Advancements in portfolio theory
Download
1 / 12

Advancements in Portfolio Theory - PowerPoint PPT Presentation


  • 69 Views
  • Uploaded on

Advancements in Portfolio Theory. Xiaoyang Zhuang Economics 201FS Duke University March 30, 2010. Contents. Fleming, Kirby, Ostdiek (2003) with our own data A review of their methodology Original results using high-frequency U.S. equities Future Directions.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about ' Advancements in Portfolio Theory' - ismael


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.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
Advancements in portfolio theory

Advancements in Portfolio Theory

XiaoyangZhuang

Economics 201FS

Duke University

March 30, 2010


Contents

Fleming, Kirby, Ostdiek (2003) with our own data

A review of their methodology

Original results using high-frequency U.S. equities

Future Directions


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


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


FKO With Our Own Data

  • Measuring Performance Gains

  • Five stocks: Alcoa (AA), DuPont (DD), Ford (F), JPMorgan Chase (JPM), Wal-Mart (WMT)

  • Target return: 5%

  • Lags for the rolling estimator = 5

  • Decay rates for rolling estimator: [0.030 (daily) 0.060 (RV)]

  • Risk-free rate = 6% (as per FKO)

  • γ = 10

(1)

(2)



Benefits of High-Frequency Data

Statistics: Whole Period (%)

mean(PerfGain) =14.6057

median(PerfGain) = 14.6566

std(PerfGain) = 3.4371

range(PerfGain) = [-22.7854 76.2392]

Statistics: 9/1/2008 – 12/25/2008 (%)

mean(PerfGain) = 15.1245

median(PerfGain) = 15.2262

std(PerfGain) = 8.6467

range(PerfGain) = [-22.7854 44.4357]


Short-Selling

Statistics: RV Estimator (%)

mean(sum(α)) =31.51

median(sum(α)) = 31.27

std(sum(α)) = 7.81

range(sum(α)) = [6.89 68.69]

Statistics: GARCH-y Estimator (%)

mean(sum(α)) = 23.59

median(sum(α)) = 23.32

std(sum(α)) = 109.46

range(sum(α)) = [-2623.40 1078.70]


Short-Selling

Statistics: RV Estimator (%)

mean(sum(α)) =31.51

median(sum(α)) = 31.27

std(sum(α)) = 7.81

range(sum(α)) = [6.89 68.69]

Statistics: GARCH-y Estimator (%)

mean(sum(α)) = 23.59

median(sum(α)) = 23.32

std(sum(α)) = 109.46

range(sum(α)) = [-2623.40 1078.70]


Questions Moving Forward

On Portfolio Optimization: How and When Do We Benefit From High-Frequency Data?

What accounts for the different leverage recommendations between the GARCH-y and multivariate RV measures?

What accounts for the unpredictable performance differences between GARCH-y and multivariate RV measures in periods of market stress?

Compare with Extreme Value Estimators?

How clueless are fund of fund managers?

Are there any benefits of “volatility timing” for fund of fund managers who know the asset class, but not the individual assets, that their fund managers are investing in?


ad