Beta Management

Résumé du document

The first step of a core-satellite approach is the beta management i.e the strategic asset allocation decision. The goal is to implement a quantitative process for the management of the European equity portion of portfolio. To design the efficient benchmark, we have used the static approach (risk diversification) but also the dynamic approach (risk hedging). To design the strategic benchmark, we minimize the variance under three constraints: no short selling (wi ³ 0), no investment in cash (?wi = 1), no excess of concentration (wi Î [1%;10%]). We estimate the variance-covariance matrix and the average return, which are the inputs, to generate the optimal allocations, which are the outputs of the Markovitz solver.

Extraits

[...] We estimate the variance-covariance matrix thanks to the same methods & the average return thanks to the average mean but also the expected mean of the Capital Asset Pricing Model. For each method, we compare the standard risk and performance indicators between the value-weighted index, the equally-weighted portfolio and the maximum Sharpe Ratio portfolio with reasonable bounds. For each sub-period, we perform a rolling-window analysis with a calibration period of one year .1/ Average mean: Indicators of the first sub-period (1995 2000) Index - E-45 - 2.33 1.64 2.30 1.75 Equally - E-71 - 2.33 1.64 2.45 1.75 Sample - E-44 - 2.33 1.64 2.32 1.77 Constant - E-60 - 2.33 1.64 2.42 1.77 Multi - E-48 - 2.33 1.64 2.35 1.78 Shrinkage - E-49 - 2.33 1.64 2.35 1.77 Single - E-49 - 2.33 1.64 2.34 1.76 Indicator Average return Volatility Sharpe Ratio Skewness Excess Kurtosis JB P-value Gaussian VaR Gaussian VaR mod Cornish-Fisher VaR mod Cornish-Fisher VaR Historical VaR Historical VaR CVaR CVaR - Indicators of the second sub-period (2000 2005) Index - 1E-76 - 2.33 - Equally - 4E-87 - 2.33 - Sample 4E-76 - 2.33 - Constant 3E-71 - 2.33 - Single 9E-76 - 2.33 - Multi 4E-76 - 2.33 - Shrinkage 1E-71 - 2.33 - Indicator Average return Volatility Sharpe Ratio Treynor Ratio Information Ratio Skewness Excess Kurtosis JB P-value Gaussian VaR 7/19 Gaussian VaR mod Cornish-Fisher VaR mod Cornish-Fisher VaR Historical VaR Historical VaR CVaR CVaR - 1.64 2.93 1.57 1.64 2.96 1.56 1.64 2.88 1.55 1.64 2.86 1.55 1.64 2.88 1.55 1.64 2.88 1.55 1.64 2.86 1.55 The maximum Sharpe Ratio portfolios are more efficient than the reference index but also than the equally weighted portfolio because they have more return ( in average vs & 4.58 and less risk ( vs & 25.95 for the second sub-period. [...]

[...] AIR LIQUIDE ALCATEL ALLIANZ (XET) ALLIED IRISH BANKS GENERALI AXA BASF (XET) BAYER (XET) BBV ARGENTARIA BNC.SANTANDER CTL.HISP. BNP PARIBAS CARREFOUR DAIMLERCHRYSLER (XET) DEUTSCHE BANK (XET) DEUTSCHE TELEKOM (XET) E ON (XET) ENDESA ENEL ENI FORTIS (AMS) FRANCE TELECOM DANONE SOCIETE GENERALE IBERDROLA ING GROEP CERTS. L'OREAL LAFARGE LVMH MUNCH.RUCK. (XET) NOKIA PHILIPS ELTN.KON RENAULT REPSOL YPF RWE (XET) SAINT GOBAIN SAN PAOLO IMI SANOFI - AVENTIS SAP (XET) SIEMENS (XET) SUEZ TELECOM ITALIA TELEFONICA TOTAL UNICREDITO ITALIANO UNILEVER CERTS. [...]

[...] Sharpe Ratio Sharpe Ratio Index Equally Sample Constant Multi Shrinkage Single Sharpe Ratio Treynor Ratio Information Ratio 0,0000 -0,0500 -0,1000 -0,1500 The Jarque-Bera statistics is equal to 0 and so the null hypothesis of a normal distribution is rejected. The efficient portfolios have less skewness 0.390 vs. - 0.03 for the first subperiod and 0.04 vs for the second sub-period), which measures the asymmetry of the probability distribution, than the index and also than the equally-weighted portfolio. TO be noted that skewness is only positive on the second sub-period. [...]

[...] The goal is to implement a quantitative process for the management of the European equity portion of portfolio. To design the efficient benchmark, we use the static approach (risk diversification) but also the dynamic approach (risk hedging) / Minimization of variance: To design the strategic benchmark, we minimize the variance under three constraints: no short selling (wi no investment in cash = no excess of concentration (wi We estimate the variance-covariance matrix and the average return, which are the inputs, to generate the optimal allocations, which are the outputs of the Markovitz solver. [...]

[...] Treynor Ratio and information ratio for the second sub-period Sharpe Ratio Treynor Ratio Information Ratio -0,1000 -0,2000 -0,3000 -0,4000 -0,5000 The Jarque-Bera statistics is equal to 0 and so the null hypothesis of a normal distribution is rejected. The efficient portfolios have more positive skewness ( 0.22 vs ) and more excess kurtosis ( 3.31 vs ) than the index and also than the equally-weighted portfolio. Illustration of Skewness and Kurtosis Skewness Excess Kurtosis Index Equally Sample Constant Single Multi Shrinkage Exponentially The efficient portfolios have almost the same historical VaR vs. - for the worst observations) and computing VaR vs. [...]