Batería de test.

Having established that taking into consideration forward skewness coefficients is important for forecasting macroeconomic variables, we now turn our attention to the stock market. In particular, for horizons of one up to twelve months ahead we

run regressions of the following form: ret+h =αh+β 0 hzt+εt+h,h, (4.15) where ret+h = 12_h

[ret+1+ret+2+...+ret+h] is the annualized h-month excess

return of the CRSP value-weighted index andzt is the vector of predictive variables

for each of the two models considered. The regression analysis covers the period 1996:01-2012:12 and for each forecasting horizon we lose h observations. Under the null of no predictability the overlapping nature of the data imposes an M A(h−1) structure to the error term εt+h,h process. To tackle this problem we base our

statistical inference on both Newey and West (1987) and Hodrick (1992) standard errors with lag length equal to the forecasting horizon. In general, the Hodrick (1992) standard errors tend to be more conservative, especially in long horizons when the null of no predictability is true (Ang and Bekaert, 2007) but have lower statistical power when the null is false (Bollerslev, Marrone, Xu and Zhou, 2012). Motivated by prior literature (see for example, Fama and French, 1988, Campbell and Shiller, 1988a,b, Lamont, 1998 and Goyal and Welch, 2008, among others) we include d- p and e-p as control variables.15 The beta coefficients reported in the subsequent tables have been scaled and can be interpreted as the percentage annualized excess market returns caused by a one standard deviation change in each regressor.

Table 4.11 reports the results for 1-, 3-, 6-, 9- and 12-month forecasting horizons when Newey-West standard errors are used. From the forward variances group,

F V(1) _{is negatively related to future stock market returns but the effect is signif-}

icant only when we consider the augmented model for horizons between six and twelve months ahead. F V(4) exhibits also some forecasting power for future mar- ket returns but only at a short 1-month horizon. Recall, however, that due to the high cross-correlations among forward variances, it is difficult to find strong individ- ual significance for these variables. Therefore, our conclusions are mainly based on the Wald tests of joint significance. From the forward skewness coefficients group,

F SC(3) _{is consistently positively and significantly related to future market returns,}

with the effect being stronger at the 6- and 9-month horizons. Moreover, F SC(4)

exhibits a negative and significant relationship with future market returns at the 3-month horizon. Recall from Section 4.5.1.1 that F SC(3) _{is positively related to}

real activity while F SC(4) is negatively related to real activity. Therefore, there is a consistent pattern for these two forward skewness coefficients with F SC(3) being related to increased economic activity and higher stock market returns and F SC(4)

being related to reduced economic activity and lower stock market returns. Re- garding the control variables, d-p is positively related to future market returns and in line with the literature its effect becomes stronger as the forecasting horizon in- creases. In contrast, e-p does not exhibit any significant relationship with future market returns during our sample period. In economic terms, a one standard de- viation increase in F SC(3) results in an annualized excess market return ranging from 3.373% to 8.244% depending on the forecasting horizon considered. With the exception of the 12-month horizon, similar figures are also observed for F SC(4)_.

Moving to the Wald tests of joint significance, forward variances are jointly significant at the 5% level when the forecasting horizon is six months ahead and at the 10% level when the forecasting horizon is nine months ahead. In contrast, forward skewness coefficients are jointly significant at the 10% level for the 3-month horizon and at the 5% level for both the 6- and the 9-month horizons. Therefore, we find that forward skewness coefficients significantly forecast future market returns over and above forward variances and their effect is stronger than that of forward variances. Furthermore, the adjustedR2 _{of the augmented model is higher than the}

adjusted R2 _{of the simple model for all but the 1-month horizon. Looking at the}

change in adjusted R2 _{across horizons depicted in Figure 4.4, we observe a hump-}

shaped pattern. In particular, the increase in adjusted R2 _{is upward trending for}

short horizons, taking its maximum value at the 4-month horizon and then gradually declining for longer horizons.

dard errors are used, are presented in Table 4.12. In this case, none of the forward variance individual coefficients appears to be significant, while the individual re- sults for forward skewness coefficients are qualitatively similar - and in some cases stronger - to those presented in Table 4.11. Turning to the Wald tests, forward variances are jointly insignificant at all horizons, while forward skewness coefficients remain significant at 10% level only at the 6-month horizon.

Collectively, the empirical results presented in this section indicate that forward skewness coefficients encapsulate important information about future stock market returns that is not embedded in forward variances. Moreover, their effect is stronger for horizons between three and nine months ahead. It should be noted, however, that the joint impact of forward skewness coefficients appears to be limited when the alternative Hodrick standard errors are employed.