Question

Consider the data in the following table:

Year	2004	2005	2006	2007	2008	2009
Stock A	-10%	20%	5%	-5%	2%	9%
Stock B	21%	7%	30%	-3%	-8%	25%

Use the above information to answer the following questions. Round your answers to four decimal places (i.e. 0.0105).

1. Estimate the average return for stock A.

2. Estimate the average return for stock B.

3. Estimate the volatility of stock A.

4.Estimate the volatility of stock B.

5 .Estimate the correlation between the two stocks.

Answer 1

1) Average return for stock A

=> The formula to calculate the average return = Sum of all returns / Total number of returns

=> Therefore the average return of stock A is 0.0350 or (3.50%)

2) Average return for stock B

=> Therefore the average return of stock B is 0.12 or (12%)

3) Volatility of stock A

=> The formula to calculate standard deviation(volatility):

, where x is the return, is the average of the returns and n is the number of observation

Note: is called the variance, so Standard deviation is the square root of variance

=> Therefore the volatility of stock A = 0.1060 or (10.60%)

Formula used:

4) Volatility of stock B

=> We can calculate the volatility of stock B by the same method

=> Therefore the volatility of stock B = 0.1565 or (15.65%)

5) Correlation between the two stocks

=> The formula to calculate Correlation:

, Where , this is called the covariance

=> We already know the value of deviation of A from its mean, deviation of B from its mean, Standard deviation of Both A and B

=> Therefore the correlation between stock A and stock B = 0.0627

formula used: