Should investors include commodities in their portfolios after all? New evidence

1. Should investors include commodities in their portfolios after all? New evidence Charoula Daskalaki1 & George Skiadopoulos1,2,3 1 Dept. of Banking and Financial Management, University of Piraeus 2Financial Options Research Centre, University of Warwick 3Cass Business School, City University October 4, 2011, Inquire Europe Seminar

2. Motivation • Investments in commodities have grown over the last years. • Large literature on the diversification benefits of commodities. However, • Some of the previous papers do not perform a rigorous analysis. • Markowitz mean-variance (MV) setting is employed. • Results are not assessed within a statistical setting. • In-sample analysis. • Financialization of commodities has not been taken into account. • We revisit the common belief that commodities should be included in investors’ “traditional” portfolios. • Should investors mix commodities with cash, stocks & bonds? Daskalaki& Skiadopoulos, Inquire Europe 2011

3. This Paper: Contributions • Rigorous in-sample analysis: Application of MV & non-MV spanning tests • Out-of-sample setting: One-period portfolio choice. • We incorporate higher moments in the asset allocation problem. • We consider alternative ways of investing in commodities. • We use an extended dataset that spans a long period (1989-2009). • We employ a number of robustness tests. • Utility functions, performance measures, commodity indexes, sub-period analysis.

4. Outline • Motivation – This Paper - Contributions. • The Dataset. • In-sample setting: Testing for spanning. • Out-of sample performance of optimal portfolios. • The effect of loss-aversion. • Further robustness tests. • Conclusions. Daskalaki& Skiadopoulos, Inquire Europe 2011

5. The Dataset • Monthly closing prices obtained from Bloomberg (Jan. 1989- Dec. 2009). • Equities: S&P 500 total return index. • Bonds: Barclays U.S. Aggregate Bond Index. • Risk-free asset: Libor one-month. • Commodities: • Commodity Indices: S&P GSCI, DJ-UBS CI. • Individual Futures Contracts: shortest Bloomberg generic series on Cotton, Copper, Crude oil, Gold, Live cattle. Daskalaki& Skiadopoulos, Inquire Europe 2011

6. In-sample analysis: Testing for Spanning Daskalaki& Skiadopoulos, Inquire Europe 2011

7. Testing for spanning: Introduction • Let Rt+1 a vector (K1) of gross returns of the K risky assets and M denote the stochastic discount factor (SDF) • Proposition (DeRoon et al, 1996): The test asset is M-spanned by the benchmark assets iff • Testable hypothesis: Daskalaki& Skiadopoulos, Inquire Europe 2011

8. Testing for spanning: MV & non-MV case • In the MV case, Ms are linear in asset returns (Hansen and Jagannathan, 1991). • MV case: Testable hypothesis • Non-MV case: Testable hypothesis • where is the first derivative of the non-MV utility function- i corresponds to the ith value of the risk aversion coefficient (i=1,2,…,n). Daskalaki& Skiadopoulos, Inquire Europe 2011

9. Testing for spanning: Results • MV case: We find that there is spanning, i.e. commodities should not be included. • Non-MV case: We find that there is no-spanning, i.e. commodities should be included. • Results hold for all utility functions and almost all commodities. Daskalaki& Skiadopoulos, Inquire Europe 2011

10. Testing for spanning: Wald test results Daskalaki& Skiadopoulos, Inquire Europe 2011

11. Optimal portfolio strategies with commodities: Out-of-sample performance Daskalaki& Skiadopoulos, Inquire Europe 2011

12. The asset allocation setting • Direct Utility maximisation by means of Full Scale Optimisation (FSO, Cremers et al., 2005). Daskalaki& Skiadopoulos, Inquire Europe 2011

13. Implementation: Out-of-sample setting • Let the sample of size T monthly observations. • Starting from t=K, use the previous K obs to estimate the optimal weights. • Use these weights and the realized monthly asset returns to calculate the realized portfolio return over [t,t+1]. • Repeat this process, until the end of the sample data is reached. • A series of T-K monthly out-of-sample returns is derived. • To ensure the robustness of the results, we use K=36, 48, 60, 72. Daskalaki& Skiadopoulos, Inquire Europe 2011

14. Performance measures • Sharpe ratio. • Opportunity cost: • Portfolio turnover for a strategy c: Daskalaki& Skiadopoulos, Inquire Europe 2011

15. Performance measures (cont’d): Risk-adjusted metric net of transaction costs • Let NW be the net of transaction costs wealth, pc the proportional transaction cost & RNTC the return net of transaction costs. pc is set equal to 50 bps per transaction for stocks/bonds, 35 bps for commodities and zero for the risk-free asset. Daskalaki& Skiadopoulos, Inquire Europe 2011

16. Portfolio choice (1989-2009): Results • Commodities should not be included in investor’s portfolios. • Gold appears to be an exception. • Compared to a portfolio that consists of only traditional assets, the inclusion of commodities yields a portfolio with • Smaller Sharpe ratio. • Loss in utility terms (negative opportunity cost). • Greater portfolio turnover. • Worse risk-adjusted performance when transaction costs are taken into account. Daskalaki& Skiadopoulos, Inquire Europe 2011

17. FSO Power Utility: Synopsis of Results (1991-2009) Daskalaki& Skiadopoulos, Inquire Europe 2011

18. The effect of Loss Aversion • Disappointment risk aversion (Gul, 1991, Ang et al., 2005, Driessen & Maenhout, 2007): • We set • Results are similar: Commodities should not be included in the optimal portfolio. Daskalaki& Skiadopoulos, Inquire Europe 2011

19. Further robustness tests: MV Analysis • Examine the out-of-sample performance of MV portfolios. • Approximate expected utility using a truncated, second-order Taylor series expansion. • Results: Commodities should not be included. • This extends the MV-spanning results. Daskalaki& Skiadopoulos, Inquire Europe 2011

20. Further robustness tests: The effect of the commodity boom • Divide the sample to two sub-periods based on commodities’ performance and repeat the previous analysis. • 1989–2004: Results are similar to the ones obtained over the full sample period. • 2005- Jun 2008: Results indicate that the investor benefits from the inclusion of commodities. • The results over the recent period should be interpreted with caution! • Commodity booms are rare events (Radetzki, 2006). • The recent commodity boom is one of the longest and broadest boom periods over the last 60 years. Daskalaki& Skiadopoulos, Inquire Europe 2011

21. The effect of the commodity boom Daskalaki& Skiadopoulos, Inquire Europe 2011

22. Some further robustness tests • Repeat the whole analysis for the period August 2007-December 2009. • Results are similar with the exception of gold! • Use enhanced commodity indices. • ‘‘Second generation’’ (or enhanced) commodity indexes: MLCX, DBLCI. • Results: Commodities should not be included. Daskalaki& Skiadopoulos, Inquire Europe 2011

23. Conclusions • Should an investor include commodities in her portfolio? • First, revisited the question in an in-sample statistical setting. • Then, evaluated the out-of-sample performance of optimal portfolios. • Employed various performance measures & robustness tests. • Findings: • In-sample: Commodities should be included only in a non-MV setting. • Out-of-sample: Commodities should not be included. • Results are remarkably robust! • Exceptions: Boom period & Gold. Daskalaki& Skiadopoulos, Inquire Europe 2011

24. Thank you for your attention and time! gskiado@unipi.gr http://web.xrh.unipi.gr/faculty/gskiadopoulos/ www.ssrn.com