1. Liability Driven Investment
Chris Nichols, Standard Life Investments
February 2006

2. Agenda Taking only risk that is rewarded and managed
Background / Liability Driven Investment Process
Hedging Strategies
Dynamic Market Risk Allocation
Risk Versus Liabilities
Risk Monitoring
Taking only risk that is rewarded and managed

3. Market Background
Liability Driven Investment Process

4. Traditional pension fund asset management
ALM Study
Manager Selection
Scheme Actuary, Investment Consultants
Investment Consultants
Liabilities
Risk Appetite
Long-term view of Asset returns
Strategic
asset
allocation
Investment
mandates for
each asset class
Alpha management
Traditional process designed to work on a long-term basis: short-term variations in asset values are not critical
This works – AS LONG AS the sponsoring company exists in its current state in perpetuity to support the scheme
This DOES NOT WORK if a significant event happens that crystallises the position when asset values < liabilities
Timescale:
10-20 years
1-3 years
Disconnect between scheme objectives and asset management

5. Results of Strategic Asset Allocation
Deficits caused by falling interest rates and longevity increases
Investment mandates were related to markets not liabilities
So whilst investors beat the benchmark they failed against requirements 80 90
100
110
120
130
140
Jul-99
Jan-00
Jul-00
Jan-01
Jul-01
Jan-02
Jul-02
Jan-03
Jul-03
Jan-04
Jul-04
Jan-05
Benchmark
Benchmark +1%
Liability Growth
There were two main problems
The market risk relative to the liabilities was not being managed
Almost all risk monitoring and control related to stock selection risk
Hence a good solution will ensure
that all market risk is managed in relation to the liabilities
that risk monitoring and controls relate to the key risks
Source: Standard Life Investments
The status-quo for pension fund asset management is open to challenge

6. The focus of investment mandates
Scheme Liabilities
Benchmark risk
Strategic Benchmark
Tactical asset allocation
Stock Selection
Risk budget
Actual risk
Target return 0%
12.5%
Long-term: Real return from asset class allocation
Short-term: ????
1.0% 1.5%
1.0% 2.0%
Traditional mandates do not manage all short-term risk

7. Impact of investment timescales
The excess return from equities over bonds has been 5% per annum over long periods
We would not expect it to be exactly 5% over 3 year intervals
But how often has it been within 2% of this level over 3 year periods?
Answer: less than 25% of the time
The long run excess return expectation will be wrong in 75% of three year periods
Distribution of excess returns from equities over bonds as a function of time horizon
-15%
-10%
-5% 0% 5%
10%
15%
20%
25% 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29
Time Horizon (Years)
Return (%)
Bounds
Outer Deciles
Median
Source: Standard Life Investments, Nov 2004

8. Impact of shorter timescales on return history
As timescales reduce, risk and return expectations vary dramatically
10 years
3 years
Return pa
Risk pa
Risk pa
UK equities
11.1%
10.3%
8.7%
16.4%
UK bonds
9.9%
4.2%
9.4%
6.2%
Overseas equities
9.5%
6.8%
17.8%
Index-linked bonds
8.3%
2.8%
8.0%
4.9%
Property
9.2%
3.7%
9.1%
7.7%
Source: Datastream rolling returns, 31/12/86 – 31/12/04
Shorter timescales have a significant impact on risk and return data
True for all asset classes, not just equity

9. Impact on traditional methodologies
100% equity
100% bonds
A traditional efficient frontier using all available data

10. Impact on traditional methodologies
Source: Datastream 31/12/ /12/2004
The ‘area of possibility’ for a traditional efficient frontier, using 10 year rolling data windows

11. Impact on traditional methodologies
Source: Datastream 31/12/ /12/2004
The ‘area of possibility’ for a 3 year rolling data windows
The efficient frontier breaks down on these timescales

12. Conclusions for portfolio design
Short-term measurements forces investors to be concerned with short-term portfolio returns, relative to the liabilities
Long-term historic return data has little correlation with short-term return data
Traditional methodologies of return optimisation and risk diversification using historical data fall apart on a short-term view
A good solution will therefore ensure
that all market risk is optimally managed in relation to the liabilities
that risk monitoring and controls relate to the key risks
Informed investment view of short-term returns from different areas of market risk required

13. Liability driven process
Scheme Specific Funding Objective
Manager Selection
Scheme Actuary, Investment Consultants
Investment Consultants
Beta management
Liabilities
Risk Appetite
Funding Objective
Investment objective
Risk budget
Alpha strategy
Investment
mandates
Alpha management
Timescale:
3-5 years
Continuum established between liabilities and assets

14. LDI Solution Spectrum MATCHING HEDGING MITIGATING Rationale Approach
Risk Elimination
Risk Management
Comfort Zone
MATCHING
HEDGING
MITIGATING
Rationale
Full matching impossible due to longevity risk
Shares features of traditional methodologies – within comfort zone
Natural first step towards a full liability driven approach
Management processes altered from traditional methodologies
Likely to involve prolonged buyer education process
Approach
Immunisation funds
Duration / Cashflow Matching
Inflation Overlay
Dynamic Market Risk Allocation (DMRA)
RPI+ and libor+ strategies

15. Pragmatism v’s Perfection
Tracking error versus uncertain cashflows
A measure of total investment and non-investment risks in liability benchmark
Possible to devise an investment solution that aims to match out a set of projected liabilities
As well as expensive, it is unnecessary and impractical
Where non-investment risks are included it is not possible to produce an asset management strategy that takes away all risk
Source: Watson Wyatt Ltd (LIABILITY DRIVEN BENCHMARKS FOR UK DEFINED BENEFIT PENSION SCHEMES, 21 June 05)
Avoid an over-engineered solution

16. “Modified Duration” = Interest rate sensitivity
Changes in interest rates are amplified in their effect on Assets and Liabilities
Asset and Liability values often change by different amounts making funding volatile
The rate at which the value changes is measurable and called “Modified Duration”
It is very important to manage the overall modified duration risk versus the liabilities
Much greater impact than performance versus a standard bond benchmark
There are investment strategies to limit the difference between Asset and Liability movements
These strategies reduce the volatility of a scheme’s funding rate
High
Scheme deficit increases if interest rates fall
Value of Scheme Assets
Value of Pension Liabilities
Low
Low
High
Interest Rates
Measuring the impact of interest rate movements

17. Duration Mismatch Example
Assume scheme liabilities are valued using the AA bond yield
Scheme assets invested in FTSE UK Gilts All Stocks
Current AA bond yield is 5%
Present Value (PV) of liabilities = £100m = Asset Value
If yield falls by 1%:
PV of liabilities rises to £115m
Value of scheme assets rise to £107m
Result = Deficit of £8m

18. Traditional bond fund options
Government bond portfolios
Gilt fund duration 7.6
Long bond fund duration 13.4
IL bond fund duration 12.0
Overseas bond fund duration 5.9
Corporate bond portfolios
Corporate bond fund duration 7.7
Long corporate bond fund duration 10.8
Government and corporate bond portfolio
UK Fixed Interest fund duration 7.7
Benchmarks may bear little resemblance to scheme liabilities

19. To whom does this matter most?
Companies where the scheme liabilities are large relative to shareholder funds / the size of the parent company
Where the liabilities are longer dated than in this example
Where a substantial proportion of scheme assets are invested in other asset classes that are insensitive to interest rates
Investing 50% in equities for example would mean the scheme assets would only respond half as much to an interest rate change
The impact could be nearer 15% of the fund

20. Example Liability vs Benchmark Cashflows
Liabilities
Benchmark
Benchmark
Liabilities
Source: CreditDelta, UBS

21. Risk Analysis Risk is decomposed into interest rate and spread risk
Benchmark
Benchmark vs Liabilities
Risk is decomposed into interest rate and spread risk
Desire to remove interest rate curve risk
Source: CreditDelta, UBS

22. Sensitivity to Swap Curve Changes
LDD1 at given tenor point indicates change in value for +1bp shift in rate
Indicates liabilities are longer duration
Source: CreditDelta, UBS

23. Calculating the Required Swap Hedge
Assume purchase of swaps with 5, 10 and 30yr maturity
Calculate nominals required to hedge LDD1 mismatch
Cost of each swap is (spread from Mid) * magnitude of LDD1
At 1bp spread, cost of swaps is £209,770
Cost represents 6.5bps of total fund
Source: CreditDelta, UBS

24. Sensitivity to Swap Curve Changes
LDD1s are matched at selected tenor points
Only small mismatches remain
Source: CreditDelta, UBS

25. Risk Analysis Interest rate risk becomes small with swaps
Benchmark
vs Liabilities
Interest rate risk becomes small with swaps
Tracking error drops from 2.8% to 1.5%
Source: CreditDelta, UBS

26. Duration Products Custom swap overlay is available to seg funds
Collateral management
Legal requirements
Pooled Fund Alternatives:
Bucketed Funds
Actuarially priced pooled funds
Share the objective of giving duration
Differences:
Legal structure
Credit spread
Active management

27. Liability Replicating Portfolio
Manage market risk against the liabilities

28. Mapping the solution to the mandate
Benchmark + 75bps
Benchmark + 75bps + fees
Liability Replicating Portfolio
ILG Gilts
ZC LPI Swaps
ZC IR Swaps
Swap LIBOR to Liability Replicating Portfolio
Inflation swaps
LPI Swaps
Plain Vanilla IR Swaps +
Netting off of positions
LIBOR + 90bps gross
Scheme Liabilities
Swap Asset Benchmark to LIBOR +
Investment Assets
50% ILG (>5 year index)
Alpha Target + 60 bps
50% ML, £, Non-gilt, Ex AAA
Alpha Target +80 bps
Beta Target +40 bps

29. LDI Solution Spectrum MATCHING HEDGING MITIGATING Rationale Approach
Risk Elimination
Risk Management
Comfort Zone
MATCHING
HEDGING
MITIGATING
Rationale
Full matching impossible due to longevity risk
Shares features of traditional methodologies – within comfort zone
Natural first step towards a full liability driven approach
Management processes altered from traditional methodologies
Likely to involve prolonged buyer education process
Approach
Immunisation funds
Duration / Cashflow Matching
Inflation Overlay
Dynamic Market Risk Allocation (DMRA)
RPI+ and libor+ strategies

30. Dynamic Market Risk Allocation (DMRA)
Increasing focus on avoiding short-term asset/liability mismatch
Market risk is the principle contributor of risk relative to the liabilities
Logical movement from static to dynamic market risk positions
Standard Life Investments’ solution:
Dynamic management of market risk based on three year view
Active views on all areas of market risk,
Optimal portfolios created to meet individual client requirements
Risk budget optimally deployed at all times

31. The ‘new balanced’ approach
Is it plausible?
Has it made money?
Is it theoretically proven?
Fund managers and traders look to add value over short time scales
Numerous active participants limit opportunities to add value over short term time horizons
DMRA is about exploiting medium term opportunities
3 to 5 year time horizon
Look to take as many diverse views as possible to exploit benchmark risk
Strategies to provide downside protection versus liabilities
Exploiting an uncrowded area

32. Evidence for Opportunities at Longer Timescales
Compare the volatilities of returns with different lengths of non-overlapping chain linked return data
Normalise to SQRT(time window). All data should be identical if markets are IID
Clearly this is not the case, but how significant is this?
Previous work has found difficulty with lack of data: we have a new technique
Compare to 40 random scrambled data series. This (on average) destroys any time series coherence, and allows us to assess significance.
Explore at index level over long timescales (BZW Equity Gilt Study.)
Explore at single stock level over long timescales (Shell)
Source: Standard Life Investments

33. Evidence in individual stock returns
Source: Standard Life Investments

34. Areas of market risk Play the right team at the right time
Market risk positions can be very broadly based
Not just an equity bond call
The risks that should be brought to bear include
FX risk
Duration risk
Credit risk
Equity market risk – including regional and sector views
Property market risk
Commodities
Volatility
Optionality
Play the right team at the right time

35. Example of Efficient Risk Deployment

36. Measuring Risk v’s Liabilities
Ex-ante analysis:
Must allow for liabilities
Overcome shortcomings of historic data
Ex-post analysis:
tracking error in absolute and relative terms:
volatility of returns of asset pool
volatility of relative returns
V-masks
Risk monitoring and control must relate to the key risks versus liabilities

37. Measures of variation and association
Source Datastream: 31/01/1995 – 31/12/2004
General characteristics of individual time series can often be easily observed from graphs.
Harder to determine the relationship, if any, between relative variations of two or more series.
Related measures of Correlation and Covariance are used to quantify this behaviour.

38. Interpreting correlation
A scatter plot helps illustrate correlation
The example shows monthly returns on two indices plotted against one another. The proximity to a ‘regression line’ through the data shows there is strong, positive, correlation between the two indices
A positively sloping line indicates positive correlation – returns on the assets move together
A negatively sloping line means negative correlation – asset returns move in opposite directions
The extreme cases of CorXY =1 and CorXY = -1 (perfect correlation) occur only if all points lie on a straight line
If CorXY = 0, the assets returns are uncorrelated
CorXY=0.96
Source Datastream: 31/01/1995 – 31/12/2004

39. Covariance Matrix
When there are many variables, the co-variation between all possible pairs can be conveniently represented in a Covariance Matrix. E.g for 3 variables:
Same format used for correlations. Elements along the leading diagonal are unity.
Example:

40. Calculating Ex-Ante Tracking Error
Tracking error is the standard deviation of the difference in returns between a portfolio and a benchmark. It is calculated as
where Cov is the covariance matrix and B is the vector of bets away from a neutral benchmark position (i.e. the difference in percentage weight, for each asset class, between the portfolio and the benchmark). The sum of bets across all asset classes is 0.
Extension to TE versus liabilities is achieved by treating liabilities, represented by a replicating portfolio, as a separate asset class. Covariance is calculated in the usual way. Weights are then against a neutral position, with the liability weight taken as –100%.
TE = 5.01%

41. Overcoming the historic data problem
Strategic Investment Group
Dr Julian Coutts
Head of Quantitative Risk
(Advisory role)
Sarah Smart
Investment Director
(Secretary)
Keith Skeoch
Chief Executive
Standard Life Investments
Lance Phillips
Head of Overseas Equities
Neil Matheson
VP and Economist
Standard Life Canada
Andrew Sutherland
Fixed Interest
Euan Munro
Head of Strategic Solutions
Chairman
Inputs:
Core & custom data pack
Asset class desk experts
Quant input
For each view the SIG produces:
Return expectations
Upside and downside expectations
Conviction
Correlation
Directly driving portfolio construction & risk monitoring
+ Conviction
Source: Standard Life Investments
Client Portfolio
Historic Risk
Expected Risk
V - Masks
Historic Correlation

42. Ex-Post Risk / Monitoring
Use V-masks for return generating processes: “Is the current experience plausible, within the context of our original opinion of the risk and return inherent in this particular position”
0.80
0.85
0.90
0.95
1.00
1.05
1.10
Nov-00
May-01
Nov-01
May-02
Nov-02
May-03
Nov-03
Cumulative Value Added
Monthly Cumulative Return
Upper and Lower Boundary
Confidence we will not overrun the budget

43. Maths of the generalised V Mask
Excess value is proposed to be R(T) = N(μT, σ2T)
“Funnel of Doubt”
Expected value R(T) = exp(μT)
UB(T) = exp{μT *σT1/2} etc
Now turn “funnel of doubt” backwards…
To end up at Actual(T) on the above return process, the expected value should have come from
R(t) = Actual(T)*exp{- μ(T-t)}
UB(t) = Actual(T)*exp{- [μ(T-t) *σ(T-t)1/2]}
Interpret this as…
“To have ended up here, with the proposed return process, we should have come from inside the (backwards) “funnel of doubt”. If the trajectory actually falls outside the UB, then the process actually operating was NOT that proposed, to UB level of certainty (1.65 = 95% certainty.)”
THE LINE’S OUTSIDE, THE STORY IS WRONG, SO REVIEW IT…

44. DMRA V-Mask Monitor: Stop Losses in Practice
Source: Standard Life Investments

45. Benefits of taking a dynamic approach
Broadens the investment universe
Examines the return potential of all areas of market risk
Targets asymmetric return expectations
Positioning in the range informs those to harness and those to avoid
Flexing the position to respond to specific circumstances
Taking a contrarian view on an asymmetric position can protect in downside scenarios – implied volatility for example
Responsive to the Investor’s risk appetite
Adjusting the hedging strategy depending on the Sponsor’s ability to make additional contributions
Investment expertise guided by quantitative discipline

46. Example: Long volatility
Strategy:
hold out of the money calls to access desired additional equity exposure and exposure to implied volatility
Rationale:
Asymmetric return expectation:
implied volatility currently right at the bottom of its range
expect it can go a lot higher but not much lower
rise in dynamic hedging means there are many institutions that will be forced traders if there is a big move in any direction
Source: Bloomberg

47. portable alpha strategies, which is another way of referring to LDI
.. portable alpha strategies, which is another way of referring to LDI. Global Investor Magazine, 08/05
..liability-driven investing, which seeks to match more closely the returns generated by a pension fund’s assets with its commitments. Financial News, 02/01/06
Liability Driven Investing is a risk preference based approach which can be used to complement or totally replace current strategies. Finance IQ Conference, 04/06
‘liability-driven investing’ (matching liability growth to the extent possible), Watson Wyatt, Canada
'liability-driven investment strategies', which involves swapping the income which they will receive from their long-dated bonds with instruments which better match their liabilities. The Observer, 22/01/06
LDI is about establishing a transparent link between liabilities and assets and minimising uncompensated risks. Hugh Cutler, Pensions Management, 01/04/05
LDI relates to the practice of using investment tools such as derivatives to help funds meet their payouts to investors even though markets may be volatile. The Standard (Hong Kong), 21/12/04
Liability-driven investing focuses on managing a plan’s liability risk while providing multiple sources of excess return. Jane Tisdale, SsgA, 17/10/05
“LDI … the process whereby an investment strategy is set with explicit reference to a specific set of liabilities.” Mercer Investment Consulting

48. What is LDI? A range of strategies and novel processes
That are evolving in response to the problems pension schemes are facing
Mark – to market
Visibility in accounts
Making optimum use of available risk budgets
Specifically, avoiding unmanaged and unrewarded risk
Employing those closest to the market to
Perform against liabilities
Over timescales that are now appropriate