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Stats › Options, shorts and positioning › Variance risk premium

The variance risk premium predicts the index one quarter ahead and no other horizon

Variance risk premium: 6.82%+6.82%Variance riskpremiumLog price earnings: 6.55%+6.55%Log priceearningsPrice dividend ratio: 4.19%+4.19%Price dividendratioConsumption wealth ratio: 4.13%+4.13%Consumptionwealth ratio

Adjusted R squared forecasting quarterly S&P 500 excess returns, January 1990 to December 2007. t statistics 2.86, minus 1.97, insignificant and 1.78. Default spread, term spread and the relative risk-free rate are all insignificant and are not shown.

Implied variance minus realised variance forecasts S&P 500 excess returns at a quarterly horizon with an adjusted R squared of 6.82%, beating the price-earnings ratio. At a monthly horizon the same predictor is not significant.

6.82%Adjusted R squared forecasting quarterly S&P 500 excess returns, t = 2.86
1.07%The same regression at a monthly horizon, t = 1.76
6.55%Adjusted R squared of the log price-earnings ratio at the quarterly horizon
19.74%Combining the two predictors with all controls

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