This case involves the estimation and analysis of market models based on weekly stock returns for the Procter & Gamble (P&G) and Hewlett-Packard (HP) Corporations, covering two years (104 weeks) from January 2005 to December 2006. Also included are the returns on the Standard and Poor's (S&P) Composite Index, which is based on 500 major U.S. firms and approximates the "market" return. The S&P Index can be interpreted as a portfolio of the component firms. The data for P&G and HP are the same as in Case #2. Note that the returns are expressed as decimal fractions, and represent price changes for a single week.'

Answer the questions below, reporting your (typed) answers first, with supporting computer printouts attached in an appendix. Work should be done individually, not in groups. The case is due on Thursday, May 3 .

The 104 observations for each firm and the S&P Index should be regarded as a sample drawn from a hypothetical population of alternative stock returns that might have occurred during this period. The returns were affected by a multitude of factors, each of which could have taken on a multitude of values. Thus, looking forward from January 1,2005 , a virtually infinite variety of returns were possible. The observed values are one "draw" (sample) from this hypothetical population.

To minimize rounding error, use at least three significant figures. For example, if your computer program returns a variance of 0.0009237156, in your calculations use 0.000924 rather than 0.00092 or 0.0009.

QUESTIONS: Set \(\alpha=0.05\) for all significance tests. For questions #1 through #4, use a computer for calculations. You may use any computer program. The market model is described in section 17.5 of the Keller textbook.

1. Compute the mean, variance, and standard deviation of returns for P&G and \(\mathrm{HP}\) individually; an equally-weighted portfolio of the two stocks; and the S\&P Index. Recall that the standard deviation is a measure of risk and explain the differences in the four standard deviations (hint: focus on the nature of P&G's and HP's product markets).
2. Use regression analysis to estimate the market model for P&G.

1. Conduct a t-test to determine if the statistical evidence supports a relation between P&G returns and the S&P Index returns (i.e., if beta is not zero). Explain your analysis and conclusion.
2. Interpret the regression slope coefficient (beta) in the context of the market model. Conduct a hypothesis test to determine if P&G's volatility, as measured by beta, is different than that of the market.
3. Interpret the coefficient of determination \(\left(R^{2}\right)\) in the context of the market model (systematic and nonsystematic risk).

3. Repeat #2 for HP.

4. Use regression analysis to estimate the market model for an equally-weighted portfolio of P&G and HP.

1. Conduct a hypothesis test to determine if the statistical evidence supports a relation between the portfolio returns and the S&P Index returns. Explain your analysis and conclusion.
2. Interpret the resulting slope coefficient in the context of the market model and compare the portfolio's volatility (beta) to that of P&G and HP.
3. Interpret the coefficient of determination \(\left(\mathrm{R}^{2}\right)\) in the context of the market model (systematic and nonsystematic risk).
4. Compare the portfolio's nonsystematic risk to that of P&G and \(\mathrm{HP}\), and explain the difference. Which of the three assets is more closely related to the market, and why?

5. (a) Compute the betas for P&G , \(\mathrm{HP}\), and the portfolio using each asset's covariance with the market index (show calculations). Use Excel's COV function to get covariances. Compare your results to the regression coefficients from #2, #3, and #4. Note that Excel's covariance functions return the population covariance, not the sample covariance, and make the appropriate adjustment (i.e., so that d.f. \(=n-1\) ).

(b) Compute the variance of the portfolio as a function of P&G and HP variances, per Section 7.3 in the Keller textbook (show calculations). Compare your answer to the portfolio variance calculated in # 1.

Price: $17.21

Solution: The downloadable solution consists of 11 pages, 621 words and 16 charts.
Deliverable: Word Document