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Problem 3-5 Characteristic Line and Security Market Line You are given the following set of data: HISTORICAL RATES OF RETURN Year NYSE -26.5% 37.2 23.8 Stock X -21.0% 19.0 15.5 5.0 11.4 19.2 20.0 4 6 7 a. Use a spreadsheet (or a calculator with a linear regression function) to determine Stock Xs beta coefficient. Round your answer to two decimal places 6.6 20.5 30.6 Beta 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. Stock X NYSE Average return,T Avg Standard deviation, σ c. Assume that the situation during Years 1 to 7 is expected to prevail in the future (i.e.,TX = 〒X,Average ,TM = 〒M,Average , and both Ox and bx 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

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Answer #1
Year NYSE Stock X
1 -26.5 -21
2 37.2 19
3 23.8 15.5
4 -7.2 5
5 6.6 11.4
6 20.5 19.2
7 30.6 20
Sum Total 85 69.1
Average Return                          12.14                     9.87
Std Deviation                          20.95                  13.54
Covariance                        262.57
Variance                        438.91
Beta Formula Covariance of X with NYSE / Variance of NYSE
Beta Coefficient                             0.60
Year NYSE Stock X
1 -26.5 -21
2 37.2 19
3 23.8 15.5
4 -7.2 5
5 6.6 11.4
6 20.5 19.2
7 30.6 20
Sum Total =SUM(C4:C10) =SUM(D4:D10)
Average Return =AVERAGE(C4:C10) =AVERAGE(D4:D10)
Std Deviation =STDEV.P(C4:C10) =STDEV.P(D4:D10)
Covariance =COVARIANCE.P(C4:C10,D4:D10)
Variance =VAR.P(C4:C10)
Beta Formula Covariance of X with NYSE / Variance of NYSE
Beta Coefficient =C14/C15
Required return = Risk free rate + Beta ( Market retrun - Risk free rate)
Required return           9.87
Market return         12.14
Beta           0.60
Recalculating the same we derive Rf = 4.31
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