Question

Problem 3-5
Characteristic Line and Security Market Line

You are given the following set of data:

		HISTORICAL RATES OF RETURN
Year		NYSE		Stock X
1		- 26.5%		- 18.0%
2		37.2		18.0
3		23.8		18.5
4		- 7.2		2.0
5		6.6		11.4
6		20.5		15.9
7		30.6		16.0

1. 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.
   Beta =  
   
2. 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.

   		Stock X		NYSE
   Average return,		%		%
   Standard deviation, σ		%		%

   
   
3. Assume 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

Using excel formula to calculate :

	A	B	C
1	Year	Stock X	NYSE
2	1	-26.5%	-18.00%
3	2	37.2%	18.00%
4	3	23.8%	18.50%
5	4	-7.2%	2.00%
6	5	6.60%	11.40%
7	6	20.50%	15.90%
8	7	30.60%	16.00%
a)	Beta	1.6058	Excel formula =SLOPE(B2:B8,C2:C8)
b)	Average Return	12.1429%	9.1143%
	Excel formula	Average(B2:B8)	Average(C2:C8)
	Standard Deviation	22.63%	13.24%
	Excel formula	STDEV.S(B2:B8)	STDEV.S(C2:C8)

c. Risk free rate =(12.1429%-1.6058*9.1143%)/(1-1.6058) =4.12%