Investments, tenth edition

  Results from Distribution of Actual Forecasts 

 A study of actual forecasts by Kane, Kim, and White (see footnote 5) found the distribution 

of over 11,000 alpha forecasts for over 600 stocks over 37 months presented in  Figure 27.3 . 

The average forecast precision from this database of forecasts provided an  R -square  of 

.00108 using ordinary least squares (OLS) regressions and .00151 when allowing separate 

coefficients for positive and negative forecasts. These are only marginally better than the 

precision used to interpret the Kane, Marcus, and Trippi study of the distribution of real-

ized information value. Kane, Kim, and White use these  R -squares to adjust the forecasts 

in their database and form optimal portfolios from 105 stocks selected randomly from the 

646 covered by the investment company. 

 Kane, Kim, and White assume that forecast quality is the same each month for all 

alpha forecasts for the 105 stocks, but act as though they do not know that quality. Thus, 

the adjustment process is performed each month by using past forecasts. This introduces 

another source of estimation error that compounds the difficulty of low forecast quality. To 

dull the impact of this real-life difficulty, the estimation of forecast quality adopts improved 

econometric technique. They find that least absolute deviation (LAD) regressions perform 

uniformly better than OLS regressions. The optimization model used both the diagonal 

index model (as in TB) as well as the full-covariance model (the Markowitz algorithm). 

 

The annualized  

M 

-square measures of performance are shown in  

Table  27.6 

. The 

 M -square values, which range from 2.67% to 6.31%, are quite impressive. The results in 

 Table 27.6  also show that using the residual covariance matrix can significantly improve 

performance when many stocks are covered, contrary to the small difference when only six 

stocks are covered, as in Spreadsheet 8.1 of Chapter 8.