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Advancements in Portfolio Theory

Advancements in Portfolio Theory. Xiaoyang Zhuang Economics 201FS Duke University March 30 , 2010. Is there a benefit to using high-frequency data in making portfolio allocation decisions?. Contents. Literature Review Papers that address the question directly

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Advancements in Portfolio Theory

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  1. Advancements in Portfolio Theory XiaoyangZhuang Economics 201FS Duke University March 30, 2010

  2. Is there a benefit to using high-frequency data in making portfolio allocation decisions?

  3. Contents Literature Review Papers that address the question directly Some fancy-schmancy tools Potential Contributions to the Literature

  4. Fleming, Kirby, and Ostdiek (2003, JFE) The Economic Value of Volatility Timing Using “Realized” Volatility • Setting • min(α) σ2 = αΣtαsubject toαTe = 1, αT = P • Risk-averse investor within a “conditional” mean-variance framework • Four asset classes: stocks, bonds, gold, and cash • Daily rebalancing • Allocation is implemented using futures on the risky assets (makes analysis robust to transaction costs and trading restrictions) • CONCLUSION • Given the daily estimator, an investor would be willing to pay 50-200 bps/year to upgrade to the 5-minute RV/RCov estimator.

  5. Fleming, Kirby, and Ostdiek (2003, JFE) The Economic Value of Volatility Timing Using “Realized” Volatility • Estimators • Covariance Using Daily Returns. • where Ωt-k is a symmetric N x N matrix of weights, and et-k = (Rt-k – ) is an N x 1 vector of daily return innovations. The weights are exponential. • Certain choices of Ωt-k causes the estimate to resemble the estimate generated by a multivariate GARCH model. • Covariance Using 5-Minute Returns. Realized Covariance. • Returns. According to the authors, assuming a constant returns vector is empirically sound.

  6. Fleming, Kirby, and Ostdiek (2003, JFE) The Economic Value of Volatility Timing Using “Realized” Volatility • Measuring Performance Gains • Quadratic Utility Approach • Each day, the investor places some fixed amount of wealth W0 into cash (6%(!!!) risk-free rate assumed) and purchases futures contracts with the same notional value. Her daily utility is • where Rpt is the portfolio‘s return (on day t), γ is the investor’s RRA, and Rf is the risk-free rate. • Define Rp1t and Rp2t as the portfolio’s return using high- and low-frequency estimators, respectively, in making the allocation decision. The (daily) performance gain from using high-frequency estimators is then ∆, such that

  7. Liu (2009, JAE) On Portfolio Optimization: How and When Do We Benefit From High-Frequency Data? • Setting • min(α) σ2 = αΣtαsubject toαTe = 1, αT = P • Risk-averse investor within a “conditional” mean-variance framework • 30 DJIA stocks • Daily rebalancing vs. monthly rebalancing • Allocation is set to track the return of the S&P 500; robust to transaction costs • CONCLUSION • High-frequency performance gains depend on the (1) rebalancing frequency and (2) estimation window: • Monthly Rebalancing and Estimation Window ≥ 12 months →No Gain • Daily Rebalancing or Estimation Window < 6 months → Statistically Significant Gain

  8. Ait-Sahalia, Cacho-Diaz, and Hurd (2008) Portfolio Choice With Jumps: A Closed-Form Solution • Setting • min(α) σ2 = αΣtαsubject toαTe = 1, αT = P • “Conditional” mean-variance (tracking volatility) framework • 30 DJIA stocks • Daily rebalancing vs. monthly rebalancing • Allocation is set to track the return of the S&P 500; robust to transaction costs • CONCLUSION • High-frequency performance gains depend on the (1) rebalancing frequency and (2) estimation window: • Monthly Rebalancing and Estimation Window ≥ 12 months →No Gain • Daily Rebalancing or Estimation Window < 6 months → Statistically Significant Gain

  9. Contributions to the Literature On Portfolio Optimization: How and When Do We Benefit From High-Frequency Data? • Evaluations of different portfolio optimization frameworks • Portfolio Optimization Framework • Mean-Variance • Mean-VaR • Optimal Portfolio Given Jumps (Ait-Sahalia, Cacho-Diaz, and Laeven, 2009) • Variance Measurement. Realized Volatility* vs. Realized Kernel vs. VaR/CVaR? • Covariance Measurement. Blahblahblah. Realized Covariance. • Time Horizon: Use 12-month vs. 6-month historical data • We Could Also Contribute • A More Realistic Scenario. Consider more asset classes and different geographies (e.g. U.S. corporate bonds, European equities, Asian sovereign debt…) • A Performance Comparison Under Market Stress. • A Notion of Liquidity Premia With Backbone. Find an analytical solution for the investor’s required liquidity premium due to his/her inability to rebalance exposure daily.

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