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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



Contents portfolio allocation decisions?

Literature Review

Papers that address the question directly

Some fancy-schmancy tools

Potential Contributions to the Literature


Fleming, Kirby, and portfolio allocation decisions?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.


Fleming, Kirby, and portfolio allocation decisions?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.


Fleming, Kirby, and portfolio allocation decisions?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


Liu (2009, JAE) portfolio allocation decisions?

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


Ait-Sahalia portfolio allocation decisions?, 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


Contributions to the Literature portfolio allocation decisions?

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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