Forecastingvolatility of portfolios of indexes
Download
1 / 25

- PowerPoint PPT Presentation


  • 84 Views
  • Updated On :

ForecastingVolatility of Portfolios of Indexes . A Portfolio Management’s Perspective Silverio Foresi Quantitative Strategies Group Goldman Sachs Asset Management. Key Points. Smoother Models, Multivariate Volatility decoupling volatilities from correlations Portfolios Diagnostics

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 '' - mercer


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
Forecastingvolatility of portfolios of indexes l.jpg

ForecastingVolatility of Portfolios of Indexes

A Portfolio Management’s Perspective

Silverio Foresi

Quantitative Strategies Group

Goldman Sachs Asset Management


Key points l.jpg
Key Points

  • Smoother Models, Multivariate Volatility

    • decoupling volatilities from correlations

  • Portfolios Diagnostics

    • optimal portfolios and their problems

    • scatterplot diagnostics

      work with Giorgio De Santis and Adrien Vesval at GSAM


Covariance matrix l.jpg
Covariance Matrix

Returns in excess

of expectations


Portfolio variance l.jpg
Portfolio Variance

  • Variance

  • Variance of portfolio w



Forecasting with smoothers l.jpg
Forecasting with Smoothers

  • Moving averages of n obs

  • Exponential smoothing of n obs

    • P controls “persistence” of vol estimates


Generalized smoothers l.jpg
Generalized Smoothers

  • Vec model (Engle)

    • Very highly parameterized

  • Special cases

    • Baba, Engle, Kroner, and Kraft

    • C = 0, AB appropriate scalars: exp. smoother


Volatilities and correlations l.jpg
Volatilities and Correlations

  • Variance decomposition

  • Constant correlation model (Bollerslev)

    • univariate GARCH for volatilities

    • constant correlations

  • Dynamic correlation (Engle , Engle & Sheppard)

    • univariate GARCH for D

    • time-varying R estimated by exponential smoothing on the residuals of GARCH


Multi decay model l.jpg
Multi-Decay Model

  • Different persistence for volatilities, Pi

  • Common persistence for correlations, Pcor

  • Assembly


Multi decay model 2 l.jpg
Multi-Decay Model (2)

  • Q-MLE: estimates for Pcor, PEQ, PFI, PFX

  • …Pcor = PEQ = PFI = PFX?

  • No

    • Volatilities differ by asset class

      PEQ = 0.65, PFI = 0.66, and PFX= 0.58

    • Correlations move more slowly than volatilities Pcor = 0.97

  • Details: De Santis-Vesval (2001)



Interesting portfolios l.jpg
Interesting Portfolios

  • Mean/Variance

  • Global Minimum Variance

  • Minimum Tracking Error

    ... optimal portfolios depend on estimated covariance matrix


Problem with optimal portfolios l.jpg
Problem with Optimal Portfolios

  • Example: true PEQ is low

    • if one uses low PEQ =Pcor : optimal portfolios change too fast (chasing correlations)

      ... underestimate vol

    • use high PEQ may look better on average

  • Implications

    • it may help decouple correlations from volatilities

    • it may help to have diagnostics based on portfolios independent of estimated covariance


Other interesting portfolios l.jpg
Other Interesting Portfolios

  • Equilibrium

  • Equally weighted

  • Random

    ... do not depend on estimated cov


Experiments l.jpg
Experiments

Pcor = PEQ

  • Simulated Data

    • Random Portfolios, no benchmanrk, sum to 1

  • Real Data:

    • Equity Returns for 18 Country Indexes from 5/5/1983 to 3/29/2002 (4931 daily obs)

      • Random Portfolios, no benchmanrk, sum to 1

      • Optimal Portfolio

        • cash benchmark (zero beta)

        • target TE = 7.5%


Diagnostics smoothing forecasts l.jpg
Diagnostics: Smoothing Forecasts

Consider many portfolios wp(p = 1, 2, ... ,P)

  • Calculate Vart-1(wp’rt) for all t,p

  • Assign portfolios to bins,by forecastedVar

    • average forecasts of all portfolios in every bin

    • average realizations in every bin

      Average out forecast error

  • Diagnostics based on scatterplot

    • realizations vs forecasts

    • vs other characteristics (past e2, corr?)

    • nonlinearities


Slide17 l.jpg

Simulated Data

Random Portfolios


More diagnostics l.jpg
More Diagnostics

Standardized portfolio residuals

Distribution

  • Unconditional

    • is E(e) = 0 and E(e2) = 1?

  • Conditional: can we explain e or e2 -1 with

    • lags of past e and e2? (autocorrelation)

    • sign of past e or e2 -1?


Slide19 l.jpg

Simulated Data

Random Portfolios


Slide20 l.jpg

Simulated Data

Random Portfolios

vol sinusoidal


Slide21 l.jpg

Real Data Random Portfolios

Interesting region


Slide22 l.jpg

Real Data

Min TE Portfolio


Slide23 l.jpg

Real Data

Min TE Portfolio


Back to key points l.jpg
Back to Key Points

  • Decoupling volatilities from correlations

    • Correlations move more slowly than vols

  • Portfolios Diagnostics

    • Random portfolios allow us to average out forecast errors

    • Nonlinearities (scatterplot diagnostics)


Diagnostics for covariance matrix l.jpg
Diagnostics for Covariance Matrix

Use estimated Covariance to standardize residuals

Distribution

  • Unconditional

    • is E(e) = 0 and E(e * e’) = I?

  • Conditional: can we explain e or e2 -1 with

    • lags of past e and e2? (autocorrelation)

    • sign of past e or e2 -1?


ad