
1. (Expected Rate of Return and Risk) B. J. Orange Enterprises is evaluating a security. One-year Treasury bills are currently paying 1.9 percent (with little risk – 1 percent). Calculate the investment’s expected return and its standard deviation. Should Orange invest in this security or the Treasury bills? You should calculate the expected return, standard deviation, and coefficient of variation.Probability Return
.15 6%
.30 5%
.40 11%
.15 14%
2. (Historic Rate of Return and Risk) Consider an investment in one of two common stocks. Given the information that follows, which investment was better, based on risk (as measured by the standard deviation), return, and coefficient of variation?
Common Stock A Common Stock B
Return Return
10% 8%
13% 15%
20% 19%
Explanation / Answer
1) The formula for calculating the expected return when probability function is given is computed as Expected return = 0.15(0.06) + 0.30(0.05) + 0.40(0.11) + 0.15(0.14) = 0.009 + 0.015 + 0.044 + 0.021 = 0.089 or 8.9% Expected return equals some risk free rate plus a market risk premium multiplied by market's beta. It is important to note that there is no guarantee that the expected rate of return and the actual return will be the same. Actual return Expected return Deviation Squared deviation 6% 8.90% -2.900% 0.000841 5% 8.90% -3.900% 0.001521 11% 8.90% 2.100% 0.000441 14% 8.90% 5.100% 0.002601 -------------------------------------------------------------------------------------------- Total 0.005404 -------------------------------------------------------------------------------------------- variance = 0.005404 / (4-1) = 0.0018 Standard deviation = Sqrt.(0.0018) = 0.0424 or 4.24% Coefficient of variation: mean = [0.06 + 0.05 + 0.11 + 0.14] / 4 = 0.09 Therefore Coefficient of variation = (Standard Deviation / Mean) x 100 = (0.0424 / 0.09) x 100 = 47.11% 2) Average return of common stock-A: Average return = 0.43 / 3 = 0.143 Actual return Average return Deviation Squared deviation 10% 14.30% -4.300% 0.001849 13% 14.30% -1.300% 0.000169 20% 14.30% 5.700% 0.003249 --------------------------------------------------------------------------------------------------- Total 0.005267 --------------------------------------------------------------------------------------------------- variance = 0.005267 / (3-1) = 0.0026335 Standard deviation = Sqrt.(0.0026335) = 0.0513 or 5.13% Average return for common stock-B: Average return = 0.42 / 3 = 0.14 Actual return Average return Deviation Squared deviation 8% 14.00% -6.000% 0.0036 15% 14.00% 1.000% 0.01 19% 14.00% 5.000% 0.0025 ------------------------------------------------------------------------------------------ Total 0.0161 ----------------------------------------------------------------------------------------- variance = 0.0161 / (3-1) = 0.00805 Standard deviation = Sqrt.(0.00805) = 0.0897 or 8.97% based on the standard deviation, Common stock-A is better investment. Coefficient of variation for common stock-A: (Standard deviation / mean) x 100 (0.0513 / 0.143) x 100 35.87% Coefficient of variation for common stock-B: (0.0897 / 0.14) x 100 64.07 Therefore, based on standard deviation and coefficient of variation, common stock -A is the better investment.
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