## Philippe-N. Marcaillou

Print publication date: 2016

Print ISBN-13: 9780198738794

Published to Oxford Scholarship Online: May 2016

DOI: 10.1093/acprof:oso/9780198738794.001.0001

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# Understanding Asset and Liability Management (ALM)

Chapter:
(p.8) 2 Understanding Asset and Liability Management (ALM)
Source:
Defined Benefit Pension Schemes in the United Kingdom
Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198738794.003.0002

# Abstract and Keywords

Chapter 2 demonstrates the author’s pragmatic approach regarding ALM and funding ratio maximization as well as his processes. It gives an overview of ALM risk management and shows how to build an ALM strategy with the right risk metrics. The chapter shows various methodologies for calculating liabilities and for each methodology, the impacts on the funding ratio, contributions, and the investment strategy. Based on actual examples, this chapter teaches decision-makers to assess where risks and tricks are located, ALM investment strategies and how to measure their risk aversion in order to select the right investment strategy (risk allocation of the return-seeking portfolio, liability hedging strategy, performance and horizon of investment). It provides techniques for assessing the efficiency of the management of the liquidity. This chapter teaches decision-makers to define the targets of each component of an ALM framework, a powerful tool for monitoring the efficiency of the investment strategy.

# 2.1 Definition of the Objectives

The objective of this book is to show how asset and liability management (ALM) of pension funds and the building blocks work and contribute to achieving what every trustee and corporate–sponsor dreams of: to ensure that the members of the pension fund receive their expected benefits.

The target is to find and maintain the right ALM structure equilibrium by managing continuously for the best risk-adjusted return. In others words, the objective is to put in place and maintain the best ‘risk/return’ ratio strategy.

Typically, in a context where pension funds have deficit issues to manage (see Figure 2.1), the objective is to put in place a de-risking strategy whilst maintaining a sufficient expected return of the assets. To that end, each decision-maker must understand how the asset and liability structure of the scheme works.

There are various and complex ways to this objective. In this book you will find practical tools to understand the ‘Alpha and Omega’ of ALM structures of defined benefits schemes in order to be able to maximize their management.

## 2.1.1 ALM Management: A Balanced Management Approach

As regards pension fund ALM, some investment decision-makers or investment experts are steeped in an ‘asset’ culture; as a result, they are focused on the asset side of the ALM and typically, on equity. Their assumptions are that, given a long-term perspective, equities generate the highest return. They also look to maximize the asset and risk allocations of the growth assets portfolio by managing the three most important factors: return, volatility as a main measure of risk management, and correlation, that is, how assets move relatively to others. Their target is to achieve an over-performance of the assets versus the performance of the liabilities.

Other decision-makers and investment experts are focused on the liability side; they are more fixed-income and derivative-driven people and this is a (p.9)

Figure 2.1. Typical asset and liability structure of a pension fund

more difficult topic to understand for non-investment experts: it is easier to understand the profit generated on a trade such as buying a stock index or a stock at 10 and selling it at 12 than hedging inflation and/or interest rate sensitivities of 100 years or more of zero-coupon cash flows with swaptions!

ALM is a very complex topic and financial instruments are difficult to understand for non-investment experts. Added to that, there are important issues such as improving the governance of a scheme, lack of flexibility, internal politics, ego, and so on to manage in order to maximize the ALM of a scheme. I think there is a background issue as well: are the decision-makers of your pension fund more experienced in equity or in fixed income?

It is pretty rare to find within a trustee board and/or in the investment advisors’ sector, people who have practical experience in a variety of market conditions, or in investing in a variety of asset classes with varied maturities and at the same time experience on the liability side, owing money to pensioners in the future.

One has to understand and to ‘feel’ how the building blocks of the ALM work and behave in absolute terms. One has also to understand how they behave in relation to others within the ALM structure. My perception of ALM is that liabilities and assets behave like a balance (this is the reason why there is a balance on the cover page!): sometimes the risk and performance of the liabilities outweighs the assets and vice versa (see Figure 2.2). (p.10)

Figure 2.2. ALM risk management

Risk-adjusted performance management is the performance of assets and liabilities relative to their risks and the purpose of this book is to explain in-depth how to maximize it.

The aim of controlling the balance (i.e. the variation) is to reduce the risk whilst maintaining sufficient performance. One has to control the variation of the balance and investment-related risk on a regular basis (at least monthly) and not on an annual or triennial basis. Consequently this improves the governance of the scheme.

As the ALM of the scheme is monitored regularly, this allows us to take advantage of market opportunities and to react quicker if market conditions change. The objective should be to design a governance process to lock in improvements of the funding ratio when they happen and protect it against downside losses when markets fall.

The decision-makers should focus regularly on the funding ratio (assets/liabilities) instead on focusing on the performance of the assets. Typically the funding ratio is defined as the return of the assets vs the return of the liabilities and risk is the volatility (or standard deviation of the funding ratio). We will see later how to efficiently monitor the performance and the risk of an ALM structure.

### 2.1.1.1 Building Blocks of the Funding Ratio

The funding ratio depends on three main factors: contributions, the portfolio of assets, and the reduction of the liability amount (see Figure 2.3).

#### Funding Ratio (Asset/Liabilities) Components

Contributions

The sponsor of a pension fund can contribute assets (cash or/and real assets) to support the improvement of the funding ratio and close its funding gap. The strength of the sponsor and its capacity to make regular contributions is an important factor.

Growth Portfolio of Assets

There is a wide range of asset classes and investment strategies. Selecting an asset class and, more importantly, deciding the timing of the investment or dis-investment is the real main issue!

An exploration of the investment universe in order to diversify the current portfolio is necessary to reduce risks and have access to investment opportunities. (p.11)

Figure 2.3. Factors that influence the funding ratio

Diversification has a positive effect on the risk structure, for example, if you invest in the retail sector, you could buy either a basket or a specific retail stock. If the specific retailer goes into bankruptcy, the loss could be 100 per cent compared to investing in a basket of various retail names where if one defaults, the basket is worth less not worthless!

The positive diversification effect can be measured.

Liabilities

On the liability side, interest rates swaps, inflation swaps, gilts, and index-linked gilts (leverage included or not) are useful tools that support the reduction of risks. They have to be monitored and managed efficiently as they may introduce new risks within the capital structure.

Typically, liabilities are the most important risks in an ALM structure and the key driver of the investment policy decisions. You have to understand deeply the liability risk of the scheme and which assets can be the most efficient ones to hedge them. ALM and the ongoing right equilibrium depend on each scheme’s context.

## 2.1.2 Funding Ratio Maximization: Design of a Strategic Solution Process

Designing a strategic solution can be pretty quick to do but its implementation can be a very long process depending on the discipline and the motivation of the people in charge of it. To start, let us consider the chart in Figure 2.4 and each step of the process.

## 2.1.3 Funding Target: Required Performance Assessment

Trustees and sponsors should define the objective: is it a buyout, a technical provision, or an accounting one that decision-makers wish to reach and at what horizon of investment? (p.12)

Figure 2.4. Design of a strategic solution process

(p.13) Let us discover valuation methodologies, the impact on the funding ratio, and the investment strategies.

### 2.1.3.1 Valuation Methodologies

The differences between these valuation methodologies are also explained in more detail in chapter 3, ‘Understanding Liabilities’.

#### Technical Provisions

This method is used by the actuaries to carry out the valuation of the liabilities. Typically all cash flows are discounted with the same rate (consistent with the duration of the liabilities of the scheme) regardless of payment dates. Trustees use this methodology to monitor the funding level and to calculate the employer’s contributions. Sometimes, the present value of the liabilities is calculated with interest rates consistent with the future cash flows to be paid. A margin corresponding to the risk of the sponsor or a mixture of similar credit risks, is added on top of the risk-free rate, for example gilt + margin.

#### Accounting Basis (IAS19)

Accounting basis (IAS19) is used by the corporate/sponsor for reporting purposes. Assets are valued at market value. Typically the present value of the liabilities is calculated with AA rated bonds and through a single discount rate consistent with the duration of the cash flows.

#### Protection Pension Fund (PPF)

This methodology is used to calculate the amount of PPF levy and the discount rate in case of a takeover by the PPF.

This methodology is used to calculate the cost of transferring the liabilities to an insurer. Typically the present values of the liabilities are calculated with various interest rates consistent with the cash flow payments (future benefits to be paid) with no margin added on top of the interest rates.

These different valuation methodologies give different funding ratio results.

### 2.1.3.2 Consequences to the Funding Ratio

Let us consider the following example and the results per valuation methodology of pension fund ABC. The cash flow distribution is as shown in Figure 2.5. (p.14)

Figure 2.5. Future benefits payment

#### Impact on the Funding Ratio

For the impact on the funding ratio, see Table 2.1.

Assumptions:

• The horizon of investment is ten years.

• The contributions stay constant over the period.

Where,

Assets: value of the assets in £m

PV liabilities: present value of the future benefits to be paid to the members of the pension scheme

Technical provisions: cash flow liabilities are discounted at:

$Display mathematics$

Buyout basis: cash-flow liabilities are discounted at risk-free rate (gilt) flat, that is, 3.50 per cent

• Assets have to generate a return of 6.90 per cent per annum on a technical provisions basis (TP), that is, 3.40 per cent over the risk-free rate

• Assets have to generate a return of 10.70 per cent per annum on a buyout basis, that is, 7.20 per cent over the risk-free rate

to reach a funding ratio of 100 per cent in ten years.

Depending on the objectives of the trustees and the valuation methodologies used, we can see the difference in returns that assets have to generate to meet these objectives (in this example, the longevity risk is not included). Of course, the required performance could be reduced by an increase of the contributions. (p.15)

Table 2.1. How do the differences of methodology impact the funding ratio?

Technical provisions

Liability

Assets

Assets (£m)

PV Liabilities (£m)

Funding ratio

Risk free rate

Margin over risk free rate

Liability discount rate

Assets return targetto be 100% funded in 10 years

Excess performanceover risk free

44

66

67%

3.50%

2.00%

5.50%

6.90%

3.40%

Liability

Assets

Assets (m£)

PV liabilities (m£)

Funding ratio

Risk free rate

Margin over risk free rate

Liability discount rate

Assets return target to be 100% funded in 10 years

Excess performance over risk free

44

106

41%

3.50%

0.00%

3.50%

10.70%

7.20%

(p.16)

Figure 2.6. Recovery plan to get a funding ratio (assets/liability) at 100 per cent in ten years

### 2.1.3.3 Consequences to the Investment Strategy

The target is to achieve a 100 per cent funding ratio in ten years’ time, that is, the amount of assets should be equal to the technical provisions (TP) value of the liabilities at the end of the horizon of investment. Ideally, the assets should be equal to the buyout value of the liabilities.

If the target is reached at the end of the recovery period, no more cash contributions are required from the sponsor (see Figure 2.6).

### 2.1.3.4 Various Rates of Return Scenarios: Consequences to the Funding Ratio

Figure 2.7 shows the difference between the various asset performances over a ten-year period on the funding ratio (it assumes that the recovery contributions are included and stay constant).

An excess performance of the assets of 1 per cent per annum improves the funding ratio by 10 per cent over the ten-year period.

In this example, we have a practical introduction to a few concepts: liability valuation, asset performance, risk-free rate, margin over risk-free rate, asset performance over risk-free rate (i.e. excess return over a risk-free rate), how the funding ratio behaves under various scenarios, and recovery contributions.

As decision-makers have defined the objective (technical provisions, buyout, or accounting), the next step is to define the horizon of investment and to make an assessment of the risks of the ALM structure. (p.17)

Figure 2.7. Asset outperformance and impact on the funding ratio (assets/liabilities) in TP

## 2.1.4 Horizon of Investment

Depending on the size of the scheme’s deficit, it is typical in the UK pension industry for the expected horizon of investment to eliminate it on a technical provisions basis to be in the range, on average, of eight to ten years.

On a buyout basis, the expected horizon of investment to reach a funding ratio of 100 per cent is in the range of twenty to twenty-five years.

# 2.2 ALM Structure of a Scheme: Risk and Performance Assessment

To start, let us define the ‘risk’ concept. There are plenty of definitions and a variety of ways to measure it. Very simply, it is the possibility that an investor loses money when they invest in an asset. We could define it also as a probability of loss for a specific investment. Every decision taken carries some risks and even if no decision is taken, there are still existing risks.

When a risk is immunized by instruments, other new risks may appear. For example, you buy an insurance contract through an insurer; if this insurer defaults on reimbursing or goes bankrupt, what are the consequences regarding the hedge? Exactly the same issue arises in terms of liability hedging and the situation of the providers who sold the hedging assets to the scheme.

## (p.18) 2.2.1 Risk and Rate of Return

One can invest in bonds (corporate bonds, government bonds, etc.), listed equities, private equity, real estate, agricultural land, and so on and as with our previous example, over ten years.

The prices of these assets can be very volatile during this period; there is a risk attached to each asset and there is a trade-off principle that says that potential return rises with an increase in risk: low levels of risk are associated with low returns whereas high levels of risk are associated with high returns.

The probability of a complete or partial loss and the recovery rate is included in the rate of return of an investment. The recovery rate could be presented as follows: if you lent money to a corporate that is now bankrupt, the corporate would have to sell assets to reimburse the lender; the amount of assets sold would reimburse the lender either completely or partially. The recovery rate is the ratio between the initial lending amount and the residual amount.

Risk tolerance is a very personal topic: what is your comfort zone in terms of risk? What is the amount of risk in percentage and sterling terms that you are willing to take in order to sleep well at night?

Let us assume that cash has an expected return of 2 per cent, corporate bonds of 3 per cent, UK equities 5 per cent and real estate 12 per cent (see Table 2.2 and Figure 2.8).

If trustees invest the scheme’s assets in these asset classes, the net present value (NPV), that is, today’s value of the amount of £1,000 that the scheme will have to pay in ten years’ time will depend on the expected return of these assets. Of course, if in ten years’ time, the prices of these assets are higher than your expectation, the pension fund will get a surplus!

But if there is an expected return for each asset, what is the risk for each of them?

Nominal amount of benefits to be paid

1000

1000

1000

1000

Horizon of investment in number of years

10

10

10

10

Assets

Cash

Bonds

Equity

Real estate

Return: degree of confidence

Guaranteed rate of return

Expected return

Expected return

Expected return

Interest rate of return per annum

2%

3%

5%

12%

Today’s value of £1,000 or Net Present Value (NPV) (2 d.p.)

820.35

744.09

613.91

321.97

(p.19)

## 2.2.2 Introduction to the Sharpe Ratio

Nobel laureate William F. Sharpe created a risk-adjusted performance measure; the ratio is calculated by subtracting the risk-free rate (is there still one?) from the rate of return for a portfolio and then, dividing the result by the volatility (standard deviation) of the portfolio returns.

The general formula is:

$Display mathematics$

Where,

Rp: effective or expected portfolio return (asset)

Rf : risk-free rate

σ‎P: portfolio or asset volatility (standard deviation)

The Sharpe ratio shows if a return of an asset is due to smart investment decisions or is the result of excess risk (volatility). The greater the ratio, the better the risk-adjusted performance. A negative ratio indicates a portfolio, a fund, or an asset that performed less than the risk-free rate.

It is a pretty simple tool to compare the adjusted performance between assets (see Table 2.3 and Figure 2.9).

It is at this point that trustees should decide on the objective (technical provisions, buyout, or accounting) and the horizon of investment. They have a more considered view on the consequences of their investment decision.

Now, they need to assess the risk and performance of the ALM structure of their scheme. (p.20)

Table 2.3. Sharpe ratio per asset class

From 2010 to 2013

Asset class

Return above risk-free rate (%)

Volatility (%)

Sharpe Ratio

High yield US

10.1

6.8

1.49

High yield Europe

10.2

10.0

1.02

Risk parity

8.9

9.1

0.98

Emerging market debt

7.5

7.9

0.95

7.4

8.1

0.91

UK government bonds

4.2

5.9

0.71

Developed markets equities

10.9

15.5

0.70

From AAA to BBB—Credit US

2.6

4.0

0.65

From AAA to BBB—Credit UK

2.2

3.7

0.59

US leveraged loans

2.8

5.5

0.51

Emerging market equities

3.0

20.9

0.14

Commodities

–0.7

17.6

n/a

Hedge Fund Macro

–2.5

3.7

n/a

Figure 2.9. The Sharpe ratio per asset class

## 2.2.3 ALM Risk and Performance Assessment: Introduction to the Building Blocks

An in-depth analysis must be undertaken in order to understand the dynamics of the ALM structure and associated risks. The aim of an ALM analysis is to support the definition of the investment policy and the risk budget (i.e. the risk appetite of the trustees).

(p.21)

Table 2.4. ALM metrics of Almanar Pension Fund

 ALM metrics TP liabilities (£m) Assets (£m) Deficit (£m) Funding ratio Almanar Pension Fund 100 83 –17 83%

This first example shows an analysis approach; we will see a complementary approach in chapter 5 ‘Investment Policy: Understanding Asset Allocation Construction’.

Let us consider an example of a typical UK pension fund.

### 2.2.3.1 Context

In 2010, the trustees are motivated to maximize the ALM structure of the under-funded pension fund that they manage (see Table 2.4).

They are more focused on the asset side of the ALM structure.

The trustee board and the investment committee are not investment experts but they are very keen to improve their technical knowledge to manage the ALM structure more efficiently and challenge the solutions provided by their investment consultants and other providers.

There are no problems between the trustee board and the sponsor who is very keen to support the process through allocating internal resources.

Both sides understand that if the pension fund is not sound, there will be a direct impact on the credit risk of the sponsor and on its stock price and if there is a deterioration of the credit risk of the sponsor, its covenant will be less robust; as a result, the consequences will be negative for the members of the pension fund.

The trustees have noticed the high volatility of the funding ratio; they do not sleep well at night and would like to know more precisely what is going on in the pension fund.

### 2.2.3.2 Asset and Risk Allocation

#### What Is the Current Asset Allocation Breakdown?

We notice that the growth asset portfolio is composed of 50 per cent equity and 50 per cent bonds see (see Figure 2.10).

The bond allocation is composed of 50 per cent of government bonds—gilts and index (inflation)-linked gilts—and 50 per cent corporate bonds.

#### What Is the Current Risk Allocation?

For an illustration of the current risk allocation, see Figure 2.11.

What is the difference between asset allocation and risk allocation? (p.22)

Figure 2.10. Asset allocation

Figure 2.11. Risk allocation

#### Introduction to Correlation

Correlation is made of two words ‘co’ (together) and ‘relation’; a correlation is a mutual relationship between two or more assets. When two or more assets are strongly linked together, we can conclude that there is a high correlation.

When they are not linked together, there is no correlation.

• Positive: the values increase together

• Nil: there is no correlation

• Negative: one value decrease as the other one increases (p.23)

Figure 2.12. Correlation measurement

(p.24) So, correlation can have a value between –1 and 1 (see Figure 2.12)

+1: there is a perfect correlation

0: there is no correlation

–1: there is a perfect negative correlation.

In our example, the risk allocation is different from the asset allocation because of the correlation effect between asset classes: for example, if equities move by 1 per cent, investment grade corporate bonds (typically BBB rating) could move by 0.40 per cent and high yield corporate bonds by 0.55/0.60 per cent or more. (p.25)

Figure 2.13. Hedging assets

In the asset management world, there are three items that have to be monitored: asset return, risk, and correlation; risk allocation is a very important item to monitor.

In our example, corporate bond values are highly correlated to equities variation; as a result, the risk allocation shows a high equity risk exposure.

#### Are Liabilities Hedged?

We saw that the bond allocation is composed of:

• 50 per cent government bonds: gilts and inflation-linked gilts (ILGs)

• 50 per cent corporate bonds

We can conclude that liabilities are 25 per cent hedged through gilts and ILGs if liabilities, gilts, and ILGs have the same duration (see Figure 2.13).

At this point, the trustees know that the equity risk exposure is too important and liabilities are not hedged enough against interest rates and inflation risks. As a result, in accordance with their comfort zone, they decide to increase liability hedge from 25 per cent to 50 per cent.

They wish to further analyse the performance and risk metrics of the ALM of the pension fund and to compare them to alternative portfolios (see Table 2.5). (p.26)

Table 2.5. Comparison of the current investment policy and three alternative portfolios

Asset Allocation

Growth Asset Portfolio Allocation—Asset classes

Liability hedging

LDI portfolio (Gilt and ILGilt)

Growth assets portfolio

Equity

UK and overseas corporate bonds

Emerging market debt

Bank loans BB rating

Multi-diversified fund: passive management

Multi-diversified fund: active management

Current portfolio

25%

75%

50%

25%

0%

0%

0%

0%

Limited to LDI portfolio

Comparison with three alternative portfolios

1. Conservative portfolio

25%

75%

25%

15%

5%

5%

25%

0%

50% of liabilities hedged with hedging assets in the LDI portfolio

2. Medium conservative portfolio

25%

75%

25%

15%

5%

5%

12.5%

12.5%

3. Dynamic portfolio

25%

75%

25%

15%

5%

5%

0%

25%

#### (p.27) Asset Allocation: Current Portfolio and Comparison to Three Alternatives

(see Table 2.5)

Where,

Asset allocation:

• LDI portfolio: cash and ILGs are the hedging assets (25 per cent)

• Growth asset portfolio: return-seeking assets

Growth asset portfolio allocation:

• Asset classes: breakdown of the growth asset portfolio

• Portfolios 1, 2, and 3 assumes that 50 per cent liability sensitivity is hedged

• Current portfolio: 25 per cent liability sensitivity hedged

• Multi-diversified fund passive management: between eight and ten asset classes are managed simultaneously. The objective is to invest in asset classes that are the least correlated to the others. The management approach is passive, that is, asset managers keep the breakdown of the asset allocation constant; there is no market view.

• Multi-diversified fund active management: similar to the previous one but the asset allocation is not constant and can change depending on the market views of the asset manager. The asset allocation is active.

Trustees would like to look at the impact in terms of performance and risks of reducing the equity and corporate bond risk exposure and introducing more diversification within the portfolio such as emerging market debt, bank loans, and multi-diversified funds active and/or passive management.

### 2.2.3.3 Historical Data Analysis: Comparison of the Performance of Portfolios

So, trustees would like to compare the historical performance and risks metrics of their current portfolio and three alternatives (see Figure 2.14).

Why choose 2007 as the departure date of the analysis and not before? Since 2007, a lot has happened—the sub-prime crisis, Lehman and Bear Stearns bankruptcies, a liquidity crisis, a convergence of the correlation between asset classes, and so on—this period of data observations is sufficient to analyse the most important metrics: return, risk, and correlation of each asset class and portfolio. The second reason is that if trustees wish to invest in funds that were founded just a few years ago, the quantity of data will not be large enough to make statistical calculations and draw conclusions.

At this point, we can see that the current portfolio performed worst and the dynamic one performed best. Typically, which metrics could you check? (p.28)

Figure 2.14. Comparison of the performance of the current portfolio to alternatives

#### Introduction to Some Performance and Risk Metrics

There are plenty of performance and risks metrics. Below are listed metrics that offer a first approach to see what is going on in the current portfolio and to compare that to alternative portfolios:

• Annualized return over a given period

• Standard deviation

• Maximum drawdown

• Value-at-Risk (VaR)

• Conditional Value-at-Risk (CVaR)

• Annualized cash return

• Sharpe ratio

Annualized Return

We could define this performance metric by the average amount of money earned by an investment each year over a specific time period. An annualized return provides a snapshot of an investment’s performance. Risk metrics are not included in it.

$Display mathematics$

Where,

r: annual return for a given year

n: maturity of the investment

Annualized return provides a geometric average rather than an arithmetic average. What is the difference between a geometric average and an arithmetic (p.29)

Table 2.6. Examples of returns

Stock performance and price

Value t0

Performance from t0 to t1

Value t1

Performance from t1 to t2

Value t2

Stock 1

100

10%

110

–9.1%

100

Stock 2

100

–40%

60

66.7%

100

average? Let us consider the following example and the returns of Stocks 1 and 2 (see Table 2.6).

The arithmetic average is:

$Display mathematics$
$Display mathematics$

There is a positive return in both cases but we notice that the value of the stock at the end of the investment period (t1:100) is the same as at the beginning period (t2:100).

Using the geometric average formula, if we make the calculation:

$Display mathematics$

Where,

ri: return for period 1, 2…n

n: maturity of the investment

We get:

$Display mathematics$
$Display mathematics$

The arithmetic average result is higher than the geometric one; the difference in the results between both calculations increases if the variations of return are greater.

Standard Deviation (Greek letter: sigma letter σ‎)

Let us consider the example of Stock A and its historical returns (see Table 2.7).

Where,

number of years of observation: 4

mean: arithmetic average

deviation vs the mean: year 1: 5 – 7.25 = –2.25 and so on

square of the deviation: Year 1: (–2.25)2 and so on

variance calculation: average of the previous calculations

standard deviation: square root of the previous result (p.30)

Table 2.7. Example of a standard deviation of a stock

Stock A/year

Return %

Mean

Deviation vs the mean

Square of the deviation

Average of the square of the deviation variance calculation

Standard deviation

1

5

–2.25

5.0625

2

6

–1.25

1.5625

3

8

0.75

0.5625

4

10

7.25

2.75

7.5625

3.6875

1.92

In Stock A, therefore, 1.92 is the standard deviation (volatility). This is the positive square root of the average of the squares of the deviations from the mean and is a measure of the dispersion of the numbers. The general formula is given by:

$Display mathematics$

Where,

$Display mathematics$

Maximum Drawdown

The drawdown is the measure of the decline from a historical peak of an asset, portfolio, or index. Maximum drawdown is an indicator of the risk and measures the largest single drop from peak to bottom in the value of a portfolio.

For example, if a portfolio starts with a worth of £100, increases in value to £130, decreases to £90, increases to £120, then decreases to £70, and then increases to £200 the max drawdown is (£130 – £70)/£130 = 46.1%.

The highest peak of £200 is not included in the calculation because the drawdown began at a peak of £130. The increase to £120 before the drop to £70 has no effect on the drawdown because £120 is not a new peak.

The general formula is:

$Display mathematics$

Where,

T: period of observation

t: departure date of observation

τ‎: end of period of observation

(p.31) Max [τε‎ (0, T)]: max over a period of time from departure date to T

Max [tε‎ (0, τ‎)] : max over a period of time t from departure date to τ‎

P: portfolio

In our case, the maximum drawdown up to time T is the maximum of the drawdown over the given analysis period.

Introduction to Value-at-Risk (VaR)

(This is also covered in chapter 4, ‘Understanding Liability Driven Investment’.)

For a given portfolio or ALM structure, probability, and time horizon, VaR is defined as a threshold value such that the probability that the loss over the given time horizon will not exceed this value. In other words, VaR is a statistical way of measuring the level of risk of an investment (within a portfolio, an ALM pension fund, or ALM of a bank) over a specific time frame. In our case, the risk managers (trustees, CIO, investment consultants, etc.) regularly monitor the level of risk that the trustees undertake and ensure that the risks are not taken beyond the level at which the pension fund can absorb a loss in the probable worst-case scenario.

VaR is measured using three variables:

• the amount of potential loss

• probability of that amount of loss or interval of confidence

• time frame.

VAR: How does it work?

For example, a pension fund may define that £5m is the maximum loss anytime in the next year in the 5 per cent worst-case scenario: it means that there is a 95 per cent chance that the loss would be equal or under £5m. As a result, a £5m loss should be expected to occur once every twenty years.

For practical reasons, a quick but imperfect approach would be to use a parametric VaR:

$Display mathematics$

Where,

W0: current price of the asset

Z0: confidence interval (90%, 95%, or 99.5%) or probability that the worst case scenario occurs

σ‎i: volatility or standard deviation of an asset, investment, or portfolio

h: horizon of investment (from three months to one year)

Let us consider the following example: an asset is valued at £100; its annual standard deviation (volatility) is 15 per cent; the horizon of investment is ten days.

What is the potential worst loss in an interval of confidence of 95 per cent? (p.32)

Figure 2.15. VaR graph representation (Gaussian distribution)

$Display mathematics$

Where,

• 252 days: there are typically 252 business days per year

• Interval of confidence of 95 per cent: 1.645

If you wanted to calculate a VaR 90th within an interval of confidence of 90 per cent, the number would be: 1.282 (instead of 1.645).

VAR Graph representation (Gaussian distribution)

Under a normal distribution, we can see the number of standard deviations: 1, 2, and 3 σ‎ and for each of them, the percentage of observations, for example, we can assume that from the mean ‘μ‎’, 68.3 per cent of the data are located in the first standard deviation = +/–1 σ‎ (see Figure 2.15).

An important parameter is the profit and loss distribution. If the risk tolerance of an investor is high, the VaR level will be high. He will expect that the probability of loss will be the lowest possible. With a Gaussian distribution, the assumption is that the distribution is ‘normal’. If the profit and loss distribution is ‘normal’, it means that there is a symmetrical probability between profit and loss, an average (mean) of returns over a period of time, and standard deviations.

You have to decide what the horizon of investment is (typically from one day to one year) and the interval of confidence to get the probabilistic measure of risk.

(p.33) Even if it is not a perfect tool, VaR is a very useful one to support investment decisions and monitor them. There are various VaR calculation methodologies and one has to be careful about the components included in the calculation. Do not hesitate to ask how the VaRs are calculated!

Conditional Value-at-Risk (CVaR)

CVaR is an extension of VaR and a complementary risk measure that is more sensitive to the shape of the loss distribution in the tail of the distribution. The VaR model allows asset managers to limit the probability of incurring losses caused by certain types of risk but not all risks. Unfortunately, the tail end of the distribution of loss is not typically assessed. If losses incur, the amount can be substantial in value. It could be defined as the probability of losses in the worst-case scenario (see Figure 2.16).

Depending on the confidence interval of the VaR (90%, 95%, or 99.7%), the CVaR shows the tail risk in the worst-case scenario.

This simple example presents a distribution of returns of a portfolio and the number of observations per return; for example, there has been a return of 0 per cent, 95 times over a given period of time.

CVaR shows that the return of this asset was negative (–5 per cent) 30 times over the given period of time. It is an interesting risk metric to monitor.

Annualized Cash Return

Similar to annualized return of assets: it is the return of cash as an asset class (e.g. LIBOR one month or three months).

Sharpe Ratio

Defined in section 2.8 in this chapter, This is a risk-adjusted performance measure; the ratio is calculated by subtracting the risk-free rate

Figure 2.16. CVaR and VaR illustration

(p.34)

Table 2.8. Historical current and alternative portfolios performance and risk analysis

Since Jan-07

Current portfolio

1. Conservative portfolio

2. Medium conservative portfolio

3. Dynamic portfolio

Annualized return

–0.40%

2.00%

3.00%

4.10%

Standard deviation

13.40%

10.40%

9.70%

9.20%

Maximum drawdown

–30.80%

–22.50%

–19.20%

–15.80%

1 yr VaR (95th percentile)

–24.20%

–19.50%

–16.20%

–12.80%

1 yr CVaR (95th percentile)

–25.20%

–20.30%

–17.10%

–13.90%

Annualized cash Return

2.60%

2.60%

2.60%

2.60%

Sharpe ratio

–0.22%

–0.06%

0.05%

0.16%

from the rate of return for a portfolio and then dividing the result by the volatility (standard deviation) of the portfolio returns.

The general formula is:

$Display mathematics$

Where,

Rp: effective or expected portfolio or asset return

Rf : risk-free rate

σ‎p: portfolio or asset volatility (standard deviation)

Now, let us go back to our example. What can we see when we compare the current portfolio and the three alternatives? (See Table 2.8.)

#### Some Observations over the Period 2007–10 Analysis

The current portfolio composed of equities and corporates bonds has generated a negative return since the beginning of the period of observation (January 2007). If emerging debt, bank loans, multi-diversified passive and/or active funds had been introduced, the risk-adjusted return would have been better.

Portfolio’s Performance Analysis

• Annualized return: as we have already seen, the current portfolio had the worst return and the dynamic one had the best.

Portfolio’s Risk Analysis

• Standard deviation (or volatility): the volatility of the current portfolio was the worst; the most dynamic one had the lowest volatility.

• Max drawdown, VaR, and CVaR: similar observations as above.

(p.35) At this point, we can conclude that the most dynamic portfolio had the best risk-adjusted performance over the 2007–10 period.

Skewness and Kurtosis: Two Other Interesting Metrics

Introduction to Skewness

Skewness measures the asymmetry of the distribution. This is the set of data that relates to the shape of the histogram. The skewness value can be positive, negative, or undefined.

If positive, the mass of distribution of returns is concentrated on the left side of the distribution resulting in a longer right tail and negative skew indicates that the tail on the left side of the probability density function is longer and fatter than the right side. A normal distribution has a skewness of zero: it indicates that the tails on both sides of the mean balance give a symmetrical distribution.

Consider the distribution of returns in Figure 2.17.

The number of bars on the right side of the distribution is different than the bars on the left side. The tapering sides are known as tails; as a result, one can easily see which of the two kinds of skewness a distribution has:

Figure 2.17. Negative and positive skewness

1. (p.36) 1. Positive skew: the right tail is longer; the mass of the distribution of returns is concentrated on the left of the figure. It has relatively few high values.

2. 2. Negative skew: the left tail is longer; the mass of the distribution of returns is concentrated on the right of the figure. It has relatively few low values.

3. 3. Zero skewness: symmetrical distribution of returns.

More formally, the coefficient of skewness is:

$Display mathematics$

Or

$Display mathematics$

Where, $x-$: mean of the numbers

N: number of data

S: standard deviation

Introduction to Kurtosis

The kurtosis is the degree of ‘peakedness’ of the probability distribution. A distribution is said to be mesokurtic if it has the same degree of peakedness as the normal distribution. If the distribution is less peaked than the normal distribution, it is said to be platykurtic, if more, leptokurtic.

Kurtosis measures how much of the total variation is due to extreme movements. A kurtosis can be approached as a measure of a fat tail. A normal distribution has a kurtosis of three; if the estimated kurtosis is higher than three, the estimated distribution is characterized by fatter tails than those of a normal distribution.

$Display mathematics$

Where,$x-$: mean of the numbers

N: number of data

S: standard deviation. (p.37)

Table 2.9. Skewness and kurtosis overview

The calculations can be made on Excel as the functions and formulae are included in the software. The next step is to use these statistics in applications.

We know that:

• the mean gives the central tendency of the data

• the median equals the middle value of an ordered list

• the mode is the most frequent value

• the standard deviation explains the dispersion about the mean

• the skewness represents the symmetry/asymmetry of the data

• the kurtosis is related to the shape.

Since a set of data can have any mean and standard deviation, we can use these statistics to determine the location and relative dispersion.

Using skewness and kurtosis, we can learn much more, as shown in Table 2.9.

Skewness and Kurtosis: Conclusion

Both have to be compared to ‘0’ (for a normal distribution).

• skewness: a positive number means that there are more positive returns over the given period (and vice versa for a negative number)

• kurtosis: the greater the number, the fatter the tails.

At this point, let us go back to our example and consider the skewness and kurtosis of the current portfolio and the three alternatives (see Figure 2.18).

It is easy to see with this approach where the positive returns per portfolio are concentrated as well as the extremely negative ones. (p.38)

Figure 2.18. Monthly returns distributions

Historically, the alternative portfolio 3 dynamic portfolio seems to be the most interesting to consider compared to the others in terms of returns and loss distributions.

### 2.2.3.4 Forward-looking Data Analysis of the Deficit

At this point, the trustees would like to assess how the current portfolio and the three alternatives would behave under the same forward-looking return, risk, and correlation assumptions.

#### What Are the Long-term Return and Risk Assumptions?

In order to analyse, build, and monitor the performance and risks of portfolios, trustees have to select the best benchmark of each asset class(see Table 2.10). It is important to compare an asset, an asset class, or a portfolio to an appropriate benchmark. There are thousands of indexes that analysts use to measure the performance and risks of any instruments, such as the FTSE100, S&P500, CAC40, Russell 2000 Index for equities and iBoxx £ Non-Gilts for corporates bonds, EMBI Global TR £ currency-hedged emerging market debt (local currencies hedged).

#### What Are the Long-term Correlation Assumptions?

In the example in Table 2.11, correlations were calculated through ten years of data observations (2000–10). (p.39)

Table 2.10. Long-term return and risk assumptions

Asset class

Expected excess return

Expected volatility

Expected Sharpe ratio

Benchmark

Assets

Equity

4.00%

15.00%

27%

FTSE All Share TR

Corporate debt

1.50%

6.00%

25%

iBoxx £ Non-Gilts

EM debt

3.00%

10.00%

30%

EMBI GLOBAL TR £ Hedged

Bank loans

3.00%

9.00%

33%

European Loan Fund

Diversified passive

4.00%

12.00%

33%

Bespoke Multi-diversified Funds Passive Index

Diversified active

4.00%

9.00%

44%

Bespoke Multi-diversified Funds Active Index

Liabilities

Nominal

1.25%

12.50%

n/a

iBoxx £ Nominal Gilts Maturities >15 yrs

Real

1.25%

12.50%

n/a

iBoxx £ Index-linked Gilts Maturities >15 yrs

Hedged

1.25%

0.50%

n/a

Libor £1m Index

One has to keep in mind that correlations between assets are not stable (they are dynamic and have to be closely monitored).

At this point, trustees have defined long-term expected return and volatility per asset class and calculated the correlation between asset class; they can continue their forward-looking analysis and compare the risks of the current portfolio to the alternative ones in two ways.

#### Probabilistic Approach: Value-at-Risk Analysis

The first approach is not perfect but gives interesting results in comparing all the portfolios (see Table 2.12).

Notice that the modifications of the growth asset portfolio would improve the expected returns and reduce the VaR: the current portfolio has the worst VaR one-year confidence interval of 95th. It means that in the 5 per cent worst-case scenario, the probability of loss is estimated at 13.2 per cent (i.e. one chance to lose 13.2 per cent of the growth portfolio value every twenty years). In sterling terms, it means that in the 5 per cent worst-case scenario the probability of loss is estimated at 13.20% × £83m = £11m approximately. (p.40)

Table 2.11. Long-term correlation assumptions

Equity

Corporate bonds

EM debt

Bank loans

Diversified passive

Diversified active

Nominal liabilities

Hedged liabilities

Equity

100%

Corporate bonds

18%

100%

EM debt

53%

25%

100%

Bank loans

–9%

–20%

–11%

100%

Diversified passive

45%

43%

70%

–8%

100%

Diversified active

45%

46%

43%

–19%

54%

100%

Nominal liabilities

–9%

76%

9%

–1%

31%

33%

100%

IL liabilities

20%

62%

30%

–7%

46%

46%

62%

100%

Hedged liabilities

–8%

–5%

–15%

24%

–13%

–6%

13%

7%

100%

(p.41)

Table 2.12. Comparison of risks metrics

Since Jan-07

Expected excess return

Expected excess volatility

Expected Sharpe ratio

Value-at-Risk 1 yr/95th percentile

Current portfolio

3.20%

10.50%

0.30

–13.20%

Alternative portfolio

1. Conservative portfolio

3.40%

8.60%

0.40

–9.80%

2. Medium conservative portfolio

3.40%

8.00%

0.43

–8.70%

3. Dynamic portfolio

3.40%

7.70%

0.44

–8.30%

For example, if trustees decide to select portfolio 2, in the 5 per cent worst-case scenario, the probability of loss is estimated at 8.70% × £83m = £7m approximately.

The difference between portfolios 1 and 2 is very important.

Alternative portfolios 1, 2, and 3 have the same expected returns because the approach is a conservative one.

Why Have the Trustees Selected an Expected Excess Return Metric Instead of a Typical Expected Return?

It is more precise to compare excess returns of various assets over the same risk-free rate (gilt, LIBOR, swap). An expected excess return corresponds to the margin over the risk-free rate.

Let us consider a no-guarantee asset XYZ with an expected return of 5 per cent: if the risk-free rate is at 1 per cent or 5 per cent, our conclusions would be different; based on a risk-free rate of 1 per cent, we would have a return of: risk-free + 4% vs risk-free flat which would be less interesting in terms of risk-adjusted return!

This approach is the same regarding the comparison between expected volatility and expected excess volatility against risk-free rate.

At this stage of the analysis, it would also be interesting to compare the current VaR in sterling terms to the annual contribution, that is, if the worst-case scenario occurs, the question is how many years of contributions are needed to compensate for the loss? Are trustees comfortable with that multiple?

### 2.2.3.5 Funding Ratio Analysis

#### Historical Funding Ratio Analysis

Let us analyse the funding ratio (assets/liabilities) since January 2007 (see Figure 2.19). (p.42)

Figure 2.19. Historical funding ratio evolution analysis (2007–10)

Table 2.13. Performance and risks metrics

Since Jan-07

Current portfolio

1. Conservative portfolio

2. Medium conservative portfolio

3. Dynamic portfolio

Funding ratio evolution

–9.40%

–4.70%

–2.60%

–0.40%

Standard deviation (volatility)

6.50%

4.90%

4.70%

4.60%

Maximum drawdown

–23.50%

–16.90%

–15.10%

–13.50%

1 yr VaR (95th percentile)

–15.20%

–12.60%

–10.50%

–8.40%

1 yr CVaR (95th percentile)

–16.40%

–13.50%

–11.50%

–9.50%

Notice that if, since 2007, trustees had hedged 50 per cent of the liabilities (nominal and inflation) and selected one of the three alternative portfolios, the result would have been better.

Let us now check the performance and risks metrics for each of them (see Table 2.13).

#### Performance and Risk Metrics

Since 2007, the combination of the alternative portfolio 3 and 50 per cent liability-hedged strategy would have been the best solution in terms of performance and risks (VaR 1 yr 95th confidence interval is 8.40 per cent vs the VaR of the current strategy which is 15.2 per cent). The conclusion would be the same using CVaR metrics.

(p.43) At this point of the assessment process, trustees would have completed the growth asset portfolio analysis (historical data analysis and forward-looking analysis based on returns, risks, and correlation hypothesis). Would there be other ways to analyse risks?

#### Risk Breakdown: Diversification Effect

Typically you could check, monitor, and manage risks per asset class (see Figure 2.20).

All existing risks in the asset and liability structure of a pension fund are shown on this type of graph (from left to right). If there were other investments (such as infrastructure investments, property, commodities), they would be included in this type of illustration.

The measure of this risk is a probabilistic one (VaR); this approach to risk measurement is presented in this chapter and also in chapter 4, ‘Understanding Liability Driven Investment’.

The deficit on the right side of the figure is the potential increase over a one-year horizon.

Let us now analyse the risks of the deficit

Figure 2.20. Pension assets and liabilities, one-year VaR confidence interval 95th (£m)

Table 2.14. Deficit Value-at-Risk: forward-looking analysis

£m

Liabilities

Assets

Deficit

1 yr VaR (95th percentile)

Deficit reduction

Current

100

83

–17

–20

Alternative 1

–12

–41%

Alternative 2

–11

–43%

Alternative 3

–11

–43%

(p.44)

Table 2.15. ‘What if?’ approach: comparison of the current portfolio to alternatives

In £m

Stress test

Impact—assets £

Impact—TP liabilities £

Impact—deficit £

Current portfolio

Equity

–30%

–12.4

0.0

–12.4

Diversified funds

–15%

0.0

0.0

0.0

Credit yield1

1%

–1.5

0.0

–1.5

EM debt yield1

2%

0.0

0.0

0.0

Long real rates1

–1%

3.0

14.4

–11.5

Long nominal rates1

–1%

0.7

3.4

–2.7

Longevity increase2

+3 months

0.0

0.7

–0.7

Total

–28.8

Alternative portfolios 1, 2, and 3

Equity

–30%

–6.3

0.0

–6.3

Diversified funds

–15%

–3.1

0.0

–3.1

Credit yield1

1%

–1.0

0.0

–1.0

EM debt yield1

2%

–0.6

0.0

–0.6

Long real rates1

–1%

3.0

7.3

–4.3

Long nominal rates1

–1%

0.7

1.7

–1.0

Longevity increase2

+3 months

0.0

0.7

–0.7

Total

–16.9

Note 1: Duration: corporate bonds seven years; emerging market debt seven years; nominal liabilities seventeen years; index-linked liabilities: seventeen years.

Note 2: Longevity risks: it could be useful to know the impact in sterling of a longevity increase. Typically actuaries can provide this information.

### 2.2.3.6 Deficit Value-at-Risk: Forward-looking Analysis

Based on the return, risk, and correlation hypothesis, we notice that implementing the strategy by selecting one of the three alternative portfolios and hedging 50 per cent of the liabilities decreases the VaR by almost two. This strategy also maintains the expected return of the growth assets portfolio.

These results are very sensitive to the hypothesis (excess return, volatility, and correlation) detailed earlier.

We used a probabilistic approach to measure risks by using VaR 1 yr 95th (see Table 2.14).

### 2.2.3.7 Stress Test

Let us now analyse the risks with a determinist approach through stress test scenarios (or ‘What if?’ approaches). This approach involves analysing how each class of a growth portfolio and hedging asset would behave under very negative scenarios (see Table 2.15).

#### (p.45) Stress Test Comments: Current Portfolio vs Alternative Portfolios

Through the deterministic approach and based on return, volatility, and correlation assumptions, implementing portfolios 1, 2, or 3 and hedging 50 per cent of the liabilities reduce the potential loss in the worst-case scenario.

## 2.2.3.8 Performance and Risk Assessment: Conclusion

Based on probabilistic and deterministic approaches, the trustees conclude that introducing more diversification within the portfolio and hedging liabilities reduces the risks while maintaining the expected return of the portfolio to reach a funding ratio of 100 per cent in eight to ten years.

Now, the final step is to understand how the liquidity and cash flows are managed.

# 2.3 Liquidity Management

Liquidity management is a very important issue that has to be defined precisely in the ALM framework and closely analysed and monitored. Liquidity risk is measured by the amount of cash flows required over a period of time.

Let us consider the following example of pension fund XYZ. As a first step, it would be useful to do the historical analysis of the in/out cash flows.

## 2.3.1 Historical Data Analysis: Is the Liquidity of the Scheme well Managed?

A simple table and graph can show the movements of in and out cash flows (see Table 2.16 and Figure 2.21).

Where,

Balance: balance at the end of the period

Contribution income: contributions from the employer and employees

In our example, notice that the net balance from one quarter to the next is positive and stable. The scheme administrator has to regularly check and monitor if the net balance is in the range of cash that is defined in the pension fund liquidity management policy.

Notice also that there is a liquidity shortfall; pension fund XYZ has to rely on the portfolio of assets to fund this shortfall with coupons generated by bonds or/and dividends generated by equities or/and by selling assets or/and receiving more employer contributions. (p.46)

Table 2.16. In/out cash flows

Jan–Mar (£000)

Apr–Jun (£000)

Jul–Sep (£000)

Oct–Dec (£000)

Balance at the beginning of the period

459

523

377

427

Contribution income (employers and employees)

329

144

293

142

Investment income (dividends + coupons + disposals + interest rates on cash deposit + property rent)

1,491

1,057

1,668

1,398

Total inflows

1,820

1,201

1,961

1,541

Benefits payments

253

266

269

276

Investment

1,502

1,082

1,642

1,338

Total outflows

1,755

1,347

1,911

1,614

Total inflows – total outflows

65

–146

50

–73

Balance at the end of the period

523

377

427

354

Figure 2.21. In/out cash flows

As a second step, the scheme administrator has to estimate the liquidity profile for the next three (or ideally five years) using payments and contributions assumptions. As a result, he has to compare the result against the objectives defined in the ALM framework and estimate if there will be a surplus or a liquidity shortfall.

## 2.3.2 Forward-looking Analysis

This exercise has to be linked to the pension fund strategy. For example, if pension fund ABC plans to increase its infrastructure allocation and decrease the bond allocation, we can expect to receive a larger income that has to be incorporated in the liquidity estimations.

Pension fund XYZ has to also estimate or confirm the employer and employee contribution amounts. Typically these will be confirmed during the next actuarial valuation process (see Table 2.17 and Figure 2.22). (p.47)

Table 2.17. Estimate of the liquidity position for pension fund XYZ for the next three years

Forward-looking

Year+1

Year+2

Year+3

Balance at the beginning of the period

354

358

363

Contribution income (employers and employees)

936

983

1,002

Investment income

5,895

6,189

6,313

Total inflows

6,831

7,172

7,316

Benefits payments

1,096

1,150

1,173

Investment

5,731

6,017

6,137

Total outflows

6,826

7,167

7,311

Total inflows – total outflows

4

5

5

Balance at the end of the period

358

363

368

Figure 2.22. Forecast of the liquidity position for pension fund XYZ for the next three years

### 2.3.2.1 Investment Income: How to Estimate Investment Income?

The administrator of pension fund XYZ must check the dividend and coupon distribution policy of the assets: some assets generate income, others not (some investments do not offer the option of paying dividends). If assets generate income, these future incomes are not known in advance but estimates can be made. A simple approach could be to estimate the expected income based on the current or expected return for each asset (see an example in Table 2.18).

Levels of return are irrelevant and are included for illustration only.

## 2.3.3 Liquidity Risk Assessment

It is also important for the scheme’s administrator to carry out an assessment of how easy it might be to sell the assets, that is, transform the assets into cash (typically property, infrastructure, and private equity are not liquid assets).

Liquidity management is also a very important issue regarding ‘collateral management’ (see chapter 4). (p.48)

Table 2.18. Example of asset allocation and expected income

Investment/Year +1

Fund

Estimated income (£000)

Equity funds

A

496

(coupons)

B

486

C

491

Bonds

D

1,486

(dividends)

E

1,462

Infrastructure debt

F

295

LDI strategy

Collateral/Gilt

596

(coupons)

582

Total

5,895

# 2.4 Asset and Liability Management Framework

At the beginning of this chapter, we saw that a typical ALM structure is as shown in Figure 2.23.

As mentioned earlier, it is my strong belief that the best ALM management approach is not to manage the asset side alone but to manage both sides as a balance in order to find the right equilibrium.

In Figure 2.6 (Recovery plan to get a funding ratio (assets/liability) at 100 per cent in ten years), we saw that the target is that both lines (liabilities and assets) must meet in the future.

To do so in a context of deficits, decision-makers have to determine a portfolio of assets that outperform the liabilities. The problem is that assets and liabilities are not exactly correlated: as assets and liabilities face the same event, they move differently because their sensitivities are different. This is termed ‘mismatches of duration’.

## 2.4.1 Duration? What Is It?

Duration is a very important concept to use to hedge the liability risks. Fundamentally it is a measure of the sensitivity of a bond’s price to any change in interest rates. The duration of a bond (or a loan) is a measure of its sensitivity and how long bond-holders will have to wait, on average, to receive cash payments. Duration is an indicator of risk: the longer the bond, the more it is price sensitive to interest rates.

In chapters 3 and 4 ‘Understanding Liabilities’ and ‘Understanding Liability Driven Investment’, we will see that one can use the sensitivity indicator (or PV01) which is close to the duration and measure the relation between the price of a bond and its yield to maturity (the internal rate of return). In other words, the sensitivity (p.49)

Figure 2.23. Typical ALM structure

or PV01 measures the change in the value of liabilities for one basis point change (0.01 per cent) in the interest and/or inflation rate (known as ‘IE01’).

Mismatches of duration between the liabilities and the assets are the only issue to manage. Trustees have to ask what the duration of liabilities and assets are in order to measure the mismatches (see Figure 2.25).

On the asset side, we saw that each asset has its own risk (volatility); they behave differently as they face the same event.

The correlation between assets within the portfolio of growth assets also has to be monitored and managed as the correlation between assets is not constant (i.e. correlation is dynamic). As a result, the performance of the funding ratio can be influenced by liabilities and/or assets risk-adjusted performance.

## 2.4.2 What Kind of Mismatches Are We Talking about?

For example, in the ALM structure (Figure 2.24), on the asset side the asset classes are equity, credit, infrastructure, property and hedge funds. On the liability side, there are interest rate and inflation risks (we will not talk about longevity issue at this point).

As we will see in chapter 4 with precise examples, the mismatches of duration are as shown in Figure 2.25.

Notice the difference of duration (sensitivities) between assets and liabilities. (p.50)

Figure 2.24. Typical building blocks of an ALM funding, monitoring, and duration management

Figure 2.25. Funding ratio monitoring and duration management illustration

Note: (*) These numbers are for illustration only. A precise analysis per asset class would present more precise durations and risks numbers.

## (p.51) 2.4.3 Except Mismatches of Interest Rates and Inflation Duration, Are There Other Mismatches to Manage?

Typically, for example, there are credit mismatches:

• on the asset side, in the growth asset portfolio, there are typically corporate bonds, loans, emerging market debt, infrastructure debt, and so on

• on the liability side of the ALM structure, the credit risk is different from the credit risk on the asset side, which is typically, for large corporates, an ‘AA’ credit risk

• as a result, the correlation between both credit risks are neither exact nor stable (i.e. the correlation is dynamic).

Figure 2.26. ALM: risk and performance management against a common benchmark

(p.52) As most pension funds are currently under-funded because of mismatches of duration, the trustees have to build a growth asset portfolio that outperforms consistently volatile pension fund liability. The problem is that it is a difficult target to reach—if not impossible!

## 2.4.4 My View about Asset and Liability Management Maximization

An efficient approach could be to separate the management of the ALM structure into two parts with a common benchmark (see Figure 2.26).

In order to reduce the deficit, the growth asset portfolio has to outperform the liability by an excess performance, that is, a margin: m per cent (see Figure 2.27).

In the Figure 2.27 above, we see that there are not enough assets today to pay future liabilities in ten years’ time. Assets have to outperform liabilities over the relevant time period of the investment:

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Schemes own a growth portfolio of assets (equity, corporate bonds, etc.) that has to generate a return greater than the liability return.

Breaking the ALM structure into two parts—management of the liability on one side and management of the assets on the other side—is an easier way to manage it.

Figure 2.27. Necessary outperformance of the assets against the liability to reduce deficit

## (p.53) 2.4.4.1Liability and Assets Risk adjusted PerformanceManagement with a Common Benchmark

On the asset side, the performance of the assets is measured by:

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and on the liability side, the performance of the liabilities is measured by:

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Assets have to outperform the liability by an excess performance (+ margin x%) As the performance of the Assets and the performance of the Liability are not correlated, the liability and the assets could be separately managed. A common benchmark could be introduced to manage and monitor the performance of each side i.e. Assets and Liability. As result, we should look for achieving the following targets:

Performance of the Assets > Performance of the common Benchmark

Performance of the Liabilities + performance of the hedging Assets < Performance of the common Benchmark

By definition, pension funds are ‘short’ on the liability side i.e. pension funds owe money in the future; the following formula says that if interest rates go up, the value of the liability goes down and vice versa.

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Where,

i: interest rate

n: period

If a scheme owes £100 in twenty years’ time, what amount does the scheme need now given a return of 5 per cent a year for twenty years?

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Currently, the scheme needs £37.68 today to meet its future obligations. However, if the twenty-year interest rate increases by 1 per cent and reaches 6 per cent, the scheme needs only £31.18.

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On the liability side, an increase of nominal rates (with an unchanged inflation rate) has a positive effect. On the asset side, a decrease of nominal rates (with an unchanged inflation rate) has a negative effect.

(p.54) In the two assets and liabilities performance formulae, notice that the common factor is the ‘benchmark’ which could be cash (LIBOR), gilts, ILGs, or an inflation index (RPI), and so on.

To put it simply, in breaking assets and liabilities into two parts, there are two positions to manage:

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If the liabilities are fully hedged against interest rate and inflation risks (i.e. liabilities are fully immunized), the formula (benchmark + margin %) would apply to measure the performance of the assets only.

## 2.4.4.2 Target: Risk Reduction whilst Maintaining the Expected Return of the Growth Assets

### Funding Ratio Risk

Notice that there are risks in liabilities and in the portfolio of assets: as a result, there are risks in the funding ratio that have to be monitored and managed continuously.

Notice in Figure 2.28 a way to manage risk in a funding ratio by defining lower and upper limits of volatility. As the funding ratio improves, decision-makers should reduce the risk tolerance by narrowing the bands of the corridor of variations (e.g. volatility). In other words, as the funding ratio improves, take less risk!

Figure 2.28. Risk management: flight path (or recovery plan) with upper and lower limits

(p.55)

Figure 2.29. Risk management of the funding ratio

### Improvement of the Funding Ratio Equals More Liability Hedged

Hedging the liabilities could at some point be the main part of a funding ratio risk management process: the more the funding ratio improves, the more the liabilities risk could be hedged as illustrated in Figure 2.29.

# 2.5 Conclusion

At this point, the trustees would have:

• decided the objective to reach: technical provisions, buyout, or accounting valuation

• decided the horizon of investment

• established the required performance to get a funding ratio of 100 per cent

• selected the instruments that will be used to discount the liability cash flows (gilt, swap, LIBOR, RPI, etc.)

• decided the way the liabilities will be discounted; using entire nominal and inflation curves (gilt or swap) is more precise than a single nominal and inflation point

• a better understanding of how the assets and liabilities behave, their performance and risks

• defined an investment policy: for the growth asset portfolio, a definition of asset and risk allocations; for liabilities management, a definition of a hedging strategy regarding nominal and inflation risks

• a clear idea about the future benefits payable and a clear strategy in terms of liquidity and collateral management (explained within chapter 4)

• (p.56) a precise idea about the credit risk of the sponsor and how to monitor it

• a better idea of how to manage an ALM structure more efficiently

From here they can build a precise ALM framework (see Table 2.19).

## 2.5.1 ALM Objective and Strategy Framework: Overview of the Core Objectives

This ALM framework template will support trustees and sponsors in defining achievable objectives and in monitoring each item regularly (at the minimum on a monthly basis) to check if the strategy is efficient or not. Eleven major items comprised this ALM framework (see Table 2.19). The objectives and key metrics measurements are given as an illustration only in order to give a more precise idea of how to define and monitor them month after month. (A precise example is presented in chapter 6, ‘ALM Risk and Performance Monitoring’.)

## 2.5.2 Comments on Selected Items

Item 1: Trustees may decide that the funding ratio (FR) must be maintained above a defined level, for example, 60 per cent (60 per cent floor). If the FR falls below the floor, action has to be taken.

Item 3: This is the actual return of the investment. The actual return of the investment has to be compared to the required return and should be superior. The required return is the minimum return to reach a funding ratio of 100 per cent at maturity of the investment, that is, the horizon of investment.

Item 4: Trustees may decide that the standard deviation (volatility) of the FR of the scheme must not be above 10 or 15 per cent.

Item 5: There could be a liability hedging mechanism as the FR improves. There could also be a mechanism to reduce the size of the return-seeking assets as the FR improves (Figure 2.30).

Figure 2.30. Dynamic ALM management as the funding ratio improves

(p.57)

Table 2.19. ALM objective and strategy framework

Item

ALM risk performance framework

Key metrics Measurement

1

Long-term funding target

To be funded on technical provisions (TP)

Required return: gilt + 150 bps p.a.

by 31 December 2023

2

Funding strategy

To reach a funding ratio (FR) of 100% on a gilt or swap

Progression from current FR to 100% with a floor at 60%

basis by 31 December 2023

3

Investment strategy

Actual return vs required return

Actual return should be superior to the required return

4

Risk budget

FR must not fall by more than 15%

VaR measures FR in worst 5% of outcome over 1 year (1 yr VaR 95% confidence)

FR must not fall below 60%

FR floor: 60%

5

Hedging strategy

As FR improves, sell off risky assets to buy gilts and/or index-linked gilts to reduce the expected FR volatility

FR (with gilt + 150 bps discount factor basis)

Inflation and nominal hedge ratios target in a range of +/– 10% max of the FR

Nominal hedge ratioInflation hedge ratio

6

Liquidity cash flow

Close monitoring of cash liquidity

Net cash flows positive over the next 3 years and negative for the following 2 years

7

Liquidity collateral

To reduce as much as possible collateral in order to use it for return-seeking assets

Risk measurement: 1 yr VaR 95th Available collateral: 2 × (1 yr VaR 99.5) > required collateral

8

To monitor cash payment vs agenda Subject to credit event

9

To monitor credit risks of the sponsor

5 and 10 years CDS of the sponsor

10

Internal financial models

Expected return, volatility, and correlation

Internal models validated by independent experts and trustees

(p.58) Item 7: Cash flow management: in my example, the scheme has an expected positive net cash flow over the next three years (contributions plus net income from dividends and coupons plus investment amount is greater than benefits paid) and this turns negative later.

Item 8: Liquidity collateral management: the trustees have to define eligible assets for collateral management purpose. In terms of liquidity risk management strategy and as a buffer, they have to define the amount of available liquid assets. Depending on the ALM structure, the amount of available liquid assets could be up to twice the amount needed:

Available eligible collateral = 2 times VaR 99.5th one-year required collateral.