Question

You must allocate your wealth between two securities. Security 1 offers an expected return of 10% and has a standard deviation of 30%. Security 2 offers an expected return of 15% and has a standard deviation of 50%. The correlation between the returns on these two securities is 0.25.

a. Calculate the expected return and standard deviation for each of the following portfolios, and plot them on a graph:

% Security
1 |
% Security
2 |
E(R) |
Standard
Deviation |

100 | 0 | ||

80 | 20 | ||

60 | 40 | ||

40 | 60 | ||

20 | 80 | ||

0 | 100 | ||

b. Based on your calculations in part (a), which portfolios are efficient and which are inefficient?

c. Suppose that a risk-free investment is available that offers a 4% return. If you must divide your wealth between the risk-free asset and one of the risky portfolios in the preceding table, which risky portfolio would you choose? Why?

d. Repeat your answer to part (c) assuming that the risk-free return is 8% rather than 4%. Can you provide an intuitive explanation for why the optimal risky portfolio changes?

Answer #1

E(R) of a portfolio = w_{1}R_{1} +
w_{2}R_{2} + ...+ w_{n}R_{n}

R_{1} = 10% , R_{1} = 15%

Standard Deviation of a Portfolio =

Cov_{12} = ?_{1}?_{2}Corr_{12} =
0.30 * 0.50 * 0.25 = 0.375

When w_{1} = 100% & w_{2} = 0%

E(R) of a portfolio = w_{1}R_{1} +
w_{2}R_{2} + ...+ w_{n}R_{n}

= (1*0.1) + (0*0.15) = 10%

= ? (1)^{2}(0.3)^{2} +
(0)^{2}(0.5)^{2} + 2(1)(0)(0.375)

= ? 0.09 + 0+ 0

= 30%

Likewise, doing the same method for all the options of portfolios :

% Security
1 |
% Security
2 |
%E(R) |
%Standard
Deviation |

100 | 0 | 10 | 30 |

80 | 20 | 11 | 68.38 |

60 | 40 | 12 | 50.24 |

40 | 60 | 13 | 53.33 |

20 | 80 | 14 | 53.25 |

0 | 100 | 15 | 50 |

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