You are given the following set of data: 1. Use a spreadsheet or a calculator wi

Question

You are given the following set of data:

1. Use a spreadsheet or a calculator with a linear regression function to estimate beta. Round your answer to two decimal places.

Beta =

2. Give a verbal interpretation of what the regression line and the beta coefficient show about Stock Y's volatility and relative risk as compared with those of other stocks. Round your answers to the nearest whole.
Stock Y is about________ percent as volatile as the market; thus, its relative risk is about______ percent of that of an average firm.

Explanation / Answer

Historical Rates of Return Year NYSE Stock Y 1 4.00 2.00 2 14.30 21.30 3 19.00 9.00 4 -14.70 -10.00 5 -26.50 -13.50 6 37.20 32.90 7 23.80 5.80 8 -7.20 2.20 9 6.60 16.00 10 20.50 24.40 11 30.60 16.00 SUMMARY OUTPUT Regression Statistics Multiple R 0.856875085 R Square 0.734234911 Adjusted R Square 0.701014275 Standard Error 8.072334027 Observations 10 ANOVA df SS MS F Significance F Regression 1 1440.208387 1440.208 22.10177 0.001538968 Residual 8 521.3006132 65.16258 Total 9 1961.509 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 4.042791904 2.889733612 1.399019 0.199363 -2.620945754 10.70652956 -2.620945754 10.70652956 4 0.614595376 0.130730146 4.701252 0.001539 0.31313112 0.916059632 0.31313112 0.916059632 RESIDUAL OUTPUT Observation Predicted 2 Residuals 1 12.83150578 8.468494218 2 15.72010405 -6.720104049 3 -4.991760123 -5.008239877 4 -12.24398556 -1.25601444 5 26.90573989 5.994260107 6 18.67016185 -12.87016185 7 -0.382294803 2.582294803 8 8.099121386 7.900878614 9 16.64199711 7.758002887 10 22.84941041 -6.849410411 Stock Beta 0.621355816 The regression estimate is that stock Y has a beta of .62 * nyse beta. It is positively correlated, but less volatile. If the scatter points were more spread out, the R-squared of the regression would likely be lower. That would indicate that the NYSE return is not as good a predictor of stock Y return. Since stock Y is more volatile, investors would likely demand a higher risk premium. If the regression line sloped down, then the two assets are negatively correlated. Stock Y's return would be expected to have the opposite sign of nyse return, and would be especially valuable as a diversifier.                                                                                                                    Stock Y is about 62.00% percent as volatile as the market; thus, its relative risk is about 62.00% percent of that of an average firm.

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