Return data on three assets A, B, and C. EXPECTEDRETURN Investment Alternatives

Question

Return data on three assets A, B, and C. EXPECTEDRETURN                                     Investment Alternatives Year Asset A Asset B AssetC                      1 100% of asset A 2007    16%     17%      14%                        2   50% of asset A and 50% of asset B 2008    17         16         15                           3    50% of asset A and 50% of asset C 2009     18       15          16                        2010     19        14          17 Calculate the STANDARD DEVIATION OF RETURNS over the 4-year period for each of the three alternatives. Return data on three assets A, B, and C. EXPECTEDRETURN                                     Investment Alternatives Year Asset A Asset B AssetC                      1 100% of asset A 2007    16%     17%      14%                        2   50% of asset A and 50% of asset B 2008    17         16         15                           3    50% of asset A and 50% of asset C 2009     18       15          16                        2010     19        14          17 Calculate the STANDARD DEVIATION OF RETURNS over the 4-year period for each of the three alternatives.

Explanation / Answer

Alternative 1: Year   Return 2007   16 2008   17 2009   18 2010   19 Average return = (16 + 17 + 18 + 19) / 4 = 17.5 Variance of returns = (16 - 17.5)^2 + (17 - 17.5)^2 + (18 - 17.5)^2+ (19 - 17.5)^2 = 5 Std dev of returns = sqrt(5) = 2.236 Alternative 2: Year   Return 2007   16.5 2008   16.5 2009   16.5 2010   16.5 Without calculation, the std dev of returns is 0, since there is novariation in returns. Alternative 3: Year   Return 2007   15 2008   16 2009   17 2010   18 Average return = (15 + 16 + 17 + 18) / 4 = 16.5 Variance of returns = 5 Std dev of returns = sqrt(5) = 2.236

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