Question

Year		NYSE		Stock X
1		- 26.5%		- 21.0%
2		37.2		17.0
3		23.8		20.0
4		- 7.2		4.0
5		6.6		9.2
6		20.5		19.7
7		30.6		17.0

A. Use a spreadsheet (or a calculator with a linear regression function) to determine Stock X's beta coefficient. Round your answer to two decimal places.

b. Determine the arithmetic average rates of return for Stock X and the NYSE over the period given. Calculate the standard deviations of returns for both Stock X and the NYSE. Round your answers to two decimal places.

c. ssume that the situation during Years 1 to 7 is expected to prevail in the future (i.e., , , and both σ_x and b_x in the future will equal their past values). Also assume that Stock X is in equilibrium - that is, it plots on the Security Market Line. What is the risk-free rate? Round your answer to two decimal places.

Answer 1

a]

Beta = Covariance(NYSE,X) / Variance (NYSE)

Covariance and Variance are calculated using COVAR and VAR functions in Excel

Beta = 0.46

b]

Arithmetic average and standard deviation are calculated using AVERAGE and STDEV functions in Excel

c]

Since X is on the SML, the CAPM equation will hold

Let us say the risk free rate is R

Expected return of X= R + (beta * (market return - R))

The expected return of X and market return are taken to be the arithmetic averages calculated earlier

0.0799 = R + (0.46 * (0.1214 - R)

0.0799 = R + 0.0554 - 0.46R

R = 0.0454, or 4.54%