Estimates of the systematic risks, or betas, of securities may depend importantly on the length of the horizon over which they are calculated—e.g., one month, three months, 12 months, 18 months. Although the betas of neutral stocks (betas close to one) do seem to be invariant to the length of the horizon, the betas of defensive stocks (betas less than one) decline significantly, while those of aggressive stocks (betas greater than one) increase significantly, the longer the horizon.

Furthermore, variations in the length of the horizon will also affect estimates of the reward to volatility performance measure. In general, the longer the assumed horizon, the higher the performance index of both aggressive and defensive stocks. Although the increases tend to be monotonic, so that the performance indexes of any pair of horizons remain highly correlated, still the order of stocks ranked by performance index may change with the horizon. Namely, it may appear that one stock outperforms the other on the basis of monthly data, but that the opposite holds true when annual data are used.

Any comparisons of securities’ systematic risk or performance should thus take into consideration the horizon problem. In particular, brokerage houses and investment services that provide data such as systematic risk should offer an array based on alternative horizons and emphasize that selection of the appropriate data depends on the investor’s own planning horizon.