Indexation to Active Management

1. SEACEN Conference December 4-7, 2007 Siem Reap, Cambodia Indexation to Active Management Nilakanta Venky Venkatesh, CFA Principal Financial Officer Sovereign Investments Partnerships World Bank Treasury nvenkatesh@worldbank.org Tsuyoshi Fukui, CFA Principal Investment Officer Investment Management World Bank Treasury tfukui@worldbank.org

2. Questions to be addressed in this presentation • How does indexation fit in with the SAA process and institutional objectives; • What are the different methods for indexation; • How do you choose the method appropriate for your circumstances; • What is risk budgeting and why is it important; • What are the pre-requisites for moving from indexation to active management; • What are the steps involved in moving from indexation to active management;

3. Key Decisions for Central Bank • SAA and corresponding strategic benchmark • dictates the chosen risk profile versus the market in terms of currency mix, interest rate risk and credit risk • Typically, responsible for approximately 90% of the risk and return of the portfolio. • Portfolio management strategy • passively follow the benchmark, which is known as indexation (or benchmark replication); or • deviate from the benchmark to attempt to achieve a superior return – known as enhanced indexation or active management, and this requires an explicit “stop-loss” limit or risk budget

4. Portfolio Indexation • A passive portfolio management strategy which aims to construct a portfolio whose risk and return replicates (to a large extent) that of the benchmark • Redirects Focus to the Strategic Asset Allocation • indexation enables investors to concentrate on the more important asset allocation decision • an existing misallocation of assets may result in underperformance for the entire portfolio • Therefore indexation facilitates the effective use of limited decision-making resources particularly for central banks, which may have limited investment management resources

5. Advantages of Indexation • Facilitates diversification of the portfolio • Using a combination of different indices may result in a portfolio with lower risk for a given level of return than is available from less diversified portfolios • Lower cost than active management • lower transaction costs associated with lower portfolio turnover rates • Lower infrastructure costs because active management requires: • Staff skilled in investment operations • Comprehensive investment management process • Complex portfolio and risk management systems and processes

6. Indexation Strategies • Full replication • this offers the lowest risk (and lowest expected excess return) versus a benchmark • replicates the benchmark by owning all the securities in the index in the same percentage as the index • Stratified sampling • divides the index into cells • replicates the benchmark with fewer bonds by matching the primary risk factors of the benchmark • Linear programming

7. Stratified Sampling Duration/Maturity 2 Year 2.5 Year 1.5 Year 1 Year Govt’s or AAA ABS/MBS or AA/A Corporates or BBB/B Credit/Sector/Country Match the risk characteristics in each cell (or bucket) with fewer securities

8. Risk Factors

9. Pros and Cons of Stratified Sampling • Advantage of this approach is its simplicity • does not require strong analytical systems, extensive databases, or even strong quantitative expertise • relies on portfolio manager expertise • Disadvantages • Could be labor intensive in stratification • Need to evaluate trade-offs • Need experience in selecting securities • May not achieve the optimal portfolio

10. Optimization Using Linear Programming • More disciplined approach • model driven minimum variance approach to minimize tracking error relative to the benchmark by taking historical correlations into account across risk factors • Has 3 components • An objective function that when maximized, increases the likelihood that the index will closely track the benchmark • A set of constraints that incorporate the target cellular structure of the index • A universe of securities from which a basket of securities can be selected

11. Advantages Creates an optimized portfolio that provides the highest expected return for the same level of risk as the benchmark Disadvantages Computation intensive Portfolio generated may not be intuitive Pros and Cons of Linear Programming

12. Practical Considerations for Indexation • Effectiveness in matching risk factors • Modified Duration • Key Rate Durations • Ease • Liquidity • Transaction costs • Idiosyncratic considerations • Transparency • Indexation instruments • Cash instruments • Derivatives

13. How Many Securities Do You Need? Index can be Replicated by : All the securities in the Benchmark Fewer Securities than the Benchmark One Security in the Benchmark

14. Why Not Buy the Entire Index? …i.e., in the same proportion as the benchmark? If you did, then • Risk would be matched perfectly • However, • Return would be less than the index return due to transaction costs • Transaction costs are due to the Bid/Offer spread • The more illiquid the bond, the higher the spread

15. Could you buy just one security? • Why not? After all…. • Only one security needed to match overall risk (PV01) of the benchmark • However…. • You will be vulnerable to non-parallel shifts in the yield curve • Which security are you going to buy? • How do you decide? • Return of the security chosen may be quite different from the total benchmark return

16. How Many Securities Do You Need? • Trade-off between matching index perfectly and incurring high transaction costs • Select several securities in order to match the risk of the benchmark in each bucket

17. The Five Roads to Indexation • Matching the risk characteristics of the benchmark Different approaches: • I. Duration matching II. Maturity Bucketing III. Duration Bucketing IV. Key Rate Duration Matching V. Principal Component Duration Matching

18. å = i n = w = Portofolio Duration * d D i i B = 1 i å w = subject to 100 % i where w : percent of the market val ue of the portfolio invested in bond i i d : modified duration of bond i i D : Benchmark Duration B Duration Matching • To eliminate interest rate risk through duration matching, the manager invests in a combination of bonds so as to match the duration of the benchmark (can be solved with 1 or 2 bonds): • However, only protects against parallel shifts of the yield curve

19. Duration Bucketing • Improvement on duration matching • To accommodate more-common non-parallel curve shift • Duration bucketing method seeks to maintain the same duration exposure across the yield curve by matching the duration of sub portions of the benchmark: • Requires breaking the benchmark into buckets • Then selecting representative securities in each bucket, to match duration of benchmark • However, does not distinguish between interest rate exposure of different cash flows of a security

20. Maturity Bucketing • Similar to duration bucketing, except that it uses ‘maturity’ rather than ‘duration’ • Suffers from similar weakness as duration bucketing, plus more… • Maturity is not a good measure of interest rate sensitivity of a security

21. What is Key Rate Duration? • A duration measure that calculates effective or empirical duration by changing the market rate for one specific maturity point on the yield curve (aka “key rate”) while holding other points constant • Done as part of a series of calculations that vary the yields for two or more maturity points on the yield curve: • Separately; and • Sequentially Source: Americanbanker.com

22. For Example… • Each of the key rate shocks lies on the parallel shift in the yield curve • The sum of the shifts is equivalent to a parallel shift of the initial yield curve

23. Key Rate Duration Matching • First step is to calculate the key rate durations of the benchmark • Then select securities in the portfolio, to match the exposure at each key rate on the curve • Select those parts of the curve most sensitive to interest-rate changes • The higher the number of key rates used the smaller the tracking error but the higher the number of bonds required • However • ignores correlations between various key-rates • System intensive

24. Principal Component Analysis • Principal components analysis (PCA) is a statistical technique used to extract the risk factors that explain the dynamics of the yield curve: • First step is to estimate the covariance matrix of yield changes • Next step is to specify a factor model explaining how the yield curve (YC) is influenced by the risk factors • Essentially PCA quantifies YC movement in terms of 3 main factors: level, slope and curvature • Indexation becomes a matter of managing exposure to these factors • However • Not intuitive • Computationally intensive

25. Which method should you use? • Depends on: • Index that is being replicated • For example, US Treasury 0 – 1 yr index is best replicated through maturity bucketing, unlike the US Treasury 1 – 3 yr index • Types of replicating instruments • Duration Bucketing works well for short to medium term Government bond indices replicated by bonds without any embedded options (i.e. no callable bonds or structured notes) • Using Key Rate Durations is a logical next step from Duration Bucketing

26. Indexation – Key Messages • SAA can be implemented through indexation • Indexation attempts to match the risk and return characteristics of the benchmark • Various methods that are used match the risk and return to different degrees • Appropriate method depends on the benchmark and the permissible asset classes • Lower cost than active management

27. Active Risk Expected return New SAA Existing SAA () Risk () Portfolio risk can be deployed in one of two ways: • Move along the efficient frontier • Try and move ahead of the frontier

28. What is Risk Budgeting? • Budgeting risk is not different than budgeting time or money • What is budgeted is the total risk we are willing to incur to generate returns (i.e. our risk tolerance) • The way we “spend” this resource is by taking exposure to asset classes and active risk

29. Rationale for Risk Budgeting • Risk constraints are specified by the Board in the Investment Policy • Need to make optimal use of available risk in order to maximize return • Some portfolio managers/ portfolio management strategies use risk more efficiently than others • i.e., generate higher alpha/information ratios • Active management is not scalable • IR decreases when tracking error increases

30. SAA Determines Benchmark and Active Management Parameters Investment Policy Prepares Board Input Strategic Asset Allocation Board/ Investment Committee Approves Analytics Group Prepares Guidelines (Active Limits, Risk Budget) Benchmark

31. Outperform (long/short versus) the benchmark portfolio Investing (long-only) in the benchmark portfolio More expensive (fees and cost of infrastructure) and skill is critical Less expensive (low fees) and requires more basic skills Historically, this has been a small part in most institutional portfolios Historically, this has been the dominant source of risk in most institutional portfolios Measurement: excess return over benchmark Measurement: total return of the benchmark Strategic vs. Active Decisions Active Decisions Strategic Decisions How much active risk (a.k.a. alpha) versus the policy benchmark? How much market or systematic risk (a.k.a. beta) to achieve institutional objectives? Main decision Implementation Costs Importance Measurement

32. Excess return over benchmark portfolio (Alpha) Total return of the benchmark portfolio (Beta) Volatility of excess return, Tracking Error (TE), Volatility of absolute returns, Language of Risk Budgeting Active Decisions Strategic Decisions Return Measure Risk Measure Sharpe Ratio (SR), ratio of returns over the risk free rate to volatility of return Information Ratio (IR), ratio of excess returns (alpha) to tracking error (TE) Efficiency Measure

33. Strategic Asset Allocation Total Risk Budget =300 bps =0.2 Active Management IR=0.40 =255 bps SR=0.65 TE=157 bps Currency Active Treasury Active MBS Active IR=0.3 IR=0.5 IR=0.7 TE=76 bps TE=30 bps TE=63 bps Portfolio managers allocate their risk budget to strategies and styles (directional bets, relative value bets, etc), or external managers Risk Budgeting Example Overall/total risk budget set by Board Director of investments delegates risk to portfolio managers This example uses tracking error as measure of risk. In allocating risk to traders stop-loss limits might be more common and TE figures need to be translated into e.g. value-at-risk or drawdown risk figures.

34. Practical Challenges: • System Issues: risk budgeting system requires separate database/system • Data Issues: Historical data hard to get; Higher data frequency provides better statistics but it also tends to produce higher risk estimates • Time Horizon: Scaling beyond one-period level tends to underestimate risk (markets exhibit momentum, serial correlation and trending)

35. Risk Budgeting – Key Messages • Total risk approved by the Board needs to be used efficiently • Strategic risk is embedded in the benchmark while active risk is limited by the risk budget • Tracking error and information ratio are used to measure the efficient use of risk • Some portfolio managers or investment strategies use risk more efficiently than others • Risk budget should be allocated based on their efficiency in using risk

36. Roadmap for Part II • Differentiating active management from index replication • The Fundamental Law of Active Management • Continuum of active management strategies

37. Benchmark Replication versus Active Management Strategies Benchmark Replication Active Management High risk-adjusted excess return Minimize tracking error Objective Yield Curve Duration Credit Security selection Minimize market risk Minimize transaction cost Security selection Strategies Stop loss Risk limits Compliance Stress test Risk Controls Compliance

38. Framework for Active Portfolio Management Active Return Benchmark Benchmark  SAA (Strategic Asset Allocation) Active  TAA (Tactical Asset Allocation) Risk Prudent active management adds value to the portfolio by enhancing the portfolio’s risk-adjusted return. This is accomplished if the active strategies satisfy certain conditions. What are the conditions?

39. Total Portfolio = Benchmark + Active Strategies • Total portfolio return depends on: • Return of the benchmark • Active (excess) return • Total portfolio risk depends on: Benchmark risk (volatility of returns) Risk of active management (tracking error) Correlation between benchmark risk and active risk

40. Correlation Between Benchmark and Active Risk (1) • Let us assume a portfolio value of $ 1 billion and • Benchmark risk = 3% ; Tracking Error =1% Portfolio risk = 4% = +/- $40 mn Correlation = 1 Portfolio risk = 3.16% = +/- $31.6 mn Correlation = 0 Portfolio risk = 2% = +/- $20 mn Correlation = 1

41. Correlation Between Benchmark and Active Risk (2) • If the overall portfolio risk is important (and not the active risk alone), the correlations between the benchmark risk and active risk are critical. Generally; • Credit sector strategies have low (typically negative) correlation with the US Treasuries; • Enhanced indexing has low correlation with US Treasuries; • Frequent and opposite directional positioning and yield curve trades have low correlation with the benchmark • Continuous duration tilt (systematic risk) has high correlation with the benchmark

42. Risk Management Approach to Portfolio Management • There are several ways to control risk in the portfolio: • On the strategic level: • Probability of negative return •  Benchmark composition and duration • On the tactical level: • Stop loss limit (overall portfolio) – maximum loss relative to • the benchmark • Risk limits (strategies) – maximum loss for an individual trade • or overall strategy •  Trade sizing

43.  Expected alpha forecast can be derived from IR estimation Fundamental Law of Active Management • Number (N) – the number of independent, active decisions available per year (e,g duration, spread, yield curve, etc); Manager’s skill (IC) - measured by the information coefficient, the correlation between forecasts and results; Transfer Coefficient (TC) - denotes the degree of constraints imposed on active management strategies;

44. Fundamental Law of Active Management IR can be improved by : • Remove constraints • Better skill or • Implementing more independent strategies;  But assuming constant skill, IR can be improved by implementing more independent strategies 450 400 IR = 1 350 300 250 IR = 0.5 200 Number (N) 150 100 50 - 0.11 0.23 0.29 0.32 0.41 0.50 0.05 0.08 0.14 0.17 0.20 0.26 0.35 0.38 0.44 0.47 Skill (IC)

45. Improving Information Ratios (IRs) Base Case Removing Constraints Expanding Asset Classes

46. 2 Steps in Improving Information Ratios

47. Continuum of Active Management: Three strategies with different risk adjusted returns • Enhanced Indexing: • Arbitrage / relative value - usually market neutral • Moderate risk strategies (e.g. repo, security selection, credit) •  Moderate risk-adjusted excess returns • Sector Rotation: • Credit diversification and rotation strategies • Governments, Agencies, ABS, MBS •  High risk-adjusted returns • Directional Trading: • Duration, yield curve and FX positions • High volatility of returns •  Returns not guaranteed !

48. Estimates of Value Added of External Managers-by Strategy 1/ Wilshire database of fixed income managers

49. Low to Moderate Risk Portfolio Strategies (Enhanced Indexing) • There are several ways to actively manage the portfolio • without taking huge risks in the portfolio. • Security Selection (Rich-cheap analysis) • Repo (Additional income from Fed funds – repo spread) • Credit products (Incremental return) • Arbitrage (Market neutral) • The risks of these strategies have low correlations with • the benchmark risk.

50. Security Selection This strategy substitutes one Treasury security for another because of some measure of relative valuation – “rich/cheap” analysis The measure of R/C is based on historical difference of actual yield and estimated yield. A bond is considered cheap or rich if a statistical measure based on R/C has an extreme value.