Question

please provide a breakdown along with equations.

3. You put half of your money in a stock portfolio that has an expected return of 14% and a standard deviation of 24%. You put the rest of you money in a risky bond portfolio that has an expected return of 6% and a standard deviation of 12%. The stock and bond portfolio have a correlation 0.55. The standard deviation of the resulting portfolio will be A. more than 18% but less than 24% B. equal to 18% C. more than 12% but less than 18% D. equal to 12%

Answer 1

5). = [{wA² x A²} + {wB² x B²} + {2 x wA² x wB² x A² x B² x (A,B)}]^1/2

= [{0.5² x 0.24²} + {0.5² x 0.12²} + {2 x 0.5 x 0.5 x 0.24 x 0.12 x 0.55}]^1/2

= [0.0144 + 0.0036 + 0.00792]^1/2 = [0.02592]^1/2 = 0.1610, or 16.10%

Hence, Option "C" is correct.

6). = [{wA² x A²} + {wB² x B²} + {2 x wA² x wB² x A² x B² x (A,B)}]^1/2

= [{0.4² x 0.35²} + {0.6² x 0.15²} + {2 x 0.4 x 0.6 x 0.35 x 0.15 x 0.45}]^1/2

= [0.0196 + 0.0081 + 0.01134]^1/2 = [0.03904]^1/2 = 0.1976, or 19.76%

Hence, Option "B" is correct.

7). According to the CAPM,

rE = rF + beta x [E(rM) - rF]

= 6% + 1.3 x [18% - 6%] = 6% + 15.6% = 21.6%