Question

7. Calculating a beta coefficient for a portfolio

Grotesque Power is a public company, and Power Fund is a relatively well-diversified mutual fund. The following two graphs show regressions for the market’s historic realized returns versus historic realized returns on Grotesque Power and Power Fund.

Graph A	Graph B
HISTORIC REALIZED RETURNS 20% -10% / O O 10% 20% HISTORIC REALIZED RETURNS ON THE MARKET (Percent) -10% O -20%

What institution is most accurately represented on graph A?

___Grotesque Power

___Power Fund

Which of the following measures the average return earned by a portfolio, over and above the risk-free rate of return, divided by the standard deviation of the portfolio’s average returns?

___Jensen’s alpha

___Sharpe’s reward-to-variability ratio

___Treynor’s reward-to-volatility ratio

The following table reports some of the regression results for Grotesque Power and Power Fund.

Institution	Regression Coefficient	t-Statistic	Probability of t-Statistic	Lower 95% Confidence Interval	Upper 95% Confidence Interval
Grotesque Power
Intercept	0.00	–0.09	0.93	–0.02	0.02
Slope (beta)	1.66	9.71	0.00	1.32	2.01
Power Fund
Intercept	0.00	0.70	0.49	0.00	0.01
Slope (beta)	1.20	0.00	21.10	1.09	1.32

Which of the following statements are consistent with the data for Grotesque Power? Check all that apply.

___The estimate for the beta for Grotesque Power is precise.

___The probability that the true beta is equal to zero is virtually nonexistent.

___There is a 95% probability that the true beta is between –0.02 and 0.02.

___There is a 95% probability that the true beta is between 1.32 and 2.01.

Answer 1

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Answer:

1. Graph B The partners fund, being a well-diversified mutual fund, should produce returns that closely resemble the returns provided by the market as a whole. Graph B is, therefore, a more accurate representation of the relationship between the market historic returns and that on the partner's fund as it shows a higher correlation between the two. Jensen's alpha Jensen's alpha is a measure of performance of a fund. It measures the return produced by that fund in excess of its expected return calculated based on the capital asset pricing model (CAPM). 3. The correct options are the following: The probability that the true beta is equal to zero is virtually nonexistent: This is because there is a 95% probability that the beta lies between 1.32 and 2.01. There is a 95% probability that the true beta lies between 1.32 and 2.01: This can be observed clearly from the given table.