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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

Advancements in Portfolio Theory

XiaoyangZhuang

Economics 201FS

Duke University

March 30, 2010

slide3
Contents

Literature Review

Papers that address the question directly

Some fancy-schmancy tools

Potential Contributions to the Literature

slide4
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.
slide5
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.
slide6
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
slide7
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
slide8
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
slide9
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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