Consider the following scenario analysis: (LO11-2) Rate of Return Scenario Probability Stocks Bonds Recession 0.20 −5% +14% Normal economy 0.60 +15 +8 Boom 0.20 +25 +4 a. Is it reasonable to assume that Treasury bonds will provide higher returns in recessions than in booms? b. Calculate the expected rate of return and standard deviation for each investment. c. Which investment would you prefer?

a.  Yes.  It is reasonable to assume that Treasury bonds will provide higher returns in recessions than in booms.  In booms, stocks perform better and yield higher rewards.

b. Expected rate of return and Standard Deviation for each investment

                                        Stocks    Bonds

Expected rate of return  0.13%       8.4%

Standard Deviation         0.096%   5.83%

c. I prefer investment in Treasury bonds.  Its expected rate of return of 8.4% is higher than Stock's 0.13%, even with its standard deviation of 5.83%.

Explanation:

a) Data and Calculations:

Rate of Return  Scenario

                          Probability    Stocks    Bonds

Recession             0.20           −5%          14%

Normal economy 0.60            15              8  

Boom                    0.20           25              4  

b) Expected Rate of Return and Standard Deviation for Stocks:

Rate of Return  Scenario

                          Probability    Stocks    Expected     Mean        Squared

                                                                  Rate      Difference  Difference

Recession             0.20           −5%         -0.01%       -0.14%        0.0196%

Normal economy 0.60            15            0.09%       -0.04%       0.0016%  

Boom                    0.20           25          0.05%       -0.08%       0.0064%

Expected rate of return                          0.13%                           0.0276%

Variance of squared differences = 0.0276%/3 = 0.0092%

Standard Deviation = 0.096%

c) Expected Rate of Return and Standard Deviation for Bonds:

Rate of Return  Scenario

                          Probability       Bonds   Expected  Mean           Squared

                                                                  Rate      Difference   Difference            

Recession             0.20                 14%      2.8%        5.6%           31.36%

Normal economy 0.60                   8    4.8%       -3.6%           12.96%

Boom                    0.20                   4   0.8%       -7.6%           57.76%

Total expected rate of return                 8.4%                          102.08%

Variance = mean of squared differences     = 102.08%/3 = 34.03%

Standard Deviation = 5.83%

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