Please show all the works. Thanks
To find the fraction of wealth to invest in Stock fund that will result in the risky portfolio with maximum Sharpe ratio | |||||
the following formula to determine the weight of Stock fund in risky portfolio should be used | |||||
w(*d)= ((E[Rd]-Rf)*Var(Re)-(E[Re]-Rf)*Cov(Re,Rd))/((E[Rd]-Rf)*Var(Re)+(E[Re]-Rf)*Var(Rd)-(E[Rd]+E[Re]-2*Rf)*Cov(Re,Rd) | |||||
Where | |||||
Stock fund | E[R(d)]= | 12.00% | |||
Bond fund | E[R(e)]= | 5.00% | |||
Stock fund | Stdev[R(d)]= | 41.00% | |||
Bond fund | Stdev[R(e)]= | 30.00% | |||
Var[R(d)]= | 0.16810 | ||||
Var[R(e)]= | 0.09000 | ||||
T bill | Rf= | 3.00% | |||
Correl | Corr(Re,Rd)= | 0.0667 | |||
Covar | Cov(Re,Rd)= | 0.0082 | |||
Stock fund | Therefore W(*d)= | 0.7515 | |||
Bond fund | W(*e)=(1-W(*d))= | 0.2485 | |||
Expected return of risky portfolio= | 10.26% | ||||
Risky portfolio std dev (answer Risky portfolio std dev)= | 32.18% | ||||
Where | |||||
Var = std dev^2 | |||||
Covariance = Correlation* Std dev (r)*Std dev (d) | |||||
Expected return of the risky portfolio = E[R(d)]*W(*d)+E[R(e)]*W(*e) | |||||
Risky portfolio standard deviation =( w2A*σ2(RA)+w2B*σ2(RB)+2*(wA)*(wB)*Cor(RA,RB)*σ(RA)*σ(RB))^0.5 | |||||
Desired return = tbill return*proportion invested in tbill+risky portfolio return *proportion invested in risky portfolio | |||||
= tbill return*proportion invested in tbill+risky portfolio return *(1-proportion invested in tbill) | |||||
0.09=0.03*Proportion invested in Tbill+0.1026*(1-Proportion invested in Tbill) | |||||
Proportion invested in Tbill (answer b-1) = (0.1026-0.09)/(0.1026-0.03) | |||||
=0.1736 (17.36%) | |||||
proportion invested in risky portfolio = 1-proportion invested in tbill | |||||
=0.8264 (82.64%) | |||||
Proportion invested in Bond fund (answer proportion invested in Bond fund) =proportion invested in risky portfolio *weight of Bond fund | |||||
=0.2053 (20.53%) | |||||
Proportion invested in Stock fund (answer b-2) =proportion invested in risky portfolio *weight of Stock fund | |||||
=0.6211 (62.11%) | |||||
std dev of portfolio (answer a) = std of risky portfolio*proportion invested in risky portfolio | |||||
0.8264*0.3218=26.59% |
Please show all the works. Thanks 7. Award: 10.00 points A pension fund manager is considering...
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A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long-term government and corporate bond fund, and the third is a T-bill money market fund that yields a sure rate of 4.9%. The probability distributions of the risky funds are: Expected Return Standard Deviation Stock fund (S) Bond fund (B) 39% 10% 5% 33% The correlation between the fund returns is .0030. Suppose now that your portfolio must yield an expected...
A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long-term government and corporate bond fund, and the third is a T-bill money market fund that yields a sure rate of 5.9%. The probability distributions of the risky funds are: Stock fund (S) Bond fund (B) Expected Return 20% 9% Standard Deviation 49% 43% The correlation between the fund returns is .0721. Suppose now that your portfolio must yield an expected...
A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long-term government and corporate bond fund, and the third is a T-bill money market fund that yields a sure rate of 4.8%. The probability distributions of the risky funds are: Expected Return Standard Deviation Stock fund (S) 18 % 38 % Bond fund (B) 9 % 32 % The correlation between the fund returns is .1313. Suppose now that your portfolio...