پیش بینی نسخه بتا میان دوره: ارزیابی

Ever since the inception of betas as a measure of systematic risk, the forecast error in relation to this parameter has been a major concern to both academics and practitioners in finance. In order to reduce forecast error, this paper compares a series of competing models to forecast beta. Realized measures of asset return covariance and variance are computed and applied to forecast beta, following the advances in methodology of Andersen, Bollerslev, Diebold and Wu [Andersen, T. G., Bollerslev, T., Diebold, F. X., & Wu, J. (2005). A framework for exploring the macroeconomic determinants of systematic risk. American Economic Review, 95, 398–404; and Andersen, T. G., Bollerslev, T., Diebold, F. X., & Wu, J. (2006). Realized beta: Persistence and Predictability. In T. Fomby & D. Terrell (Eds.), Advances in Econometrics, vol 20B: Econometric Analysis of Economic and Financial Times Series., JAI Press, 1–40.]. This approach is compared with the constant beta model (the industry standard) and a variant, the random walk model. It is shown that an autoregressive model with two lags produces the lowest or close to the lowest error for quarterly stock beta forecasts. In general, the AR(2) model has a mean absolute forecast error half that of the constant beta model. This reduction in forecast error is a dramatic improvement over the benchmark constant model.

Beta, emanating from the pioneering work of Sharpe (1964) and Lintner (1965), is a foundation stone of modern finance theory, and is a focal point of countless investment and financing decisions. Despite the widespread usage of beta, its effectiveness as a parameter in asset pricing, cash flow evaluation and portfolio management is severely hindered by forecast error, and therefore a high degree of attention is paid to its precise measurement. In this paper we reduce the forecast error by half, relative to the constant model which has been the industry standard for around 40 years. Forecasting betas has puzzled academics and practitioners for decades, as they are recognized to be time-varying in nature (Breen et al., 1989, Ferson, 1989, Keim and Stambaugh, 1986 and Mandelker, 1974). To date, a forecasting technique that can outperform the constant beta model is still lacking. Ghysels (1998) examined various parametric time-varying beta models, including models from Ferson (1989), Ferson and Harvey, 1991 and Ferson and Harvey, 1993 and Ferson and Korajczyk (1995), but showed that these well known models are less accurate than the constant beta model, even though beta is known to be time-varying. The beta of a security represents its sensitivity to movements in the market. The beta of a portfolio is the weighted average of the individual betas of the securities comprising the portfolio. Market players form portfolios with a specific portfolio beta corresponding to their desired purpose, such as tracking portfolios with a beta of one and hedging portfolios with negative betas. Betas also have strong implications in the valuation of cost of capital. Beta forecasting techniques therefore directly benefit portfolio managers and have valuation applications. Wang (2003) emphasizes the importance of having accurate beta forecasts, and Ghysels and Jacquier (2005) stress the crucial importance of good beta forecasts for hedge fund managers who need to neutralize risk factors, or pension fund managers. Beta is generally estimated as a constant parameter, despite the extensive empirical research that suggests that beta is time-varying. The recent advances in non-parametric volatility measurement follow on from the seminal work of French, Schwert, and Stambaugh (1987) and Schwert (1989), and are encapsulated in the recent realized beta measurement framework of Andersen et al., 2005 and Andersen et al., 2006. A realized beta is the ratio of the stock and market return realized covariance to the market realized variance. These non-parametric measures of covariance and variance have recently been heavily documented by people such as Andersen and Bollerslev (1998), Andersen et al., 2000, Andersen et al., 2001 and Andersen et al., 2003 and Barndorff-Nielsen and Shephard, 2001, Barndorff-Nielsen and Shephard, 2002a, Barndorff-Nielsen and Shephard, 2002b and Barndorff-Nielsen and Shephard, 2004. It has been demonstrated that traditional autoregressive time series models, computed on realized variance, outperform popular models such as GARCH (Bollerslev, 1986 and Engle, 1982). These volatility forecasting evaluations were performed by Andersen et al. (2003); Andersen, Bollerslev, Diebold, and Ebens (2001); Maheu and McCurdy (2002); Martens, van Dijk, and de Pooter (2004); Ghysels, Santa-Clara, and Valfanov (2006); and Koopman, Jungbacker and Hol (2005). Our forecast evaluation methodology for betas follows a similar approach to these works, based upon realized measures. In this paper we compute realized betas for the UK stock market, using daily data. Out-of-sample betas are forecasted using the constant, autoregressive and random walk models. Experimentation is conducted with in-sample estimation sizes of 20, 40, 60 and 80 quarters. This leads to a finding that the autoregressive model with two lags, based upon the previous 80 quarterly realized betas, is the dominant model. The results demonstrate dramatic improvements in beta forecasting for firms. On average, the mean absolute error values of the constant beta model forecasts are reduced by approximately one half when using the autoregressive models with a specification containing two lags. For stocks where data is only available for a short period of time, for example only 5 years, the AR(1) model is the most accurate forecaster. This paper is organized as follows: Section 2 describes the sample of UK stocks, Section 3 describes realized beta measurement and Section 4 provides an evaluation of the constant, autoregressive and random walk models for one-quarter-ahead forecasting of beta for a range of in-sample estimation sizes. The final section concludes the study.

The purpose of this paper was to evaluate competing models for beta forecasting over a two decade period. Beta is a central pillar of finance theory, and is used by practitioners, academics and regulators in a wide variety of settings. Whilst sophisticated models have been designed to attempt to outperform the constant beta model, they have failed to capture mainstream support, as they have performed worse than the constant beta model. Thus, the constant model has remained the benchmark model and is in popular usage. However, we find that, in general, an autoregressive model with two lags, estimated on the previous eighty quarters of realized betas, far surpasses the constant beta model. For some stocks the improvement is phenomenal. For example, Boots Group's MSE was reduced by 80.76% when using the AR(2) rather than the most accurate constant beta model. Averaged over 40 companies, the MSE values for the AR(2) model are 63.64% lower than those of the constant beta model. This is a remarkable discovery across all stocks. For stocks where data is available for only a short period of time, for example only 5 years, the AR(1) model is the most accurate forecaster. These findings have fundamental implications for portfolio management, asset pricing, risk management and market regulation. It is hoped that this paper will prompt further research activity across all branches of finance that readdresses issues that were previously examined using a constant beta model.