In: Finance
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
Beta =
NYSE | Stock X | |||
Average return, | % | % | ||
Standard deviation, σ | % | % |
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%