Pension Fund Risk Management Conference

1. Pension Fund Risk Management Conference The Counterintuitive Impact of Constraints on Risk Colm O’Cinneide Quantitative Strategies Deutsche Asset Management November 5, 2006

2. Investment constraints Positives … … Negatives • Protect against a worst-case breakdown in risk controls • Facilitate a dialogue between manager and investor • Facilitate performance evaluation of managers • Facilitate coordination of multiple managers • Often fail in their main goal of containing risk • Neglect the central theme of investing: diversification • Limit hedging opportunities • May force managers towards unreasonable portfolios

3. Constraints aim to control risks – but are they effective? Exposure constraints • Beta neutrality (equity market beta, bond duration) • Risk-index neutrality (value, size, …) • Industry beta neutrality Other • No derivatives • No short-selling • Turnover limits Position constraints • Position limits and investment universe • Gross exposure limits or leverage limits • Active position limits Risk constraints • Total risk limits • Active risk limits • MCR limits

4. The counterintuitive impact on risk Slope of OA: Information ratio of an unconstrained portfolio Slope ofOB: Information ratio with regulatory constraints added Slope ofOC: Information ratio with client constraints added Risk due to regulatoryconstraints Risk due to client constraints alpha B C A Target alpha 150bps Excess risk required to achieve alpha target O 200 bps 300 bps 500 bps tracking error For illustrative purposes only.

5. Constraints for a perfect world • In a perfect world, the only constraint necessary would be a limit on total risk • The investor specifies his/her risk aversion • All other constraints place limits on breadth, i.e., on the manager’s ability to express investment ideas • Despite this, other constraints are often imposed: • some for investment reasons • some for pragmatic reasons

6. Constraints for an imperfect world • Investment motivations for adopting constraints: • They anchor our portfolio to economic and financial principles – e.g., the long-only constraint helps ensure that the equity risk premium is captured • They help control risk in a world where we do not agree on how to measure risk • Pragmatic motivations for adopting constraints: • They facilitate coordinating and evaluating managers • They communicate the investor’s beliefs to the asset manager • They help ensure that any likely losses will be acceptable ex post • These constraints may have unintended consequences and may not serve their intended purposes • Reduce breadth • Limit hedging opportunities • Tie our portfolio to a bad strategy

7. Constraints relative to a benchmark • Constraints often tie a portfolio to a benchmark/index • Constraint on active risk • Constraint on active weights • Constraint on active exposures • But are we confident that the index itself is a good investment? • Indexing has many desirable properties: • Guarantees average returns • Objective and transparent • Low turnover, low costs, and tax-efficient • But there are some serious problems: • Arbitrary index definition, challenges in reconstitution • Compelling empirical evidence of suboptimality of indexing as an investment strategy • The equilibrium-theory justification is based on unrealistic assumptions • Why tie ourselves to such a strategy?

8. Constraints on beta • Investment motivation: • Manager’s relative performance will be due to skill • Ensure there is no hidden leverage – e.g., a portfolio of high-beta Emerging Market stocks may imply more exposure to EM than was intended • Statistical issues: • Beta is difficult to estimate – trade-off between precision and timeliness • Investment issues • Beta is time varying

9. Constraints on beta • Forecasting beta is intrinsically difficult • Cyclical beta • The value premium and time-varying beta • If you can forecast beta, start a hedge fund! • So constraints on beta are of limited effectiveness Don’t expect these to be close Realized beta Beta forecast NEWS “Dogs that didn’t bark” (which matter ex ante but not ex post) …

10. Constraints on volatility – Et tu, Brute? The picture here is the same as for beta • Investment motivation • Express investor’s risk aversion • Statistical issues: • Trade-off between precision and timeliness • Investment issues: • Volatility is driven by unforecastable macroeconomic changes • If you can forecast volatility, start a hedge fund, not a risk management company!

11. Constraints on volatility How can we constrain volatility when it is so hard to forecast? Source: MSCI/Barra and Deutsche Asset Management

12. Typical constraints in an equity portfolio We simulate a US equity portfolio • Universe: S&P 500 • Risk model: Barra, as of June 2006 • Alphas selected at random (simulated) • These constraints: • Long-only • Beta-neutral • Size-neutral What is the impact of each of these constraints?

13. How constraints impact optimal active weights Removing one constraint at a time: Source: MSCI/Barra and Deutsche Asset Management simulations

14. What is driving the large impact of the long-only constraint? Distribution of S&P 500 weights as of 06/30/2006. (Source: BARRA) Number of firms Size (fraction of total capitalization)

15. The impact of constraints on risk and return in equity portfolios • Reduction in breadth • For stocks with small index weights we can only implement positive positions • Example: 90% of all S&P 500 stocks have a weight lower than 50 bps • Theoretically, our Information Ratio drops by 30% • Unintended size (small-cap) bias • Overweights need to be finance by underweights, but as small stocks offer little opportunity for underweighting we eventually need to use large caps: positive small cap bias • Difficulty in outperforming the S&P 500 in times of large-cap outperformance is due to the small cap bias • Impair our ability to hedge stock price risk • Typical risk of a long-short strategy is 8% but long-only risk is more like 16% • A relative-value trade between two small-cap stocks is impossible to implement

16. A step towards removing the short constraint: The mechanics of 130/30 investing Assets Liabilities Cash Invest $100M in S&P 500 stock Client Borrowed stock Raise cash by selling $30M of borrowed stocks Invest $30M in S&P 500 stock Broker +$130M S&P 500 stock - $30M S&P 500 stock Net exposure $100M in S&P 500; market beta of approximately 1 (If we borrow $30M cash – not stock, the beta would be approx. 1.3)

17. Utility loss and leverage Source: MSCI/Barra and Deutsche Asset Management

18. Technical note: Measuring the impact of constraints • The utility is the risk-adjusted return of the portfolio • The impact portfolio is the difference between the constrained optimal and the unconstrained optimal portfolio • The loss in utility due to the constraints is proportional to the variance of this impact portfolio • The impact portfolio is made up of characteristic portfolios of the constraints • Characteristic portfolio: the minimum-variance portfolio having unit exposure to a factor • Example: The characteristic portfolio of beta is the market index • The impact of a constraint is defined as the marginal contribution of its characteristic portfolio to the risk of the impact portfolio • When measured this way, the loss in utility is the sum of the separate impacts across all constraints

19. Conclusions • Constraints may fail to achieve their purpose • Beta and risk are hard to forecast, so hard to constrain ex ante. This in itself is a source of risk • Constraints decreasing investment breadth • Leads to higher risk unless we reduce alpha target • Reduces hedging opportunities • Constraints may increase risk for other reasons • Benchmarks are flawed and constraining that ties us to them also tie us to their flaws • Relaxing constraints offers many benefits from the risk viewpoint • Relax “long-only”: Capture hedging opportunities from short-selling, as well as the value of negative information on firms • Relax “no futures”: Capture tactical asset allocation alpha; portable alpha strategies • Relax “low active risk”: Avoid index inefficiencies and make better use of skill

20. Appendix

21. Important information This presentation is intended only for the exclusive benefit and use of our clients and prospects. This presentation was prepared, in order to illustrate, on a preliminary basis, a specific investment strategy and does not carry any right of publication or disclosure. Neither this presentation nor any of its contents may be used for any other purpose without the prior written consent of Deutsche Asset Management. The information in this presentation reflects prevailing market conditions and our judgement as of this date, which are subject to change. In preparing this presentation, we have relied upon and assumed without independent verification, the accuracy and completeness of all information available from public sources. We consider the information in this update to be accurate, but we do not represent that it is complete or should be relied upon as the sole source of composite performance or suitability for investment. MARS 18387 (08/06)