1 / 9

Time-Varying Beta Model: HAR-Beta

Time-Varying Beta Model: HAR-Beta. Kunal Jain Economics 201FS Duke University April 21, 2010. Background. CAPM Model R a,t+1 = B a,t *R m,t Conventional CAPM model uses a constant beta computed from monthly returns over a 5-year time period. (Banz, Journal of Financial Economics , 1981)

tbolinger
Download Presentation

Time-Varying Beta Model: HAR-Beta

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  1. Time-Varying Beta Model: HAR-Beta Kunal Jain Economics 201FS Duke University April 21, 2010

  2. 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

  3. 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

  4. 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

  5. Constant Beta

  6. 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)

  7. Mean Squared Error’s

  8. Mean Squared Error’s

  9. Future Research • Analysis with more equities • Different Sampling Frequencies • Test HAR-Beta estimates with weekly returns • Specific Literature

More Related