4. The risk of a stock can be quantified through simple regression by relating t

Question

4. The risk of a stock can be quantified through simple regression by relating the markets' overall return to the individual stock's return. The slope of the resulting regression equation is then defined as the stock's beta factor and represents a measure of the stock's risk or volatility. The following table shows the quarterly percentage returns for S&P; 500 and Horizon Technology stock for ten quarters. S&P; 500 1.2 -2.5 -3.0 2.0 5.0 1.2 3.0 1.0 0.5 2.5 Horizon -0.7-2.0 5.5 4.71.8 4.1 2.6 2.0 1.3 5.5

Explanation / Answer

b)        The regression equation is:
horizon = 0.275 + 0.950*(S& P 500)

Predictor    Coef    SE Coef     T      P
Constant   0.2747   0.9004    0.31 0.768
S& P       0.9498   0.3569     2.66 0.029

S = 2.66413   R-Sq = 47.0%   R-Sq(adj) = 40.3%

The estimated Beta factor for the stock is 0.950.

The slope of the regression equation suggests that with one unit increase in S&P 500, the change in horizon value.

So it means that with one unit change in S&P 500,the value of horizon changes by value 0.950.

d) The 99% prediction interval for the return on Horizon Technology stock for a quater in which S & P 500 is 4.5% is:

     99% P.I=(-5.776, 14.873)

and the fitted horizon value is 4.549.

The 99% P.I means that when S&P 500 value is 4.5%,the horizon value is expected to lie in the interval (-5.776,14.873) in 99% of the cases.

e) We can see that the R-squared value comes out to be 47% which means that 47% of the total variation in the horizon technology stocks return can be explained by the return on S&P 500.

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