Forecasting volatility is fundamental to forecasting parametric models of value-at-risk. The exponentially weighted moving average (EWMA) volatility model is the recommended model for forecasting volatility by the Riskmetrics group. For monthly data, the lambda parameter of the EWMA model is recommended to be set to 0.97. In this study, we empirically investigate if this is the optimal value of lambda in terms of forecasting volatility. Employing monthly realized volatility as the benchmark for testing the value of lambda, it is found that a value of lambda of 0.97 is far from optimal. The tests are robust to a variety of test statistics. It is further found that the optimal value of lambda is time varying and should be based upon recent historical data. The article offers a practical method to increase the reliability and accuracy of value-at-risk forecasts that can be easily implemented within an Excel spreadsheet.
The relation between market risk and asset returns can be modelled with the Security Market Line (SML), a positive linear relation between expected excess asset returns and the asset's β. Pettengill et al. (1995) make the case that tests of β must be conditioned upon excess market returns to obtain meaningful results. This study proceeds from and extends the work of Pettengill et al. (1995), and in the process introduces the notion of the Security Market Plane (SMP). The SMP is a conditional relation between expected excess asset returns, β and realized excess market returns and is derived directly from the market model. Econometric testing on equities traded at the Australian Securities Exchange (ASX) based on a model motivated by the SMP offers strong evidence of the relevance of β to asset returns. The analysis does not reject the hypothesis that factors other than the market portfolio may be relevant to excess portfolio returns.
The maturity effect is re-examined using the S&P 500 futures contract. A model is estimated in which daily volatility, measured on the basis on intraday data, is determined by its previous value and the number of days remaining to maturity. The estimation results do not support the maturity effect. This finding is in line with existing evidence that indicates the absence of the maturity effect in financial futures prices.
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