To find the fraction of wealth to invest in stock fund that will result in the risky portfolio with minimum variance | |||||
the following formula to determine the weight of stock fund in risky portfolio should be used | |||||
w(*d)= ((Stdev[R(e)])^2-Stdev[R(e)]*Stdev[R(d)]*Corr(Re,Rd))/((Stdev[R(e)])^2+(Stdev[R(d)])^2-Stdev[R(e)]*Stdev[R(d)]*Corr(Re,Rd)) | |||||
Where | |||||
stock fund | E[R(d)]= | 20.00% | |||
bond fund | E[R(e)]= | 9.00% | |||
stock fund | Stdev[R(d)]= | 49.00% | |||
bond fund | Stdev[R(e)]= | 43.00% | |||
Var[R(d)]= | 0.24010 | ||||
Var[R(e)]= | 0.18490 | ||||
T bill | Rf= | 5.90% | |||
Correl | Corr(Re,Rd)= | 0.0721 | |||
Covar | Cov(Re,Rd)= | 0.0152 | |||
stock fund | Therefore W(*d)= | 0.4301 | |||
bond fund | W(*e)=(1-W(*d))= | 0.5699 | |||
Expected return of risky portfolio= | 13.73% | ||||
Risky portfolio std dev (answer Risky portfolio std dev)= | 33.45% | ||||
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) | |||||
0.18=0.059*Proportion invested in Tbill+0.1373*(1-Proportion invested in Tbill) | |||||
Proportion invested in Tbill (answer b-1) = (0.1373-0.18)/(0.1373-0.059) | |||||
=-0.5453 (-54.53%) | |||||
proportion invested in risky portfolio = 1-proportion invested in tbill | |||||
=1.5453 (154.53%) | |||||
Proportion invested in bond fund (answer proportion invested in bond fund) =proportion invested in risky portfolio *weight of bond fund | |||||
=0.8807 (88.07%) | |||||
Proportion invested in stock fund (answer b-2) =proportion invested in risky portfolio *weight of stock fund | |||||
=0.6646 (66.46%) | |||||
std dev of portfolio (answer a) = std of risky portfolio*proportion invested in risky portfolio | |||||
1.5453*0.3345=51.69% |
A pension fund manager is considering three mutual funds. The first is a stock fund, the...
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: Expected Return Standard Deviation Stock fund (S) 20 % 49 % Bond fund (B) 9 % 43 % The correlation between the fund returns is .0721. Suppose now that your portfolio...
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 4.1%. The probability distributions of the risky funds are: Expected Return 11% Stock fund (S) Bond fund (B) Standard Deviation 33% 25% 8% The correlation between the fund returns is 1560. 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 4.9%. The probability distributions of the risky funds are: Expected Return 10% Standard Deviation 39% Stock fund (S) Bond fund (B) 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 4.8%. The probability distributions of the risky funds are: Expected Return 18% Standard Deviation Stock fund (S) Bond fund (B) 38% 98 32% The correlation between the fund returns is .1313. 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 4.9%. 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 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...
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 5.3%. The probability distributions of the risky funds are Expected Return Standard Deviation Stock fund (S) Bond fund (8) 14% 43% 7% 37% The correlation between the fund returns is 0459 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 3.0%. The probability distributions of the risky funds are Expected Return 12% Stock fund (S) Bond fund (B) Standard Deviation 41% 30% 5% The correlation between the fund returns is .0667. 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-teerm government and corporate bond fund, and the third is a T-bill money market fund that yields a sure rate of 5.8 %. The probability distributions of the risky funds are: standard Deviation Expected Return 191 98 Stock fund (8) Bond fund (B) 488 42 The correlation between the fund returns is .0762. Suppose now that your portfolio must yleld an...
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 4.5%. The probability distributions of the risky funds are: Expected Return Standard Deviation Stock fund (S) 15 % 35 % Bond fund (B) 6 % 29 % The correlation between the fund returns is .0517. Suppose now that your portfolio...