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Advancements in Portfolio Theory

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Advancements in Portfolio Theory

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Advancements in Portfolio Theory

XiaoyangZhuang

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

Some fancy-schmancy tools

Potential Contributions to the Literature

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.

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.

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

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

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

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.