Risk Budgeting

1. Risk Budgeting

2. Index • Risk Management Framework • What is Risk Budgeting? • Rationale for Risk Budgeting • SAA Determines Benchmark and Active Management Parameters • Portfolio risk • Strategic v. Active Decisions • Key Inputs for Risk Budgeting • Eight Steps to Risk Budgeting IX. Risk budgeting example X. Allocating risk optimally XI. Conclusion

3. I- Risk Management Framework Risk Management is an ongoing process of: 1. Risk Measurement What is our risk? How do we measure our risk? 2. Risk Attribution Where does our risk come from? Which decisions contributed to risk? 3. Risk Allocation How do we utilize/manage risk going forward? How do we want to allocate risk? When risk is allocated, we go back to step1 Stage I & II are the foundations to Risk Budgeting

4. II- 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

5. III- Rationale for Risk Budgeting • Risk constraints are specified by the Board in the Investment Policy • Need to make optimum use of this available risk in order to maximize return • Some portfolio management strategies use risk more efficiently than others • How do you decide how much risk to allocate to each portfolio strategy/manager?

6. IV- SAA Determines Benchmark and Active Management Parameters Board Prepares Investment Policy Input Input Board/ Investment Committee Middle Office Input Strategic Asset Allocation Prepares Approves + TE Guidelines (Active Limits) Benchmark

7. Active Risk New SAA Expected Return Existing SAA Risk (Volatility) V- Portfolio risk can be deployed in one of two ways: • Move along the efficient frontier • Try and move ahead of the frontier Source: World Bank

8. Strategic Decisions Active Decisions How much active risk (a.k.a. alpha) versus the policy benchmark? How much market or systematic risk (a.k.a. beta) versus liabilities? Main decision Outperform (long/short versus) the benchmark portfolio Investing (long-only) in the benchmark portfolio Implementation Expensive (fees and cost of infrastructure) and skill is critical Cheap (low fees) and does not require much skill Costs Historically, this has been a small part in most institutional portfolios Historically, this has been the dominant source of risk in most institutional portfolios Importance Measurement Measurement: excess return over benchmark Measurement: total return of the benchmark VI- Strategic vs. Active Decisions Source: World Bank

9. Excess return over the benchmark portfolio, Alpha Total return of the benchmark portfolio Volatility of excess return, Tracking Error (TE), Volatility of absolute returns, VI- Strategic vs. Active Decisions 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 Source: World Bank

10. VI- Allocating Risk Between Strategic and Active Decisions: Theory • Institutional investment objective is to maximize wealth of the portfolio subject to overall risk tolerance under certain expectations of Sharpe Ratio for strategic (benchmark) decision and Information Ratio of active management • Given the overall risk budget, the optimal split between strategic and active risks for expected Sharpe Ratio (SR) and Information Ratio (IR) and assuming no correlation between the twois determined by:

11. VI- Allocating Risk Between Strategic and Active Decisions: Reality • Given this framework, if the SR = IR the optimal allocation between strategic and active risks is equal!!! • Then why do most institutions allocate only a small proportion of the total risk to active management? • This implies that most institutions are not very confident of achieving consistent IR, net of fees

12. 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 Source: World Bank

13. VII- Key Inputs for Risk Budgeting • What are we budgeting for? • Active Risk, Total Risk, Surplus Risk… • Time Horizon: • one month is too short, 10 years is too long… • A Measure of Risk: • Tracking Error, Value at Risk, Drawdowns, Surplus at Risk… • A Measure of Opportunities • Information Ratio, Sharpe Ratio, … • Correlation Assumptions

14. VIII- Eight Steps To Risk Budgeting: • Step 1: Determine benchmark. The benchmark determines the neutral point for risks in portfolio. Active views are taken relative to the benchmark • Step 2: Determine investment constraints. Establish explicit limits on portfolio exposures, of the kind “maximum 30% of corporate bonds,” or “the duration deviation from the benchmark should not exceed one year” Source: World Bank

15. VIII- Eight Steps To Risk Budgeting: • Step 3: Determine permissible active investment strategies. Once constraints are known, determine what strategies can be utilized (e.g. currency exposures) • Step 4: Determine maximum amount of tracking error for each strategy. Maximum tracking error (TE) is determined by multiplying average deviation of the particular risk times the estimated volatility of that risk Source: World Bank

16. VIII- Eight Steps To Risk Budgeting: • Step 5: Estimate excess return per unit of risk for each strategy & correlation of excess returns between strategies. The estimation of return per basis point of TE measures how strategy will be going forward • Step 6: Determine target excess return or target TE. Allocation of risk should maximize excess return given target level of risk Source: World Bank

17. VIII- Eight Steps To Risk Budgeting: • Step 7: Determine optimal amount of risk to each strategy. Use mean-variance optimization technique to allocate tracking error to each investment strategy • Step 8: Carefully monitor realized risk characteristics of total portfolio and individual strategies. Correct potential problems by comparing ex ante assumptions with ex post behavior Source: World Bank

18. 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 IX- Risk Budgeting Example Overall/total risk budget set by Board Director of investments delegates risk to portfolio managers Source: World Bank

19. X- Allocating Risk Optimally… The maximization problem can be formulated as: Where w is the vector of (net) portfolio weights, w·α equals the expected (excess) return of the portfolio, and TEmax is the overall risk budget

20. X- Allocating Risk Optimally… • Optimal risk allocation: maximize expected return subject to a constraint on risk • Inputs: • Overall risk budget set by oversight committee • Expected (target) information ratios • Correlation assumptions

21. XI- Conclusion • Active management can produce high risk-adjusted returns while maintaining, or even reducing, total portfolio risk • To allocate or distribute total risk more efficiently, a risk budgeting framework is needed • Practical issues should be considered carefully: • Beware of hidden beta: don’t pay alpha-fees for beta-products • Consider removing constraints on active managers

22. XI-Conclusion • Separate allocation to alpha sources from beta allocation • Consider sourcing alpha from markets that are not in your policy benchmark

23. Case Study & Thank you