# Fight Finance

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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:

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:

 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?