Question

In: Finance

You are given the following set of data: HISTORICAL RATES OF RETURN Year      NYSE         Stock X...

You are given the following set of data:

HISTORICAL RATES OF RETURN
Year      NYSE         Stock X
1 - 26.5% - 19.0%
2 37.2    16.0   
3 23.8    15.5   
4 - 7.2    3.0   
5 6.6    9.1   
6 20.5    19.4   
7 30.6    19.5   

The data has been collected in the Microsoft Excel Online file below. Open the spreadsheet and perform the required analysis to answer the questions below.

Open spreadsheet

  1. Use a spreadsheet (or a calculator with a linear regression function) to determine Stock X's beta coefficient. Do not round intermediate calculations. 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. Do not round intermediate calculations. Round your answers to two decimal places.
       NYSE            Stock X        
    Average return, % %
    Standard deviation, σ % %
  3. Assume that the situation during Years 1 to 7 is expected to prevail in the future. Also assume that Stock X is in equilibrium - that is, it plots on the Security Market Line. What is the risk-free rate? Do not round intermediate calculations. Round your answer to two decimal places.

Solutions

Expert Solution

Use a spreadsheet (or a calculator with a linear regression function) to determine Stock X's beta coefficient. Do not round intermediate calculations. Round your answer to two decimal places.

Beta = 0.56

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. Do not round intermediate calculations. Round your answers to two decimal places.

   NYSE            Stock X        
Average return, 12.14% 9.07%
Standard deviation, σ 22.63% 13.72%

Assume that the situation during Years 1 to 7 is expected to prevail in the future. Also assume that Stock X is in equilibrium - that is, it plots on the Security Market Line. What is the risk-free rate? Do not round intermediate calculations. Round your answer to two decimal places.

return of stock X = risk free rate + beta (market rate - risk free rate)

9.07% = risk free rate + 0.56 * (12.14% - risk free rate)

9.07% = risk free rate + 6.83% - 0.56 * risk free rate

Risk free rate = 2.24% / 0.44

Risk free rate = 5.12%


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