Consider the following information on a portfolio of three stocks: |
State of Economy |
Probability
of State of Economy |
Stock A Rate of Return |
Stock B Rate of Return |
Stock C Rate of Return |
Boom | .14 | .05 | .35 | .47 |
Normal | .52 | .13 | .25 | .23 |
Bust | .34 | .19 | –.24 | –.38 |
Required: | |
(a) |
If your portfolio is invested 42 percent each in A and B and 16 percent in C, what is the portfolio’s expected return, the variance, and the standard deviation? (Do not round intermediate calculations. Round your variance answer to 5 decimal places (e.g., 32.16161) and input your other answers as a percentage rounded to 2 decimal places (e.g., 32.16).) |
Expected return | % |
Variance | |
Standard deviation | % |
(b) |
If the expected T-bill rate is 4.4 percent, what is the expected risk premium on the portfolio? (Do not round intermediate calculations. Enter your answer as a percentage rounded to 2 decimal places (e.g., 32.16).) |
Expected risk premium |
% |
A
Expected return in Boom=0.42*0.05+0.42*0.35+0.16*0.47 = 0.2432
Expected return in normal=0.42*0.13+0.42*0.25+0.16*0.23 = 0.1964
Expected return in Bust=0.42*0.19+0.42*-0.24+0.16*-0.38 = -0.0818
portfolio Expected return = Prob. of boom* Expected return in boom+Prob. of Normal* Expected return in Normal+ Prob. of bust* Expected return in bust
=0.14*0.2432+0.52*0.1964+0.34*-0.0818 =0.10836= 10.84 %
Expected Variance= Prob. of boom* (Expected return in boom- Portfolio Expected return)^2+(Prob. of Normal* Expected return in Normal- Portfolio Expected return)^2+ Prob. of bust* (Expected return in bust- Portfolio Expected return)^2
=0.14*(0.2432-0.10836)^2+0.52*(0.1964-0.10836)^2+0.34*(-0.0818-0.10836)^2
=0.018871
Expected Standard Deviation=Variane^1/ = 0.018871^1/2 =0.13737=13.74%
B Expected risk premium = Expected return-Risk free rate= 10.84%-4.4%=6.44%
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