Statistics  |  JUL 1996

An Alpha Indicator for Bonds by Frank Ritchie

Alpha measures the performance of a stock compared with the stock market. Here, the alpha between a cyclical stock group and the Treasury bond market is used as an indicator for trading T-bonds to signal trends. By Frank Ritchie The alphaY“ of a stock has long been used as a tool for portfolio selection. Investors want to know if the market's return was a certain number and, all things being equal, what the stock's return should be. Further, if the stock market was unchanged, would the stock's return be positive or negative? The stock's alpha is the statistic that answers this question. Alpha is derived by linear regression using the one-month return for an individual stock as the dependent variable and the one-month return for a market index (such as the Standard & Poor's 500 index) as the independent variable. IMAGINE THIS To calculate this, first imagine the two sets of returns plotted on a chart with each observation plotted as a dot. The dots would be scattered, but a line could be plotted through the dots that best fits the trend of the dots. This line is called the regression line . All straight lines can be described by the formula Y = a +bX , where a is the y- intercept (the value of y when x is equal to zero) and b is the slope of the line. Returning to our example of analyzing a stock's return, the y -intercept term from the regression is the stock's alpha. Therefore: One-month return (stock) = Alpha + Beta (one-month return for S&P 500)

by Frank Ritchie