Dave owns a stock with a Beta of 1.2. The Beta of Dave\'s stock is based on the

Question

Dave owns a stock with a Beta of 1.2. The Beta of Dave's stock is based on the S&P500 Index as a proxy variable for the market portfolio. Last Thursday the market as measured by the S&P500 Index went up by 1.1%. Dave's stock went down by 0.5% on that day. Dave says that proves that the Beta is wrong because, if the market went up by 1.1%, his stock should have gone up by 1.32% (1.1% x 1.2) and it did not.

Explain to Dave why the Beta of 1.2 for his stock is correct (assume the math is correct) despite the difference in results between the S&P500 and his stock on that day.

Explanation / Answer

Beta is based on regression analysis, finding the best fit curve through the points that represent returns on the S&P 500 (x variable) and the stock (y variable). There is not a perfect correlation, which means that sometimes the movement of his stock will be higher than that predicted by beta and sometimes it will be lower. This was one of the days when it was lower. The beta is the number that minimizes the errors (actually the squares of the errors) between the actual return and the predicted return, that's why it is considered a best fit.

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