Time-Varying Beta Model: HAR-Beta
This study investigates the HAR-Beta model, a framework for estimating time-varying betas in financial returns, contrasting it with the conventional CAPM model, which assumes constant beta. The analysis employs daily, weekly, and monthly realized betas from a dataset of equities including SPY, KO, and others between 2001 and 2009. By calculating and simulating returns over specified time intervals, we explore the efficacy and predictive capability of the HAR-Beta model in capturing market dynamics and enhancing the accuracy of return predictions.
Time-Varying Beta Model: HAR-Beta
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Time-Varying Beta Model: HAR-Beta Kunal Jain Economics 201FS Duke University April 21, 2010
Background • CAPM Model • Ra,t+1= Ba,t*Rm,t • Conventional CAPM model uses a constant beta computed from monthly returns over a 5-year time period. (Banz, Journal of Financial Economics, 1981) • Harvey (1989), Ferson and Harvey (1991,1993), Jagannathan and Wang (1996) all question the notion of a constant beta element • Try different modeling strategies to estimate a time varying beta. • HAR-Beta Model • Calculate Realized Betas over a 1-day, 5-day, and 1-month time interval to build the conditional betas. • t=1 corresponds to daily realized Beta, t=5 corresponds to weekly realized Beta, t=22 corresponds to monthly realized Beta. βt+1 = β0 + αDβt + αWβt-5,t + αMβt-22,t + εt+1
Motivation • Motivation: Test the validity of the HAR-Beta model, using daily, weekly, and monthly realized Betas, to substantiate a time-varying Beta model to estimate daily returns. • Method: • Find mean return from 5 year-daily data • Compute differentials over a specified time interval to find MSE • Calculate Constant Betas from monthly 5-year data • Simulate returns using constant Beta to find MSE over specified time interval • Calculate HAR-Beta Coefficients • Model calculated Beta Coefficients over specified time interval to find predicted Betas. • Simulate returns using time-varying HAR-Beta to find MSE over specified time interval
Data • SPY • January 2, 2001 – January 3, 2009 • KO, PEP, MSFT, BAC, JNJ, WMT, XOM, AMZN, JPM (9 equities) • January 2, 2001 – January 3, 2009 • Calculated Time Interval • January 2, 2001-January 2, 2006 • Simulated Time Interval • January 3, 2006 – January 2, 2008 • Sampling Frequency- 10 minutes • Units – Annualized Standard Deviation
HAR-Beta (KO,SPY) • Calculate HAR-Beta coefficients over calculated time interval (January 2, 2001-January 2, 2006) • Calculate Beta predictions using calculated HAR-Beta coefficients over simulated time interval (January 3, 2006 – January 2, 2008) • Use Beta predictions to calculate expected return and compare with actual return to find differentials. • MSE: .17317 (Annualized Standard Deviation Units)
Future Research • Analysis with more equities • Different Sampling Frequencies • Test HAR-Beta estimates with weekly returns • Specific Literature
