We compare the predictive ability and economic value of implied, realized, and GARCH volatility models for 13 equity indices from 10 countries. Model ranking is similar across countries, but varies with the forecast horizon. At the daily horizon, the Heterogeneous Autoregressive model offers the most accurate predictions, whereas an implied volatility model that corrects for the volatility risk premium is superior at the monthly horizon. Widely used GARCH models have inferior performance in almost all cases considered. All methods perform significantly worse over the 2008-09 crisis period. Finally, implied volatility offers significant improvements against historical methods for international portfolio diversification.
Investors often adopt mean-variance efficient portfolios for achieving superior risk-adjusted returns. However, such portfolios are sensitive to estimation errors, which affect portfolio performance. To understand the impact of estimation errors, I develop simple and intuitive formulas of the squared Sharpe ratio that investors should expect from estimated efficient portfolios. The new formulas show that the expected squared Sharpe ratio is a function of the length of the available data, the number of assets and the maximum attainable Sharpe ratio. My results enable the portfolio manager to assess the value of efficient portfolios as investment vehicles, given the investment environment.
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