Question

1. When the annualized monthly percentage rates of return for a stock market index were regressed against the returns for ABC and XYZ stocks over the most recent 5-year period, using an ordinary PROBLEMS least squares regression, the following results were obtained: CFA Statistic Alpha Beta R2 Residual standard deviation ABC -3.20% 0.60 0.35 13.02% XYZ 73% 0.97 0.17 21.45% Explain what these regression results tell the analyst about risk-return relationships for each stock over the sample period. Comment on their implications for future risk-return relationships, assuming both stocks were included in a diversified common stock portfolio, especially in view of the following additional data obtained from two brokerage houses, which are based on the most recent two years of weekly returns. Beta of ABC 0.62 0.71 Beta of XYZ 1.45 1.25 Brokerage House

Answer 1

Based on the results of regression, we can establish the following relationship between the risk-return profile of each the stocks. The results have been summarized in the table below. The column under "Linkage" tells you how each of the rows has been calculated / arrived at.

Parameter	Linkage	ABC	XYZ
Alpha		-3.20%	7.30%
Beta		0.60	0.97
R2		0.35	0.17
Residual standard deviation	$\sigma (e_{i})$	13.02%	21.45%
We can derive the equation for returns of the stock in excess of risk free rate, R	R = Alpha + Beta x Rmp	R = -3.20% + 0.60 x Rmp	R = 7.30% + 0.97 x Rmp
Variance of the return	$\sigma^2 =\frac{ \sigma^2 (e_{i})}{1 - R^2}$	0.02608	0.05543
Standard deviation of return	$\sigma = \sqrt{\sigma^2}$	16.15%	23.54%

• Based on the data from brokerage houses, it can be noted that beta for each of the two stocks are higher than what has been predicted by the regression equation.
• Regression has been done on the data for last 5 years, while brokerage house data are based on recent 2 years.
• Upward shift in beta is noted.
• For future risk return relationship, beta based on brokerage house data should be used.
• Systematic risk (as measured by the beta of the stock) is on rise in recent years.