Jonathan J. Reeves

Constant versus Time-Varying Beta Models: Further Forecast Evaluation

Recent advances in the measurement of beta (systematic return risk) and volatility (total return risk), demonstrate substantial advantages in utilizing high frequency return data in a variety of settings. These advances in the measurement of beta and volatility have resulted in improvements in the evaluation of alternate beta and volatility forecasting approaches. In addition, more precise measurement has also led to direct modeling of the time variation of beta and volatility. Both the realized beta and volatility literature have most commonly modeled with an autoregressive process. In this paper we evaluate constant beta models, against autoregressive models of time-varying realized beta. We find that a constant beta model computed from daily returns over the last 12 months generates the most accurate quarterly forecast of beta and dominates the autoregressive time series forecasts. It also dominates (dramatically) the popular Fama-MacBeth constant beta model which uses 5 years of monthly returns.

Optimal modelling frequency for foreign exchange volatility forecasting

For the major foreign exchange rates, it is found that the optimal modelling frequency of volatility is weekly for forecast horizons ranging from 1 week up to 1 month. Autoregressive modelling is based on realized volatility measures computed from 30 min returns.

Betas and the Myth of Market Neutrality

Market neutral funds are commonly advertised as alternative investments that offer returns which are uncorrelated with the broad market. Utilizing recent advances in financial econometrics, we demonstrate that using standard forecasting methods to construct market (beta) neutral funds is often very inaccurate. Our findings demonstrate that the econometric methods that are commonly employed for forecasting the beta (systematic) risk typically lack sufficient accuracy to permit the successful construction of market neutral portfolios. The results in this paper also highlight the need for higher frequency returns data to be utilized more commonly. Using daily returns over the past year, we demonstrate an approach that is easy to implement and delivers a substantial improvement, relative to other methods, when attempting to construct a market neutral portfolio.

Monthly Beta Forecasting with Low, Medium and High Frequency Stock Returns

Generating one-month-ahead systematic (beta) risk forecasts is common place in financial management. This paper evaluates the accuracy of these beta forecasts in three return measurement settings; monthly, daily and 30 minutes. It is found that the popular Fama-MacBeth beta from 5 years of monthly returns generates the most accurate beta forecast among estimators based on monthly returns. A realized beta estimator from daily returns over the prior year, generates the most accurate beta forecast among estimators based on daily returns. A realized beta estimator from 30 minute returns over the prior 2 months, generates the most accurate beta forecast among estimators based on 30 minute returns. In environments where low, medium and high frequency returns are accurately available, beta forecasting with low frequency returns are the least accurate and beta forecasting with high frequency returns are the most accurate. The improvements in precision of the beta forecasts are demonstrated in portfolio optimization for a targeted beta exposure.

Dynamic asset beta measurement

The recent advent of high-frequency data and advances in financial econometrics allow market participants to evaluate the accuracy of different beta (systematic risk) measurements. Benchmarking against the monthly realized beta formed by 30-minute data, we compare the popular Fama--MacBeth betas, the monthly realized betas formed by daily returns and our Hodrick--Prescott filtered betas, with the smoothing parameter, λ, set to 100. We find our filtered betas reduce the measurement error substantially relative to other beta measures. These results enable market participants to measure betas with greater precision and efficiency even with only daily returns in hand.

Forecasting Stock Return Volatility at the Quarterly Frequency: An Evaluation of Time Series Approaches

The last decade has seen substantial advances in the measurement, modelling and forecasting of volatility which has centered around the realized volatility literature. To date, most of the focus has been on the daily and monthly frequencies, with little attention on longer horizons such as the quarterly frequency. In finance applications, forecasts of volatility at horizons such as quarterly are of fundamental importance to asset pricing and risk management. In this article we evaluate models for stock return volatility forecasting at the quarterly frequency. We find that an autoregressive model with one lag of quarterly realized volatility with an in-sample estimation period of between 60 and 80 quarters produces the most accurate forecasts, and dominates other approaches, such as the recently proposed mixed-data sampling (MIDAS) approach.

Monthly Forecasts of Systematic Risk: An Evaluation

Recent advances in covariance and variance estimators coupled with improvements in the quality of intra-day data have made possible more precise measurement of beta (systematic risk). In this paper we examine the forecastability of monthly betas for Dow Jones stocks. The out-of-sample forecasting exercise conducted in our study results in a dramatic reduction of forecast error of beta on average by over 80%, relative to the industry standard of the constant model. This finding has vast implications for all aspects of finance as precise forecasting of the beta parameter is of crucial importance. Presented at the 2007 North Americian Summer Meetings of the Econometric Society at Duke University.

An Analysis on the Predictability of CAPM Beta for Momentum Returns

This paper demonstrates that the forecasted CAPM beta of momentum portfolios explains a large portion of the return, ranging from 40% to 60% for stock level momentum, and 30% to 50% for industry level momentum. Beta forecasts are from a realized beta estimator using daily returns over the prior year. Periods such as 1969 to 1989 have been found in earlier studies to contain abnormal profits from momentum trading,however, we show that these were spuriously generated by measurement error in systematic risk. These results cast further doubt on the ability of standard momentum trading strategies to generate abnormal profits.

Level Shifts in Beta, Spurious Abnormal Returns and the TARP Announcement

Using high frequency data, we develop an event study method to test for level shifts in beta and measure abnormal returns for events that produce such level shifts. Using this method, we estimate abnormal returns for the Troubled Asset Relief Program (TARP) announcement and find that its abnormal returns are largely realized on the first day. The abnormal returns in the remaining post event period, which show up as a drift using standard methodology, are attributed to level shifts in beta.

Targeting Market Neutrality

Neutralizing portfolios from overall market risk is an important part of investment management particularly for hedge funds. In this paper we show an economically significant improvement in the accuracy of targeting market neutrality for equity portfolios. Key features of the approach are the relatively short forecast horizon of one week and forecasting with realized beta estimators computed using high quality, error corrected, intraday returns. We also find that too long and too short estimation windows result in poor beta forecasts and that the optimal length of estimation window depends on the frequency of return observations.