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## 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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# Investment Policy

## Understanding Asset Allocation Construction

Chapter:
(p.164) 5 Investment Policy
Source:
Defined Benefit Pension Schemes in the United Kingdom
Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780198738794.003.0005

# Abstract and Keywords

On the asset side, trustees must build a robust return-seeking asset portfolio in accordance with the risk and performance strategy defined in the ALM framework and the LDI strategy. This chapter provides the building blocks of an efficient investment portfolio strategy. Readers will understand the positive effect of diversification on the risk/return profile of portfolios and how to measure the skills of portfolio managers in security selection and the passive replication of risk-adjusted return of indexes. An overview is provided of the asset class universe and various management styles, the way to look at asset classes in terms of risk-adjusted returns. How to build various portfolios and undertake simulations in order to select the most appropriate portfolio to meet the objectives of performance and risk aversion are explained. Based on case studies, readers will learn how to analyse investment portfolios, simulations, build efficient frontiers and draw conclusions.

# 5.1 Introduction

At this point, trustees and sponsors:

• Know the size of the deficit and the margin over a benchmark (gilt, swap, RPI etc.) that has to be generated to get a funding ratio (FR) of 100 per cent over an agreed horizon of investment.

• Have defined a precise ALM framework which seeks to maximize the probability of reaching an FR of 100 per cent at maturity of the horizon of investment. They have defined a risk budget: they looked for a strategy that minimizes downside risk whilst maintaining a sufficient expected return on the assets.

• Have defined an efficient ALM strategy: in terms of ALM strategy, assets and liabilities are separated; the scheme is ‘long’ (trustees invest employer and employees contributions into assets) on the asset side and ‘short’ on the liability side (the scheme will pay cash flows in the future to pensioners). In terms of performance: on the asset side, assets have to deliver ‘benchmark + a margin’; on the liability side, liabilities have to deliver ‘benchmark – a margin’. There is a common benchmark and as a result, the margin that has to be generated by the assets has to be superior to the margin that has to be generated the liability.

• Understand how liabilities work.

• Have defined a precise liability hedging strategy.

Now, trustees have to build a robust return-seeking assets portfolio in accordance with the risk and performance strategy defined in the ALM framework (see Figure 5.1).

Where,

• Investment universe: asset class universe with the objective of investing in low correlated assets

• (p.165) Managers selection: passive or active

• Risk-adjusted performance objectives: required performance is to reach a FR of 100 per cent at the end of the horizon of investment.

# 5.2 Asset Management and Portfolio Construction: Introduction to Basics

Investments should be diversified by market exposure (asset classes, geographical zones, etc.); it is the simplest way to improve the ‘risk/return’ profile of the portfolio.

Alpha (skills of the portfolio manager about security selection) and Beta (no market view; passive replication of the risk-adjusted return of indexes) management styles combine complementary ways to maximize the Sharpe ratio.

$Display mathematics$

Active management should enhance risk controls and expected returns. Through dynamic asset allocations, asset managers rebalance asset classes within a given universe of assets.

Due to the long duration of their liabilities, pension funds should take advantage of their long-term investments allowing them to invest in illiquid assets.

Let us examine the items included in the Figure 5.1.

# 5.3 Asset Class Universe

Rather than investing heavily in equities, there is a broad investment universe to consider. This diversification allows the decision-makers to capture wider investment opportunities.

## 5.3.1 What Are Asset Classes?

Typically, a pension fund can invest in the asset classes illustrated in Table 5.1.

Figure 5.1. Growth asset management formula

(p.166) As investment solution providers such as consultants, asset managers, fiduciary managers build portfolios, they make assumptions in terms of expected return and expected volatility for each asset class (see Appendix III, ‘Growth Asset Portfolio Construction Principles’).

Table 5.1 is an example of expected returns and volatility per asset class over a particular horizon of investment. This approach is a support for building convictions about which asset classes to select and for defining of the risk allocations of schemes.

There are single asset class (equity, bonds, etc.) and multi asset class funds (diversified asset class funds) that can be actively or passively managed (see Figure 5.2). Concerning the multi asset class funds, there are a lot of options in

Table 5.1. Asset classes

Asset classes

Spread over cash

Annual Volatility

Beta return

Alpha return

Expected return

Cash

0.0%

0.0%

0.0%

0.0%

Government bonds/gilts

0.6%

0.0%

0.6%

3.5%

Index-linked gilts

0.6%

0.0%

0.6%

9.0%

Corporate bonds

1.6%

0.6%

2.2%

6.5%

High yield bonds

2.4%

0.8%

3.2%

9.5%

Emerging market debt

2.4%

0.8%

3.2%

9.5%

Developed market equity

3.1%

1.1%

4.2%

17.0%

Emerging market equity

4.1%

1.1%

5.2%

25.0%

Property/infrastructure

2.1%

0.1%

2.2%

12.0%

Hedge funds

1.1%

2.1%

3.2%

8.0%

Commodities

4.1%

0.1%

4.2%

25.0%

Private equity

5.1%

0.1%

5.2%

35.0%

Risk parity passive

3.1%

1.1%

4.2%

11.9%

etc.

Figure 5.2. Investment universe style

(p.167) terms of the way they can be managed: for example, if a scheme has defined objectives in terms of return and volatility, the asset allocation of the portfolio of asset classes can be bespoke.

What does Figure 5.2 teach us?

As mentioned earlier, there are single assets (equity, bonds, etc.) and diversified assets (or multi-assets). They can be passive, that is, there is no market view: asset managers replicate an index or a basket of indexes.

They can be active: asset managers have convictions about trends or take positions as they notice anomalies in the valuation of assets prices; it is a dynamic approach with more or fewer constraints depending on the objectives of the investors. The constraints can be defined in terms of limit of risks (volatility), credit risks per rating or sectors, leverage, and so on. In this instance, you can ask the asset manager to generate a performance of a few basis points above an index (index plus a performance margin) or a performance with no-correlation to indexes (absolute return).

Asset managers can be ‘long’ only, which means that they are only buyers of assets. Asset managers can be ‘long/short’, which means that they can buy assets when they think these assets are cheap and at the same time, they can sell other assets when they think that they are expensive.

# 5.4 Alpha and Beta

## 5.4.1 Alpha (α‎) Definition

Alpha is the risk-adjusted excess return of an investment. It is a measure to assess an investment manager’s performance over a benchmark index or ‘risk-free rate’ investment. This way, through active investment management decisions, asset managers (absolute return funds and hedge funds) should make more money than passive strategy investments (Beta).

Alpha is the additional return above the Beta. It is the return generated by taking idiosyncratic risk (see section 5.4.3.2). If an active manager aims to achieve an outperformance of 3 per cent per annum over benchmark, the 3 per cent corresponds to the Alpha.

## 5.4.2 Beta (β‎) Definition

Beta is the return generated from a portfolio exposed to overall market returns. It is the return that can be achieved in investing in index-tracking funds. It is the equivalent of being exposed to systematic risk (see section 5.4.3.1).

## (p.168) 5.4.3 Systematic and Idiosyncratic Risk Definition

### 5.4.3.1 Systematic Risk Definition

Systematic risk is the risk that comes from investing in any security within the market. It is represented by Beta exposure.

### 5.4.3.2 Idiosyncratic Risk Definition

Idiosyncratic risk is the risk that comes from investing in single securities. It is represented by Alpha exposure. When there is more than one Alpha position in the portfolio, the portfolio will reflect the addition of each Alpha position’s idiosyncratic risk.

## (p.169) 5.4.4 Alpha–Beta Framework

At some point, a pension fund can decide to ask an asset manager to generate a performance comprising Beta and Alpha: for example, he could be asked to generate a performance of benchmark + 2 per cent per annum.

Figure 5.3 gives an example of overall performance dominated by Alpha manager skills.

Figure 5.3. Breakdown of the performance between beta and alpha

## 5.4.5 What Is the Breakdown between the Beta and Alpha of a Scheme?

### 5.4.5.1 Expected Return Breakdown

Let us consider the following growth asset portfolio and expected returns (Table 5.2).

There are two asset classes: equity and bonds.

The expected return for equity is 7 per cent and for bonds 4 per cent.

The expected return from Alpha is 0.9 per cent for the equity and 1.1 per cent for the bonds. Consequently, the expected return of the portfolio is 6.85 per cent (4.90% + 1.95% = 6.85%).

Approximately 29 per cent of the return comes from Alpha.

### 5.4.5.2 Risk Breakdown

What is the breakdown of risks between Beta and Alpha?

Let us assume that the risk (standard deviation) is 15 per cent for the equities and 7 per cent for the bonds and the correlation between the two assets is 0.30, the standard deviation of the portfolio is 7.58 per cent.

Where,

$Display mathematics$

where,

WA= weighted amount of asset A

WB= weighted amount of asset B

σ‎A = volatility of asset A

σ‎B = volatility of asset B

ρ‎AB = correlation between A and B

What is the risk from Alpha?

You have to measure the risk that the asset manager is willing to take. We can make the assumption that the risk can be measured as a multiple of the active return, that is, the standard deviation is twice the targeted outperformance. For example, if the targeted excess return over a benchmark is 1 per cent (FTSE 100 + 1%), the standard deviation is 2 per cent.

In our example, Alpha is 3 per cent for equities, we can assume that the additional standard deviation is 6 per cent.

For the bonds, as Alpha is 1.50 per cent, we can assume that the additional standard deviation is 3 per cent.

As a result, the risk coming from Alpha is:

$Display mathematics$
(p.170)

Table 5.2. Illustration of the breakdown of the expected return of a portfolio

Asset Allocation

Breakdown

Targets Benchmark +

Alpha

Expected Return

Breakdown Expected return

Expected return from Alpha

Total Expected Return

Equities

30%

FTSE 100 +

3%

7%

2.10%

0.9%

Bonds

70%

iBoxx £ Gilts over 15 yrs +

1.50%

4%

2.80%

1.1%

Total

100%

4.90%

1.95%

6.85%

(p.171)

Table 5.3. Beta and Alpha management, per asset class, from liquid to illiquid

Beta and Alpha

From liquid asset classes to illiquid ones

Equity

Corporate bonds

Infrastructure debt

Diversified assets

ABS, RMBS

Infrastructure Equity

Government bonds

High yield

Property

Commodities

Leverage loans

Private equity

CTA (futures and indexes)

Emerging market debt

Unlisted property

Currency

Listed property

Direct SME lending

Hedge funds

Distressed debt

The total risk is:

$Display mathematics$

In the above formula, notice the 30 per cent correlation between Alpha and Beta.

Normally, the correlation would be nil as the aim of Alpha strategies is to generate un-correlated performance.

If we assume that there is no correlation between Beta and Alpha, it means that there would not be additional risk due to an additional performance.

We saw earlier that criteria to invest could be:

• expectations on trends, that is, are we convinced about potential outperformance of asset classes

• investment style: active or passive management.

Another one would be the liquidity of the asset classes and our preference to secure regular cash flows in the future, that is, fixed income, debt.

We could mix the above factors of the equation—asset classes, investment style (Alpha and Beta), liquidity, and credit in a table as in Table 5.3.

In Table 5.3, for example, notice that equity or government bonds can be passively (Beta management) or actively managed (Alpha management).

Some asset classes can be liquid (equity, government bonds, etc.) or illiquid (infrastructures, property etc.).

## 5.4.6 Conclusion

I think that scheme sponsors are typically too focused on Beta management which aims to generate a return in excess of the liability. The schemes should balance the exposure to Alpha and Beta. By definition, Alpha is not highly correlated to other asset classes and as mentioned, the additional expected (p.172)

Table 5.4. Overview of Alpha and Beta

Beta

Alpha

Overall market returns

Asset manager skills

As the objective replicates the return of an index with no market views, no experience is required to select asset managers

Experience is required of the decision-makers to select skilled asset managers

Low correlation

Correlation to Beta or other Alpha varies

Low fees

High fees

Fixed fees + performance fees above a hurdle rate

e.g. fixed management 2%

performance fees: 20% above 5% return

return adds little risk. Consequently, active management should improve the Sharpe ratio (see Table 5.4).

In terms of liquidity, as typically pension funds in the UK have twenty years’ duration, they should take advantage of this situation to invest in illiquid asset classes such as real assets like property, infrastructure, and so on, hedge funds, private equity, and so on, to diversify sources of return and make opportunities to generate Alpha.

# 5.5 Growth Asset Portfolio: Risk-adjusted Performance Objectives

In chapter 2, ‘Understanding Asset and Liability Management’, we saw that the first step of an ALM restructuring process is to calculate the size of the deficit and the required performance to get a FR of 100 per cent at the end of the agreed horizon of investment.

We saw also that trustees would compare the current ALM strategy, that is, the current investment strategy to other ALM strategies in order to select the most appropriate one in terms of risk-adjusted performance.

## 5.5.1 Case Study

Let us consider an example of an analysis of a typical UK pension fund:

• The current FR is at 80 per cent in technical provisions.

• Trustees have a 100 per cent FR objective in ten years.

• The pension fund has a twenty-year duration with 70 per cent inflation-linked and 30 per cent not linked to inflation (nominal cash flows, i.e. fixed cash flows).

• (p.173) The amount of the growth asset portfolio is £1,000m.

• Liabilities are discounted with over fifteen years’ duration UK liquid no-govt inflation

• Linked bonds and over fifteen years’ duration liquid UK corporate bonds.

• Forward-looking analysis assumptions:

• Assets: assumptions were made on expected returns, volatility, and correlation over the ten-year investment period on various asset classes. You can find at the end of case study Table 5.10 which includes returns, volatility, and correlation assumptions used for the analysis.

• Based on a conservative approach, liabilities were discounted with an inverted yield curve.

### 5.5.1.1 ALM Structure

ALM structure is illustrated in Figure 5.4.

The current asset allocation is shown in Figures 5.5–5.6.

### 5.5.1.2 What Are the Metrics above?

#### Item 1

Based on the expected returns per asset class (see Table 5.5), an expected return of the portfolio is calculated (Table 5.6). As the return per annum of the portfolio is invested, consequently, this generates a return as well (compound interest).

Figure 5.4. Typical ALM structure of a defined benefit pension fund

(p.174)

Figure 5.5. Overview of the current asset allocation

Figures 5.6 Breakdown of the current asset allocation

#### Item 2

It is the expected standard deviation of the portfolio based on the assumptions of risk of each asset class and the correlation between them. (p.175)

Table 5.5. Breakdown of the current asset allocation

Asset Class

Asset Allocation (%)

Expected compound Return (%)

Expected Risk (%)

UK equity

24.00%

7.75%

15.00%

UK corporates equity

22.50%

6.25%

6.00%

Overseas ex-UK equity

25.00%

8.00%

17.00%

Emerging market equity

1.50%

9.50%

24.00%

Global infrastructure fund

3.00%

8.75%

13.00%

UK nominal gilt > 15 years

12.00%

3.50%

5.00%

UK ILG > 15 years

12.00%

2.50%

6.50%

Total

100.00%

Table 5.6. Overview of the metrics of the current asset allocation

Item

Risk and Performance Metrics

1

Expected compound return

6.80%

2

Expected portfolio volatility

8.90%

3

Expected Sharpe ratio

0.42

4

Portfolio 1 yr VaR (£m)

137

5

Expected deficit volatility

9.69%

#### Item 3

This is the Sharpe ratio

$Display mathematics$

Where,

Risk-free rate: gilt 3.50%

The higher the ratio, the better.

#### Item 4

This is the amount of the VaR of the growth portfolio of assets (see how VaR works in chapter 2, ‘Understanding Asset and Liability Management’).

Then, this result has to be compared to the:

1. a-annual contributions paid by the sponsor

2. b-shareholder’s equity of the sponsor

3. c-free cash flow generated by the sponsor

4. d-operating profit generated by the sponsor.

If this loss occurs and is large relative to four points above, deterioration of the credit risk of the sponsor and the valuation of the stocks (if the sponsor is listed) may happen.

(p.176) There are other VaRs to examine such as the VaR on deficit, liquidity, and collateral management (we saw this last item in the conclusion of chapter 2), credit VaR, and so on.

In order to simplify this case study, we examine the VaR of the portfolio of growth assets.

#### Item 5

This is the expected annual volatility (standard deviation) of the deficit (the deficit of 80 per cent has been included in the calculation).

### 5.5.1.3 Constraints of the Analysis

Part of every analysis are the constraints which have been defined based on the convictions and the risk aversion of the trustees.

The constraints in this instance are the following:

• In order to hedge the liabilities with derivatives, the scheme has to hold cash equal to at least 30 per cent of the swaps.

• Trustees want at least 30 per cent of the portfolio invested in equity.

• Trustees want a minimum of 50 per cent of total equity invested in UK equities.

• Trustees want the percentage of the amount invested overseas not to be greater than the UK equity exposure.

• The alternatives exposure cannot be above 30 per cent of the total asset allocation.

• Each alternative is limited to a maximum 10 per cent allocation.

• Property allocation exposure equals the allocation in infrastructure.

At this point, we can examine various asset allocations and liability coverage and select the most appropriate ones relative to the ALM framework defined by the trustees and their constraints (see Table 5.7 and Figure 5.7).

The definition of a portfolio’s efficient frontier and how to build it is explained in Appendix III, ‘Growth Asset Portfolio Construction Principles’.

Notice in Figure 5.7 the current portfolio in terms of expected returns and expected volatility of the assets and liabilities. You can compare the current portfolio strategy to other portfolios.

Each liability cash flow has been discounted with the appropriate nominal gilts and Indexed-linked gilts (ILGs) plus a margin (AA rating). For example, the five-year liability was discounted with the five-year government bonds (gilt or ILG) plus a margin. (p.177)

Table 5.7. Portfolios simulation

Item

Risk-free rate

3.50%

Portfolios simulation

Metrics (%)

Current Portfolio

A

B

C

D

E

F

G

H

I

J

1

Expected compound return

6.8%

5.4%

5.8%

6.3%

6.6%

7.0%

7.4%

7.8%

8.1%

8.4%

8.8%

2

Expected volatility

8.9%

8.0%

8.1%

8.2%

8.4%

8.5%

8.8%

9.5%

10.6%

11.5%

12.8%

3

Deficit volatility

9.7%

5.5%

5.8%

6.2%

6.6%

7.0%

7.4%

8.2%

9.3%

10.8%

12.9%

4

Expected Sharpe ratio

0.38

0.24

0.29

0.33

0.38

0.41

0.45

0.45

0.43

0.43

0.41

5

Duration coverage

18.1%

56.8%

54.4%

51.7%

49.0%

46.0%

42.3%

37.4%

34.4%

23.4%

5.3%

Breakdown per asset class (%)

6

UK cash

11.3%

11.7%

12.1%

12.6%

13.0%

13.3%

12.9%

12.2%

7.2%

7

UK gilts

11.8%

8

UK corporate

23.0%

12.6%

22.7%

29.8%

36.6%

34.6%

18.3%

4.0%

9

UK long Gilts

10

UK long corporate (over 15 yrs)

18.1%

13.6%

9.3%

6.1%

2.8%

11

UK government inflation-linked long duration

11.8%

35.9%

27.1%

19.2%

11.6%

4.0%

12

European high yield bonds

8.8%

16.4%

21.0%

22.6%

13

Emerging Markets Debt

7.4%

11.8%

6.8%

14

UK equity

24.0%

19.7%

18.2%

17.0%

16.1%

15.4%

15.0%

15.0%

15.0%

15.0%

20.3%

15

Overseas equity ex-UK equity

25.0%

9.8%

9.1%

8.5%

8.1%

7.7%

7.5%

7.5%

7.5%

7.5%

10.1%

16

Emerging markets equity

1.5%

0.5%

2.7%

4.4%

5.8%

6.9%

7.5%

7.5%

7.5%

7.5%

10.1%

17

UK leveraged buyout

0.2%

3.5%

10.0%

10.0%

18

Mezzanine debt

4.8%

5.0%

5.0%

5.0%

5.0%

5.0%

5.0%

5.0%

19

Commodities

0.0%

0.8%

1.9%

4.8%

1.5%

20

Property

0.9%

2.5%

3.9%

7.6%

10.0%

10.0%

10.0%

10.0%

21

Infrastructure

3.0%

0.9%

2.5%

3.9%

7.6%

10.0%

10.0%

10.0%

10.0%

22

30-year swap

37.7%

39.0%

40.5%

41.9%

43.4%

44.4%

43.0%

40.6%

24.0%

0.0%

Asset allocation (%)

Fixed income allocation

46.5%

65.2%

65.0%

63.3%

60.1%

56.4%

47.9%

40.0%

40.0%

40.0%

29.4%

Equity allocation

50.5%

30.0%

30.0%

29.9%

30.0%

30.0%

30.0%

30.0%

30.0%

R30.0%

40.6%

Other allocation

3.0%

4.8%

5.0%

6.7%

9.9%

13.6%

22.1%

30.0%

30.0%

30.0%

30.0%

Total allocation

100%

100%

100%

100%

100%

100.0%

100.0%

100.0%

100%

100%

100%

(p.178)

### (p.179) 5.5.1.4 Based on the ALM Framework Defined by the Trustees, Which Portfolio Strategies Offer the Best Solutions?

Let us examine more closely portfolio E in Table 5.8.

A thirty-year swap is included in the asset.

Figure 5.7. Efficient frontier

Table 5.8. Risk and performance metrics of portfolio E

Risk and performance metrics

Item

Item

Portfolio E

1

Expected compound return

7.04%

2

Expected portfolio volatility

8.54%

3

Expected Sharpe ratio

0.45

4

Portfolio 1 yr VaR 95th (£m)

124

5

Expected deficit volatility

7.00%

Table 5.9. Comparison of the risk and performance metrics of the current strategy and portfolio E

Risk and performance metrics

Item

Item

Current portfolio

Portfolio E

1

Expected compound return

6.80%

7.04%

2

Expected portfolio volatility

8.90%

8.54%

3

Expected Sharpe ratio

0.42

0.45

4

Portfolio 1 year VaR 95th (£m)

137

124

5

Expected deficit volatility

9.69%

7.00%

(p.180)

Figure 5.8. Portfolio E

Let us now compare the metrics of the current strategy to strategy E in Table 5.9.

#### Comments

Portfolio E seems to be an interesting one to select as:

• The expected return is higher (7.04 per cent vs 6.80 per cent)

• The expected volatility of the portfolio is lower (8.54 per cent vs 8.90 per cent)

• The Sharpe ratio is higher than the current portfolio (0.45 vs 0.42)

• The 1 yr VaR 95th is lower (£124m vs £137m)

• The expected volatility of the deficit is a lot lower (7.00 per cent vs 9.69 per cent).

# 5.6 Implementation Risk of the Strategy

## 5.6.1 Relative Value of Hedging Assets

Trustees have to be careful about the implementation: typically, UK pension funds wish to implement the same strategy at the same time. They buy the same hedging assets (nominal and inflation-linked) and hedge the same maturities. This creates anomalies in the curves.

Consequently, these assets become very expensive.

## (p.181) 5.6.2 Basis Risk

If the actuary of the scheme uses gilts and ILGs to discount the liabilities and swaps are used to hedge the liabilities, there is a basis risk: the liabilities are sensitivity hedged but not in terms of spread. Swaps do not behave like government bonds. The spread between both is not constant over time.

If swap rates are below gilt rates, the negative spreads reduce the attractiveness of the swap instruments.

## 5.6.3 Liquidity Risk

Consequently with this strategy, trustees have to be careful about the liquidity of the corporate bonds (nominal and inflation-linked).

## 5.6.4 Inflation Risk

Long dated inflation bonds are difficult to buy.

# 5.7 Conclusion

We saw that a strategy is about how you define an asset and a risk allocation with the objective of reaching an FR of 100 per cent at the horizon of investment.

We saw also that diversification across various asset classes, regions, and sectors is an important issue as well as balancing Beta and Alpha. As Alpha is not highly correlated to other sources of returns (Alpha and Beta), it is an interesting investment approach without increasing the level of risks.

As the duration of the pension fund is quite long, more should be invested in illiquid assets (real assets such as property, infrastructure, social housing, or private equity, etc.).

Usually, because of the illiquidity, there is a premium in terms of return that pension funds should capture.

The selection of an asset manager is very important; the definition, the monitoring of the performance and the risk of the investment policy, and making regular tactical and opportunistic adjustments is a lot more important. The risk allocation has to be dynamic to reflect the dynamism of the financial markets (for example, switching from growth assets to liability hedging assets, from equity to credit bonds, loans, or structured finance).

I believe that designing and managing a sustainable risk-adjusted performance portfolio is both a science and an art.

Understanding how participants perceive the market, what drives investment decisions, what drives the returns of the asset classes of your portfolio, how they behave together, judging the timing to invest or disinvest is beyond statistics and modelling; it is an art that few participants master successfully over a long period of time.

If you wish to know more about the ‘efficient frontier’ topic, you can read Appendix III, ‘Growth Asset Portfolio Construction Principles’.

Table 5.10. Expected compound return, volatility, and correlation hypothesis

Expected return/volatility/correlation

Expected compound return

Volatility

Sharpe

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

24

25

26

27

1

UK cash

3.50%

0.50%

0.00

1.00

2

UK gilts

3.50%

5.00%

0.00

0.23

1.00

3

UK corporate

6.25%

6.00%

0.46

–0.13

0.53

1.00

4

UK long gilts

3.75%

8.25%

0.03

0.16

0.97

0.60

1.00

5

UK long corporate (over 15 yrs)

4.25%

7.75%

0.10

0.09

0.93

0.73

0.98

1.00

6

UK govt. inflation-linked (over 15 yrs)

3.25%

6.50%

–0.04

–0.05

0.59

0.54

0.62

0.64

1.00

7

European high yield bonds

7.75%

15.00%

0.28

–0.30

0.08

0.45

0.13

0.22

0.45

1.00

8

Emerging markets debt

7.50%

12.50%

0.32

0.14

0.28

0.26

0.27

0.29

0.38

0.44

1.00

9

UK equity

7.75%

15.00%

0.28

–0.17

–0.12

0.32

–0.05

0.05

0.18

0.59

0.45

1.00

10

UK small cap equity

8.00%

21.50%

0.21

–0.24

–0.10

0.32

–0.01

0.08

0.23

0.61

0.46

0.46

1.00

11

Overseas ex-UK equity

8.00%

17.25%

0.26

–0.10

–0.06

0.22

0.01

0.07

0.24

0.61

0.61

0.61

0.78

1.00

12

US large capitalization

7.50%

17.00%

0.24

–0.06

–0.07

0.15

–0.01

0.04

0.16

0.51

0.61

0.61

0.69

0.96

1.00

13

Europe ex-UK equity

8.00%

20.50%

0.22

–0.12

0.00

0.27

0.07

0.13

0.28

0.65

0.52

0.52

0.79

0.93

0.93

1.00

14

Japanese equity

7.50%

18.75%

0.21

–0.03

0.04

0.21

0.09

0.12

0.27

0.38

0.49

0.49

0.58

0.71

0.71

0.57

1.00

15

Asia ex-Japan equity

9.50%

23.50%

0.26

–0.15

–0.06

0.21

0.01

0.07

0.21

0.61

0.48

0.48

0.75

0.83

0.83

0.76

0.60

1.00

16

Emerging markets equity

7.75%

24.00%

0.18

–0.16

–0.09

0.23

–0.01

0.06

0.23

0.65

0.52

0.52

0.79

0.87

0.87

0.82

0.62

0.95

1.00

17

US REITS

6.50%

24.25%

0.12

–0.15

–0.08

0.29

0.13

0.18

0.35

0.42

0.43

0.43

0.50

0.57

0.57

0.56

0.41

0.44

0.46

1.00

18

European REITS

7.50%

19.50%

0.21

–0.29

–0.15

0.42

0.20

0.27

0.40

0.56

0.45

0.45

0.66

0.64

0.64

0.66

0.48

0.53

0.55

0.74

1.00

19

Diversified hedge funds

5.50%

7.50%

0.27

–0.20

–0.21

0.29

–0.14

–0.04

0.17

0.45

0.20

0.50

0.50

0.49

0.33

0.51

0.38

0.57

0.65

0.15

0.28

1.00

20

Directional hedge funds

8.50%

9.50%

0.53

–0.28

–0.22

0.33

–0.13

–0.02

0.22

0.64

0.28

0.67

0.67

0.68

0.54

0.69

0.47

0.70

0.78

0.36

0.47

0.91

1.00

21

Non-directional hedge funds

8.00%

6.50%

0.69

–0.31

–0.17

0.46

–0.10

0.03

0.29

0.60

0.17

0.49

0.49

0.43

0.28

0.45

0.30

0.53

0.61

0.28

0.41

0.85

0.85

1.00

22

UK LBO

7.00%

23.50%

0.15

–0.33

–0.15

0.36

–0.05

0.04

0.25

0.51

0.23

0.66

0.66

0.64

0.56

0.66

0.42

0.55

0.62

0.61

0.67

0.57

0.71

0.60

1.00

23

Mezzanine debt

8.25%

12.50%

0.38

–0.30

–0.07

0.45

–0.02

0.11

0.46

0.78

0.43

0.51

0.51

0.50

0.40

0.49

0.34

0.53

0.57

0.49

0.56

0.50

0.65

0.71

0.54

1.00

24

Commodities

7.00%

16.00%

0.22

–0.03

0.01

0.17

0.07

0.10

0.27

0.26

0.26

0.30

0.30

0.35

0.26

0.30

0.37

0.35

0.40

0.13

0.25

0.34

0.32

0.40

0.29

0.26

1.00

25

Real estate

8.25%

12.50%

0.38

–0.29

–0.05

0.34

0.09

0.16

0.31

0.50

0.38

0.60

0.60

0.57

0.52

0.59

0.43

0.48

0.50

0.67

0.90

0.27

0.44

0.39

0.62

0.52

0.23

1.00

26

Infrastructure

8.75%

12.75%

0.41

–0.07

–0.18

0.21

0.21

0.15

0.12

0.20

0.19

0.21

0.21

0.21

0.19

0.22

0.17

0.17

0.18

0.27

0.37

0.07

0.13

0.12

0.21

0.19

0.09

0.32

1.00

27

30-year swap

0.45%

9.50%

–0.32

0.30

0.74

0.41

0.74

0.72

0.35

0.02

0.24

–0.16

–0.06

–0.06

–0.05

–0.03

0.03

–0.01

–0.04

0.10

0.07

–0.15

–0.17

–0.15

–0.08

–0.06

0.04

0.00

0.12

1.00

(p.183)