Question

Suppose you have collected the following historical returns for 2 stocks (Stock A and Stock B). Your task is to summarize the data using the following statistical measures: expected return, variance, standard deviation, covariance, and correlation.

	Stock A	Stock B
2010	0.10	0.07
2009	-0.02	0.01
2008	0.08	-0.03

1. Estimate the expected return for each stock. In a short description, what do these numbers represent? (For the quiz, provide the expected return for Stock A.)

2. Estimate the return variance and standard deviation for each stock. In a short description, what do these numbers represent? (For the quiz, provide the volatility of the returns for Stock A.)

3. Estimate the covariance and correlation between these two stock returns. In words, what do these numbers represent? (For the quiz, provide the correlation between the returns for Stock A and Stock B.)

Answer 1

The required statistical measures are shown below along-with the formula used

Year 2010 2009 2008 Expected Return Variance Standard Deviation Covariance Correlation Stock A 0.1 -0.02 0.08 5.33% 0.004 0.064 0.001 0.268 Stock B 0.07 0.01 -0.03 1.67% 0.003 0.050

Stock A 10.1 Year 2010 2009 2008 Expected Return Variance Standard Deviation Covariance Correlation -0.02 0.08 =AVERAGE(C4:06) =VAR(C4:06) =STDEV(C4:C6) =COVAR(C4:C6,04:D6) =CORREL(C4:06,04:06) Stock B 0.07 0.01 -0.03 =AVERAGE(D4:D6) =VAR(D4:06) =STDEV(D4:06)

Answer to Part-1

The expected return for Stock A is 5.33% where-as that for Stcok B is 1.67%. This implies that based on the annual returns of these two stocks for the last three years, an investor can expect a return of ~5.33% from Stock A and ~1.67% from Stock B. Thus, purely from a return perspective, Stock A is a better investment opportunity

Answer to Part-2

The variance for Stock A is 0.004 and for Stock B is 0.003. Ths standard deviation of returns, which measures the volatility, for Stock A is 0.064 and for Stock B is 0.050.

Based on the alculated variance and standard deviation, it can be concluded that the returns of Stock A are more volatilie than Stock B i.e. the inherent risk in Stock A is higher than Stock B

Answer to Part-3

The covariance is 0.001 and the correlation is 0.268. This implies that there is a mild positive correlation between the returns of these 2 stocks i.e. the returns move in the same direction. However, since the covariance and correlation values are low, the relationship between the two stock returns is not very high