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

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

9. VI- Strategic vs. Active Decisions
Strategic Decisions
Active Decisions
Total return of the benchmark portfolio
Excess return over the benchmark portfolio, Alpha
Return Measure
Volatility of absolute returns,
Volatility of excess return, Tracking Error (TE),
Risk Measure
Sharpe Ratio (SR), ratio of returns over the risk free rate to volatility of return
Efficiency
Measure
Information Ratio (IR), ratio of excess returns (alpha) to tracking error (TE)
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 two is 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
In reality, due to various constraints, IR decreases when tracking error increases
Therefore, it is important to efficiently allocate risk across different strategies/ managers

12. Strategic Asset Allocation
Risk Budgeting Example
=300 bps
Total Risk Budget
Overall/total risk budget set by Board
TE=157 bps
Active Management
IR=0.40
Strategic Asset Allocation
=255 bps
SR=0.65
=0.2
Director of investments delegates risk to portfolio managers
TE=30 bps
Treasury Active
IR=0.3
TE=76 bps
Currency Active
IR=0.7
TE=63 bps
MBS Active
IR=0.5
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.
Portfolio managers allocate their risk budget to strategies and styles (directional bets, relative value bets, etc), or external 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
IX- Risk Budgeting Example
=300 bps
Total Risk Budget
Overall/total risk budget set by Board
TE=157 bps
Active Management
IR=0.40
Strategic Asset Allocation
=255 bps
SR=0.65
=0.2
Director of investments delegates risk to portfolio managers
TE=30 bps
Treasury Active
IR=0.3
TE=76 bps
Currency Active
IR=0.7
TE=63 bps
MBS Active
IR=0.5
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.
Portfolio managers allocate their risk budget to strategies and styles (directional bets, relative value bets, etc), or external 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
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