Core Portfolio Construction with Stock Market Indices

Transcription

1 EDHEC ETF Summit 2006 November 21st, 2006, Core Portfolio Construction with Stock Market Indices Felix Goltz EDHEC Risk and Asset Management Research Centre EDHEC Institutional Days & ETF Summit 2006

2 Introduction Background: Increasing variety of indices Increasing interest in indexing Use in the core portfolio Quality requirements Global Indexed Assets (US $ trillion) This presentation: 1. Overview and Problem Outline 2. Remedies June 2001 Dec 2001 June 2002 Dec 2002 June 2003 Dec 2003 June 2004 Dec 2004 June 2005 Dec 2005 June 2006 Source: Pensions & Investments. The exact numbers are extracted from surveys of the leading index managers conducted by Pensions & Investments semi-annually during the period of June 2001 to June The data of indexed assets are total worldwide assets under internal indexed mgmt.

3 Introduction A benchmark is a reference portfolio (representative for the risks of the managed portfolio). Choosing a benchmark means fixing objectives in terms of the systematic risk exposure (strategic allocation) of the portfolio and managing risk (tracking error control). If an index is a good benchmark, it should provide - an optimal risk return trade-off (efficiency) - a tool for building optimal allocations (stable risk exposure) Are indices good benchmarks?

4 Outline 1. The Role of Indices - in the finance literature - in the asset management industry 2. Lack of Stability 3. Lack of Efficiency 4. Consequences for Core Portfolio Management and Remedies 5. Conclusions

5 The market portfolio in financial theory Index Construction The literature Capitalisation weighting: w i = N N i= 1 i N P i i P i where is the price of asset i is the quantity of asset i N i P i CAPM: Market portfolio is observable and efficient Roll (1977, JFE) critique: Market portfolio is not observable Empirical tests: Proxies for the (extended) market portfolio are not efficient: e.g. Stambaugh (1982, JFE), Shanken (1985, JFE) Multifactor models: Existence of other priced risk factors (e.g., size, B/M) will impact upon portfolio choice

6 Index Construction The literature Alternatives to Value Weighted Indices Different Weighting Criterion - Ad hoc: Price-, Equal-, Free-float adjusted value-weighted - Fundamental criteria: Dividend Yield, Earnings Growth, etc. - Optimisation: Factor Analysis, Minimum Variance Different Forms of Rebalancing - Buy-and-Hold - Ad hoc - Optimal Rebalancing Some alternatives resemble systematic active strategies. Asset allocation or statistical techniques seem to be more convincing.

7 Index Construction The market Broad Market Indices: European Region Index Dow Jones Euro Stoxx Dow Jones Euro Stoxx 50 Euronext 100 FTSEurofirst 80 FTSEurofirst 100 FTSEurofirst 300 MSCI Europe S&P Europe 350 Covered countries NA No of Components Weighting Free-float Free-float Cap Freefloat Free-float Free-float Free-float Free-float Reconstitution Quarterly Annual Quarterly Annual Annual Quarterly Quarterly Annual Established 12/ / / / / / / Mkt. Share Funds 0.04% 41.66% NA 2.33% 0.26% NA 46.60% 9.11% Mkt. Share Futures NA 99.28% NA 0.64% 0.08% 0 NA NA Notes: The index information is taken from the index providers web sites. The index number and AuM data is the sum of traditional index funds and ETFs, The traditional index funds data are based on the information from the Top 100 AMCs ranked by the IPE (July/August 2005), as of 27/09/2005. The ETF data used for calculation are mainly based on "Porfolio Trading & Index Strategy", Weekly Analysis, Deutsche Bank, 27/09/2005. The data of index futures are calculated according to information from Eurex and Euronext Liffe, as of 27/09/2005. The exchange rate used for calculation is from 27/09/2005. (Free float adjusted) value weighting clearly dominates. Trend towards Fundamental or Strategy Indices (FTSE, Dt. Börse)

8 Empirical Tests Data and Questions Selected indices (October 1995 to September 2005 ) European Country Europe Japan United States FSTE 100 Eurostoxx 50 (Eurozone) Nikkei 225 S&P 500 DAX 30 Eurostoxx 300 (Eurozone) Topix 500 Russell 2000 CAC 40 Stoxx 600 (Eurozone plus other European countries) Dow Jones Industrials Are these indices useful for core portfolios? 1) Stable risk exposure? 2) Efficiency?

9 Style Stability An Example: Dow Jones Dow Jones Industrials: Results of RBSA (36 months rolling window) ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' ' Based on monthly returns data for the period of 10/1995 to 09/2005. MSCI Growth, Value and Small Cap Indices are used in a Sharpe returns-based style analysis. ' ' ' ' ' ' ' ' 100% 80% 60% 40% 20% 0% Small Cap Value Growth Style Exposure

10 Style drift score (SDS) (Idzorek and Bertsch (2004)): where 2 σ k Style Stability Style Drift Scores 3 2 SDS = σ k k = 1 denotes the variance of the style exposure for the k-th style over time Cac 40 DAX 30 FTSE 100 DJ Euro Stoxx 50 DJ Euro Stoxx 300 DJ Stoxx 600 Nikkei 225 Topix 500 S&P 500 Russell 2000 Dow Jones Industrials 30 SDS 4.2% 5.5% 4.2% 4.9% 2.6% 5.5% 17.6% 8.2% 2.3% 11.0% 26.0% Based on monthly returns data for the period of 10/1995 to 09/2005. MSCI Growth, Value and Small Cap Indices are used in a Sharpe returns-based style analysis.

11 Explaining Style Drift Returns Volatility or Index Construction? Style Drift Score (SDS) and Returns Volatility SDS Returns Volatility Rank SDS Rank Volatility Cac % 20.4% 8 3 DAX 30 FTSE % 4.2% 24.7% 13.9% Spearman rank correlation coefficient: DJ Euro Stoxx 50 DJ Euro Stoxx 300 DJ Stoxx 600 Nikkei 225 Topix % 2.6% 5.5% 17.6% 8.2% 20.7% 19.8% 16.8% 18.9% 16.7% rho=0.055 p-value: 44% H 0 : rho = 0 H 1 : rho > 1 S&P % 15.6% Russell % 20.2% 3 4 Dow Jones Industrials % 15.9% 1 9 Based on style weights shown above. Volatilities are based on the monthly returns for the period October 1995 to September 2005.

12 Sector Stability An Example: DAX (Prime All Share) DAX (Prime All Share) Sector Exposure: Based on Sector Capitalisation Weights 100% 90% PRIME SOFTWARE PRIME UTILITIES 80% 70% 60% 50% 40% PRIME TRANSPORT&LOG. PRIME TELECOMM PRIME TECHNOLOGY PRIME RETAIL PRIME PHARMA & HLTC. PRIME MEDIA PRIME INSURANCE 30% 20% PRIME INDUSTRIAL PRIME FOOD & BEV. PRIME FINANCIAL SVS. 10% Style 0% Drift Score based on sector capitalisations 29/09/ /03/ /09/ /03/ /09/ /03/ /09/ /03/ /09/ /03/ /09/ /03/ /09/ /03/ /09/ /03/ /09/ /03/ /09/ /03/ /09/2005 PRIME CONSUMER PRIME CONSTRUCTION PRIME CHEMICALS PRIME RESOURCES PRIME BANKS PRIME AUTOMOBILE Based on monthly capitalisation data for the period of 10/1995 to 09/2005. The broad market indices corresponding to the large cap index are used where sector indices are not available for the narrower large cap index.

13 Sector Stability Sector Drift Scores Sector Drift Score based on sector capitalisations Geographical Zone Germany United Kingdom Eurozone Europe Japan USA Index Prime All Share Index 380 FTSE All Share Index 700 DJ Euro Stoxx 300 DJ Stoxx 600 Topix 1666 S&P 500 Sector Drift Score 10.4% 7.1% 7.2% 6.6% 7.0% 7.3% Based on monthly capitalisation data for the period of 10/1995 to 09/2005. The broad market indices corresponding to the large cap index are used where sector indices are not available for the narrower large cap index. Indices are choices of risk factor exposure - These choices are not stable over time - These choices imply views on expected returns and covariances

14 Efficiency Are Broad Market Indices efficient? We conduct mean variance analysis over two subperiods (10/ /2000 and 10/2000 to 09/2005): Minimise var( R P ) = n n i= 1 j= 1 Under the following conditions: n x i x E( RP ) = xie( Ri ) = E n x i i= 1 = 1 i=1 x i 0, i = 1,..., n where xi denotes the proportion of asset i held in the portfolio; E( Ri ) denotes the expected return of asset i; cov( R, R ) denotes the covariance between asset i and asset j. i j j cov( R, R ) i j Number of components used in our tests Indices CAC 40 DAX 30 FTSE 100 Eurostoxx 50 DJ Euro Stoxx DJ Stoxx 600 Nikkei 225 Topix 500 S&P 500 Russell 2000 Dow Jones 30 Market Index [1] [2] [3] 30 [1] Number of shares on March 31st [2] Number of shares on November 30th [3] Number of shares on October 31st October 1995 September 2000 EW Index 33 to to to to to to to to to to Efficient Frontier

15 Efficiency Broad Market Indices are inefficient 70% 60% Dow Jones 30: 10/ / % Return 40% 30% 20% 10% Efficient Frontier DOW JONES 30 Opti1 Opti2 SharpeMax 0% 0% 5% 10% 15% 20% 25% 30% 35% 40% 45% 50% 70% 60% Russell 2000: 10/ /2000 Volatility 50% Return 40% 30% Efficient Frontier 20% RUSSELL 2000 Opti1 10% Opti2 SharpeMax 0% 0% 5% 10% 15% 20% 25% 30% 35% 40% 45% 50% Risk Volatility

16 Efficiency Broad Market Indices are inefficient Oct Sept Index DOW JONES 30 EUROSTOXX 50 DAX 30 CAC 40 FTSE 100 S&P 500 TOPIX 500 NIKKEI 225 DJ EURO STOXX 300 DJSTOXX 600 RUSSELL 2000 Avg. Rank 1 2 3ex 3ex ex 9 9ex 11 Avg. Rank of Indices We computed the Euclidian distance between each stock market index and the efficient portfolios (optimal portfolio with same return (Opti 1), optimal portfolio with same risk (Opti 2),portfolio with max Sharpe ratio). For each of the three distances, we rank indices from the lowest distance (score1) to the highest distance (score 11) and compute the average of the three scores for each index. The table displays the average rank during the two subperiods.

17 Ranking the indices Efficiency and Stability Ranks Ranks of Indices 11 Russell DJ Euro Stoxx 300 DJ Stoxx Topix 500 Nikkei 225 Efficiency 6 5 S&P 500 FTSE Cac 40 DAX DJ Euro Stoxx 50 Dow Jones Industrials Stability This illustration is based on the results presented above. The rank obtained for the efficiency criterion is indicated on the vertical axis while the rank obtained for style stability is indicated on the horizontal axis. The lines at the centre indicate a rank of 5.5, which corresponds to the average rank among the 11 indices.

18 Asset Allocation Remedying the lack of stable exposure Constructing Completeness Portfolios The returns of a fixed mix R fix, with w fix, k denoting the target weights allocated to asset k: R fix K () t = w R () t k= 1 fix, k k The returns of a cap weighted portfolio R cap, with with w cap, k denoting the cap weights of asset k: R cap K () t = w R () t k = 1 cap, k k The returns of the completeness portfolio, with weights fix, k cap k completene : ss R completeness K () t = ( w fix, k wcap, k ) Rk () t k = 1 w w = w,

19 Asset Allocation Remedying the lack of stable exposure Implementation: Take the w fix. as the mean cap weights over the ten-year period. Alternatives: e.g. set w fix,k = 1/N with N the number of sectors considered. Completeness portfolios are obtained by setting the weights to w completeness. This is a zero investment strategy, i.e K ( w fix, k wcap, k ) = 0 k= 1 8% 6% 4% 2% 0% -2% -4% -6% -8% -10% -12% -14% -16% Completeness portfolio for the S&P CONSUMER DISCRETIONARY CONSUMER STAP LES ENERGY FINANCIALS HEALTH CARE INDUSTRIALS INFO TECHNOLOGY MATERIALS TELECOM SERVICES UTILITIES The graph indicates the sector composition of the completeness portfolio over the entire sample period of 10/1995 to 09/2005. The completeness portfolio was calculated based on data for the monthly observations of the market value of sector indices obtained from Datastream. The industry sectors used are displayed in the legend on the right hand side of the graph

20 Asset Allocation Remedying the lack of stable exposure Stable portfolios versus capitalisation weighted portfolios: Performance statistics Average Return* Max Drawdown Volatility* Downside Risk* Mod. VaR*** Sharpe- Ratio*/** Sortino Ratio*/** Prime All Share 380 (Germany) Stable 11.61% 60.61% 21.14% 15.18% 9.61% Prime All Share 380 (Germany) Cap Wghtd. 8.74% 68.67% 21.44% 15.65% 10.06% FTSE All Share 700 (UK) Stable 11.00% 38.09% 13.74% 11.36% 6.47% FTSE All Share 700 (UK) Cap Weighted 9.17% 42.62% 13.70% 11.09% 6.58% DJ Euro Stoxx 300 (Eurozone) Stable 13.08% 54.66% 19.73% 14.69% 9.15% DJ Euro Stoxx 300 (Eurozone) Cap Wghtd % 59.70% 20.00% 14.70% 9.28% DJ Stoxx 600 (Europe) Stable 11.58% 52.74% 17.10% 12.93% 8.07% DJ Stoxx 600 (Europe) Cap Weighted 10.23% 56.16% 17.10% 12.84% 8.14% Topix 1666 (Japan) Stable 3.46% 47.63% 16.40% 9.37% 7.41% Topix 1666 (Japan) Cap Weighted 1.43% 53.20% 16.82% 9.61% 7.86% S&P 500 (USA) Stable 12.67% 38.31% 15.51% 10.52% 6.92% S&P 500 (USA) Cap Weighted 10.92% 44.66% 15.64% 10.64% 7.18% The table indicates the performance statistics over the entire sample period 10/1995 to 09/2005. Based on the monthly observations for the returns of sector indices obtained from Datastream Thomson Financial. * Annualized statistics are given; ** the risk-free rate and MAR are fixed at 2%; *** non-annualised 5%-quantiles are estimated.

21 Asset Allocation Remedying the lack of efficiency Constructing Global Minimum Variance Portfolios Estimation Risk is a major problem with mean variance analysis We compute the minimum variance portfolio (Chan, Karceski and Lakonishok (1999)) and impose weight constraints (Jagannathan and Ma (2003)). Details: Calibration window: daily return observations for the past year. Every 3 months, we redo the analysis, rolling the sample forward. Maximum Weight for each asset = 20%, No Short Selling, No Lending or Borrowing

22 Asset Allocation Remedying the lack of efficiency Minimum variance portfolios versus capitalisation weighted portfolios: Performance statistics Risk Dimension Risk-Adjusted Performance Average Return* Maximum Drawdown (in %) Volatility (in %)* Downside Risk (in %)* Modified Value-at- Risk (in %)*** Sharpe-Ratio*/** Sortino Ratio*/** Prime All Share 380 (Germany) MinVar 7.15% 49.90% 11.58% 9.05% 1.26% Prime All Share 380 (Germany) Cap Weighted 4.07% 77.34% 23.75% 17.18% 2.45% FTSE All Share 700 (UK) MinVar 8.76% 40.13% 12.82% 10.17% 1.37% FTSE All Share 700 (UK) Cap Weighted 6.56% 50.79% 16.42% 12.16% 1.70% DJ Euro Stoxx 300 (Eurozone) MinVar % 49.62% 15.96% 12.25% 1.65% DJ Euro Stoxx 300 (Eurozone) Cap Weighted 7.71% 68.12% 21.15% 15.64% 2.17% DJ Stoxx 600 (Europe) MinVar 8.46% 48.80% 14.91% 11.53% 1.56% DJ Stoxx 600 (Europe) Cap Weighted 6.93% 63.21% 19.13% 14.18% 1.97% Topix 1666 (Japan) MinVar 1.69% 35.41% 13.67% 9.49% 1.37% Topix 1666 (Japan) Cap Weighted -2.11% 59.28% 19.64% 13.83% 2.04% S&P 500 (USA) MinVar 5.50% 47.63% 14.86% 10.78% 1.50% S&P 500 (USA) Cap Weighted 8.11% 50.78% 18.54% 12.92% 1.85% The table indicates the performance statistics over the out-of-sample period of 10/1996 to 09/2005. Based on the daily observations for the returns of sector indices obtained from Datastream Thomson Financial. No results are available for the period of 10/1995 to 09/1996 since this data was needed for the initial calibration period. * Annualized statistics are given; ** the risk-free rate and MAR are fixed at 2%; *** non-annualised 5%-quantiles are estimated.

23 Asset Allocation Remedying the lack of efficiency Out-of-sample results (10/1996 to 09/2005): Minimum variance vs. cap-weighted portfolios Sharpe Ratio of Minimum Variance Portfolio Sharpe- Ratio of Cap Weighted Index Efficiency Loss (-)/ Gain (+) of cap weighted index Rank S&P 500 (USA) Topix 1666 (Japan) DJ Stoxx 600 (Europe) FTSE All Share 700 (UK) DJ Euro Stoxx 300 (Eurozone) Prime All Share 380 (Germany) The table indicates the performance statistics over the out-of-sample period of 10/1996 to 09/2005. Based on the daily observations for the returns of sector indices obtained from Datastream Thomson Financial. No results are available for the period of 10/1995 to 09/1996 since this data was needed for the initial calibration period. The weight constraints used are: Max weight of 20% for individual assets, no short selling, no borrowing.

24 Conclusions Conclusion: Stock market indices come with numerous problems. Pragmatic solutions exist. These are based on indices for sub-segments of the equity market. Explanation: Broad stock market indices imply an allocation by sub-segments. Sector indices and style indices allow investors to gain control over their asset allocation in the core portfolio.