Sample Portfolio Problems

### Calculate the covariance of returns in a joint distribution. Given the following equally likely outcomes for two joint variables, A and B.

Instance | Return of | Return of | Ret A - EV(A) | Ret B - EV(B) | (Ret A - EV(A))(Ret B - EV(B)) |
---|---|---|---|---|---|

Security A | Security B | ||||

1 | 0.24 | 0.15 | -0.0025 | -.0.0625 | 0.0000391 |

2 | 0.16 | 0.12 | -0.0825 | -0.0925 | 0.0019078 |

3 | 0.26 | 0.25 | 0.0175 | 0.0375 | 0.0001641 |

4 | 0.31 | 0.33 | 0.0675 | 0.1175 | 0.0019828 |

- | - | - | - | - | - |

EV = | 0.2425 | 0.2125 | covariance = | 0.0040938 |

### Calculate the correlation coefficient, $\rho$, between the returns on two securities A and B if you know the covariance between them to be 24. The variance of security A is 25 and the variance of security B is 36.

##### Recall

(1)\begin{align} \rho=\frac{cov(A,B)}{\sigma_A\times\sigma_B} \end{align}

##### Recall

(2)\begin{align} \sigma=\sqrt{variance} \end{align}

##### Thus

(3)\begin{align} \rho=\frac{24}{\sqrt{25}\times\sqrt{36}}=\frac{24}{5\times6}=0.8 \end{align}

page revision: 2, last edited: 09 Feb 2009 19:15