A Test of Stone's Two-Index Model of Returns

The purpose of this paper has been to empirically test Stone's Two-Index Model. The results are mixed, but generally favor the model. Adding a bond index term for the bank sample only marginally improves the model's explanatory power although the index is more important than the equity index. The lack of importance of the bond index for banks is not surprising upon further consideration, however. Banks and their earnings should be more sensitive to short-term rather than long-term rates, and the index reflects primarily long-term rates. To the extent that short- and long-term rates moved in different directions during the sample period, negative correlation is introduced between bank's returns and the index.The bond index improves in performance for the 30 Dow Jones firms and contributes to the explanatory power of the model in 80 percent of the cases. There is some instability in signs and, contrary to Stone's speculations, omission of the bond index does not bias the equity beta estimates.Finally, we caution the reader against generalizing about the long-run value of the two-index model. The short time period used here does not allow us to say anything about the relationship between interest rate movements and the stability of beta. Moreover, during the 1969–1972 period the returns on the bond and equity indexes did not behave as Capital Market Theory would predict. The average monthly return on the bond portfolio was .5 percent and the average return on the equity portfolio was .2 percent. Our findings must, therefore, be interpreted with care, but overall the introduction of interest rate effects into the single-index model looks promising.