The following table shows a sample of historical total returns of shares in two different companies A and B.

Stock Returns | ||

Total effective annual returns | ||

Year | ##r_A## | ##r_B## |

2007 | 0.2 | 0.4 |

2008 | 0.04 | -0.2 |

2009 | -0.1 | -0.3 |

2010 | 0.18 | 0.5 |

What is the historical sample covariance (##\hat{\sigma}_{A,B}##) and correlation (##\rho_{A,B}##) of stock A and B's total effective annual returns?

Two risky stocks A and B comprise an equal-weighted portfolio. The correlation between the stocks' returns is 70%.

If the variance of stock A **increases** but the:

- Prices and expected returns of each stock stays the same,
- Variance of stock B's returns stays the same,
- Correlation of returns between the stocks stays the same.

Which of the following statements is **NOT** correct?

All things remaining equal, the higher the correlation of returns between two stocks:

**Question 559** variance, standard deviation, covariance, correlation

Which of the following statements about standard statistical mathematics notation is **NOT** correct?

The covariance and correlation of two stocks X and Y's annual returns are calculated over a number of years. The units of the returns are in percent per annum ##(\% pa)##.

What are the units of the covariance ##(\sigma_{X,Y})## and correlation ##(\rho_{X,Y})## of returns respectively?

**Hint**: Visit Wikipedia to understand the difference between percentage points ##(\text{pp})## and percent ##(\%)##.

What is the covariance of a variable X with itself?

The cov(X, X) or ##\sigma_{X,X}## equals:

What is the covariance of a variable X with a constant C?

The cov(X, C) or ##\sigma_{X,C}## equals:

**Question 988** variance, covariance, beta, CAPM, risk, no explanation

Price Data Time Series |
|||||||||||

Sourced from Yahoo Finance Historical Price Data | |||||||||||

Date | S&P500 Index (^GSPC) | Apple (AAPL) | |||||||||

Open | High | Low | Close | Adj close | Open | High | Low | Close | Adj close | ||

2007, Wed 3 Jan | 1418 | 1429 | 1408 | 1417 | 1417 | 12.33 | 12.37 | 11.7 | 11.97 | 10.42 | |

2008, Wed 2 Jan | 1468 | 1472 | 1442 | 1447 | 1447 | 28.47 | 28.61 | 27.51 | 27.83 | 24.22 | |

2009, Fri 2 Jan | 903 | 935 | 899 | 932 | 932 | 12.27 | 13.01 | 12.17 | 12.96 | 11.28 | |

2010, Mon 4 Jan | 1117 | 1134 | 1117 | 1133 | 1133 | 30.49 | 30.64 | 30.34 | 30.57 | 26.6 | |

Source: Yahoo Finance. | |||||||||||

Which of the following statements about the above table which is used to calculate Apple's equity beta is **NOT** correct?