Performance Attribution for Strategic Asset Allocation Decisions

Performance Attribution for Strategic Asset

Allocation Decisions

A Practical Approach for Pension Funds

D. Visser January, 2009

Abstract

In this paper a model is presented to measure performance attribution in terms of actual funding ratio risk and return, for a strategic asset allocation decision of a pension fund. For the period 2006-2008, I find that the decision for aggressive investments by adopting stock funds in the strategic asset allocation results in performance attribution which is linked to the asset-class return and an increase in funding ratio risk. On the other hand, conservative investments by adopting fixed income, inflation linked bonds and a swap overlay decrease funding ratio risk. Performance attribution for including these asset classes is determined by the return on liabilities. Overall, this model can be practically applied by pension funds.

JEL classification: G11, G23

Performance Attribution for Strategic Asset

Allocation Decisions

A Practical Approach for Pension Funds

D. Visser Pioenstraat 139 9713 XW Groningen s1487108@student.rug.nl Master Thesis MSc Business Administration Specialization Finance University of Groningen

Faculty of Economics & Business Supervisor University of Groningen: Dr. A. Plantinga

ACKNOWLEDGEMENTS

This thesis is the final part of the program Business Administration specialization Finance and is written during a 5 month internship at TKP Investments in Groningen. I would like to thank Auke Plantinga of the University of Groningen for his role as supervisor in providing helpful feedback and suggestions during our meetings. I also would like to thank Roelie van Wijk-Russchen and Coos Luning of TKP Investments for offering the opportunity to conduct an interesting research in a pleasant working environment. Finally, I would like to thank the rest of my colleagues at TKP Investments for their willingness to be of assistance in the process.

CONTENTS

ACKNOWLEDGEMENTS ...III CONTENTS ... IV

1. INTRODUCTION ... 1

2. BACKGROUND... 3

2.1 Approach and Regulation... 3

2.2 Liabilities... 4

2.3 Surplus Optimization... 6

2.4 Liability Driven Investing... 7

2.5 Strategic Asset Allocation... 8

3. DATA... 10 3.1 Correlation... 10 3.2 Asset Classes ... 11 3.3 Actual Portfolio ... 19 3.4 Funding Ratio... 21 3.5 Specific Questions ... 22 4. METHODOLOGY ... 23

4.1 Funding Ratio Return... 23

4.2 Return Models ... 24 4.3 Risk Models ... 30 5. RESULTS... 31 5.1 Actual Statistics ... 31 5.2 Performance Attribution... 32 5.3 Swap Overlay... 35

5.4 Alternative Asset Allocations ... 36

1. INTRODUCTION

Asset allocation strategies for Dutch pension funds have become a complex issue in the last few years. On the one hand, the introduction of the Financial Assessment Framework1 _{in 2007 tends}

towards a more conservative approach. Based on the protection of the pension beneficiaries, it forces pension funds to give a clear understanding about the structure of their assets versus liabilities; providing a fair valuation along with transparency of risks involved. On the other hand, a more aggressive approach is favoured to manage the risk-return trade-off of the assets. Employers demand low pension contributions against the demand for high pensions for beneficiaries, which forces pension funds with the task of earning high returns on their investments. This means pension funds must find a suitable strategy which determines the overall risk profile of the investments. Pension funds therefore shifted to strategies that take liabilities and their respective risks into account to design their strategic asset allocation.

The major cause of the shift towards a liability driven investment strategy is the equity bear market crisis in the period 2000-2002. During the equity bull market of the ‘90s, pension funds increased the proportion of stocks; earning high returns and creating sometimes large surpluses. This increased exposure to stocks, caused a dramatic decrease in their plan asset holdings in the respective bear period. In addition, falling interest rates increased plan liabilities; jointly causing a dramatic reduction of the funding ratios2. By 2002, the total funding ratio of fortune 500 defined benefit plans decreased from 123 to 81%3_.

The core business of a pension fund is to make sure that pensions are paid. Therefore emphasis on hedging liability risk is required. Hence, several new asset classes are included in the strategic asset allocation. These asset classes include inflation linked bonds and interest rate swaps to hedge inflation and interest rate risk. In addition, alternative assets such as real estate, commodities and hedge funds have become part of the asset allocation strategy to increase the opportunity for return enhancement and diversification.

Since 2005, TKP Investments follows the rules of the Financial Assessment Framework in a defined benefit plan. Every year, an Asset Liability Management (ALM) study is conducted

1 _{In the Netherlands: Financieel Toetsingskader}

2 _{Funding ratio: Nominal assets divided by nominal liabilities}

3 _{Numbers from Zion. D. and Carchashe, Pension Plans Getting Weaker This Year, CSFB Pension Update,}

which identifies the most favourable strategic asset allocation for a single fund. The ALM study adapts portfolio management process while managing liability constraints, in which enhanced active management is allowed to increase profitability. As a part of that; hedging risk of the liabilities is referred to as the conservative approach and adopting assets to increase profitability as the aggressive approach on liability driven investing. In practice, strategic asset allocation is designed as a trade-off between both approaches. There is no performance measure which identifies performance attribution for these approaches on actual risk and return of the funding ratio. Therefore the research question assumed in this paper is:

What is the performance attribution for a strategic asset allocation decision in terms of actual funding ratio risk and return?

This strategic asset allocation decision considered is the decision to include a specific asset class in the strategic portfolio, or make use of a swap overlay. The asset class considered can either be useful for hedging risk of the liabilities, or to generate returns. In this paper a model is developed based on funding ratio return by Leibowitz, Kogelman and Bader (1994) to measure the performance attribution for this choice. The actual funding ratio return is compared to a benchmark; which is an otherwise identical portfolio in which the asset class considered is being left out. In addition, performance attribution of a one percent increase in strategic weight allows comparing among asset classes, determined by the marginal funding ratio return. These models are applied to a pension fund which is managed by TKPI over the time period 2006-2008. By using this model, pension funds have a performance measure with respect to funding ratio risk and return; given their strategic choices concerning liability driven investing. The results are useful to determine the consequences of the Financial Assessment Framework on the performance of a pension fund.

2. BACKGROUND 2.1 Approach and Regulation

Traditional pension funds were adopting an actuarial approach in which assets were valued according to book value methods and rules of thumb, in which liabilities were discounted using a fixed actuarial interest rate. The actuarial interest rate even up the present value of the pension payments and the expected contributions, also called the ‘equivalence principle’ (Scherer 2003). The approach was to stabilize contributions and pay-out policies, in which risk was smoothed due to accounting approaches. This actuarial approach implied a self-constructed representation of the solvency position without any link to financial markets (Ponds and Quix 2002). Jackson and Hamilton (1968) were one of the first to point out that with respect to assets current market values produce more meaningful values than traditional approaches. A similar argument regarding liabilities is given by Waring (2004b); that a liability is a financial instrument, a set of future cash flows which are considered as an asset class held short in a portfolio. A fixed interest rate for liabilities has no correlation with asset values, therefore an economic version of the liability helps a pension fund better manage the natural hedge between assets and liabilities.

Following this argument; pension funds moved towards a liability driven investment system. The rationale behind this system is to coordinate the economic risks of the liabilities, by including assets in the portfolio which have the same risk characteristics. Asset Liability Management (ALM) studies provide a helpful tool in setting up asset allocation policies to better hedge the risk of the liabilities.

The comprehension of asset liability management is particularly important for defined benefit plans, in which pension payouts are determined by a formula based on years of employment and wages earned. Employers make contributions on behalf of their employees, therefore the investment risk and asset management is completely under their control. A nominal guarantee of pension payments is offered to the beneficiaries, which is regularly adjusted for purchasing power by indexation policies4. This is different for a defined contribution plan, in which an individual portfolio in created where part of the salary is contributed on behalf of the employee. The investment risk in a defined contribution plan will therefore be carried by the beneficiaries, often

4 _{Indexation is the decision to correct nominal pension rights for price and wage inflation. The amount of}

being involved in the risk-return trade-off. In the Netherlands, around 91% of the occupational pension funds follow a defined benefit plan5_.

In the new Dutch pension act, the Financial Assessment Framework (FTK) pointed out the rules for market valuation of the liabilities from 2007 onwards. To judge the solvability of a pension fund both assets and liabilities have to be market-to-market; this means market valuation accounts for both assets and liabilities. This will increase transparency of the pension fund since solvency problems are detected immediately. The FTK requires the funding ratio being sufficiently high so no solvency problems arise in times of bear markets, or in times of increasing market values of liabilities. A surplus over liabilities is required; with a funding ratio of at least 105%, and that the chance of the funding ratio falling below 100% is at most 2.5%. These solvency rules are applied for the guaranteed nominal liabilities of a pension fund. The conditional terms of the pension rights is determined by the policy of the pension fund; including indexation and contribution rates.

2.2 Liabilities

For a pension fund, the liabilities basically are a stream of future cash flows in the form of pension payments. Given the argument that a liability is seen as an asset held short, one can model its market-related risks just like any other financial instrument (Waring 2004a). The market value of the liabilities is the present value of the projected future liabilities. To calculate liability returns; Ryan and Fabozzi (2004) constructed a liability index, based on the market value of liabilities. The change in the value of the liability index is a result of changing nominal interest rates. In terms of the FTK, the actual yield curve of interest rates determined by ‘De Nederlandse Bank’6 _{(DNB) is used to determine the present value. This yield curve is determined by the}

n-year zero coupon rates of the DNB. The market value of the liabilities serves as an input for calculating the funding ratio which determines the solvency of the pension fund in terms of regulation. Moreover, the DNB discount rate serves effectively as a benchmark for the minimum acceptable return on achieved assets (Sortino, Van der Meer and Plantinga, 1999). This will require the return on assets to be higher than the return on liabilities for the solvency position to increase. Leibowitz, et. al. (1994) emphasize this principle in their definition of funding ratio return, which is based on difference between the return on assets and the return on liabilities. Van Ewijk and Teulings (2007) argue the separation of formal guaranteed nominal benefits and conditional real benefits such as liabilities corrected with indexation in the current Financial

Assessment Framework. Beneficiaries are particularly interested in the purchasing power of their pensions, reflected in the real pension payments. Therefore the real funding ratio7 _{is a more}

appropriate term for evaluating performance in terms purchasing power of the pensions. After determining value of real liabilities, the real value can be decomposed in the nominal value and the value of future price and wage inflation. As an illustration figure 1 shows the value of the expected payments of a pension fund8 _{over time. The lower layer is the present value of the}

nominal liabilities; the upper layers are the present values of the price and wage inflation corrections respectively. In terms of purchasing power; real liabilities are considerable higher than nominal liabilities on the long run.

FIGURE 1

Expected payments in nominal and real terms (mln. €)

Source: ALM study TKPI 2008

Indexation corrects the nominal payments to payments in real terms. The execution of this correction depends on the value of the nominal funding ratio. If the solvency position is sufficiently high, full indexation is provided. When the solvency position is lower, indexation is 80% and in the worst cases even zero. Therefore the value of the real funding ratio is affected by the value of the nominal funding ratio in the long term.

The value of the liabilities is exposed to several important risk factors. Most important risk factors are interest rate risk and inflation risk. When discounting cash payments with the DNB yield curve of interest rates a small change in the yield can have impact on the value of the

7 _{Real Funding ratio: Nominal assets divided by real liabilities, in which real liabilities are nominal}

liabilities with future indexation for price and wage inflation included.

liabilities. Therefore liabilities have a nominal interest duration, which determines the sensitivity of changes in the nominal interest rate and the present value of the liabilities. A decrease of interest rates will cause the present value of the liabilities be higher; resulting in a lower funding ratio. An increase of interest rates will have the opposite effect. Furthermore, Fisher (1965) decomposes nominal interest in a real interest rate and an expected inflation rate9_{. With the}

present value of liabilities separated in nominal and real terms, this decomposition is useful in determining the risk factors of the liabilities. Goodman and Marshall (1988) first observed that liabilities have separate real interest and inflation durations and are not only sensitive to unexpected interest rate changes, but unexpected changes in inflation in addition. When determining the risk of the liabilities in terms of the FTK regulations; the risk of changes in nominal interest rate is appropriate. In terms of purchasing power of pension benefits; the risk of changes in the real interest rate is appropriate, this includes inflation risk. Therefore the nominal interest duration of the liabilities has effect on changes in the nominal funding ratio.

2.3 Surplus Optimization

Within portfolio theory, the work of Markowitz (1959) identifies the problem of balancing risk against expected return in the mean-variance framework. Furthermore he emphasizes the role of diversification in reducing portfolio risk. Based on this research, Sharpe (1964) and Lintner (1965) develop the Capital Asset Pricing Model (CAPM). With respect to risk and return, this model assumes there is a risk premium above a risk free rate, as opposed to the market. The risk premium above the risk free rate is the compensation that an investor expects for bearing the risk of the asset. Portfolio decisions due to the outcome of the model are based on the variance-covariance framework of the universe of assets. The mean-variance optimization method of Markowitz and the CAPM are still important methods for identification of optimal portfolios with risky assets. With the growing importance of liabilities in a portfolio; surplus optimization has been widely discussed and deals with the optimization of the surplus, instead of asset-only optimization10_.

The surplus of a pension fund is defined by the value of the assets minus the value of the liabilities. Ezra (1991) emphasizes two reasons why a pension fund should focus on the surplus.

9_{(1+i)=(1+r)(1+π)}

First, any satisfactory risk model starts by defining a cash flow match between assets and liabilities as having zero risk for the employer. In other words: making sure that the pensions are paid. The only way to achieve that is to focus on the difference between assets and liabilities. Second, as a business objective, a pension fund should minimize the pension drain on the employers’ cash. This cash drain is minimized when surplus is maximized. Therefore with a considerable increase in focus on the surplus; the characteristics of the funding ratio are important for performance evaluation of a pension fund. Surplus optimization deals with the portfolio choice for which given a level of surplus risk, surplus return is maximized. Surplus risk and return is a function of the risk and return characteristics of both assets and liabilities, therefore the functional changes in surplus can explain characteristics of the funding ratio. The higher the return of assets relative to the return on liabilities, the better is the performance.

Sharpe and Tint (1990) argue the traditional mean-variance optimization methods having an all-or-nothing approach to liability consideration; either asset return or surplus is maximized; and a middle ground is not offered. Surplus optimization is accomplished by changing only the risk that is considered, it should involve a willingness to accept lower expected return and/or greater risk to increase the ability of an asset mix to hedge against increases in liability values. They stress the importance of the covariance of asset and liability returns in optimal allocation for surplus optimization. This leaves the possibility for pension funds to determine the liability hedging effect of greater or lesser emphasis on other assets in the strategic asset allocation. Bazdarich (2006) finds that the shift from an asset only framework to a surplus framework (while holding target returns constant), results in the same shift in the optimal portfolio, regardless of the plans risk tolerance.

2.4 Liability Driven Investing

For hedging liability risk; there are two strategies: cash-flow matching and duration matching. A cash-flow matching strategy ensures that the cash flows from the strategic portfolio occur at the time that liabilities are committed. A Problem with this strategy is that cash flows have to be matched perfectly and it is difficult to find assets which meet those requirements. If cash-flow matching cannot be perfectly realized there is mismatch risk. Duration matching offers a more dynamic approach; it involves hedging the residual interest rate risk created by the different characteristics of assets and liabilities due to immunization techniques. These immunization techniques concern making durations of the strategic portfolio and the liabilities equal. These techniques involve choices for asset classes which returns are highly correlated with the returns of the liabilities. A pension fund should identify the optimal combination of the matching techniques to control risk relative to liabilities and aiming for high return by including less correlated asset classes.

2.5 Strategic Asset Allocation

The strategic asset allocation is the most important decision in the investment process. Asset allocation is defined as how to allocate wealth across the broad asset classes, such as bonds,

stocks or cash. It concerns the decision of a pension fund to invest in a particular range of asset

categories to create the long-run portfolio. This portfolio determines the overall risk profile of the pension fund. Nowadays, this decision is not an easy one for pension funds. The shift towards liability driven investment strategies caused the strategic asset allocation becoming a problem finding the balance between taking risk and earning a high return, and hedging changes in market value of the liabilities.

The core activity of TKP Investments is to manage the investments of Dutch pension funds. By mutual agreement with the employer TKPI sets out a strategic asset allocation policy. In addition, strategic support is provided towards the employer. TKPI receives contributions from active members through the employer which are invested according to the set policy, serving as collateral for future benefits. Also, TKPI provides payments of pensions to the retired members of the fund, which have the right to receive their retirement benefits.

The strategic asset allocation of TKPI faces a trade-off in managing the risk-return framework in presence of liabilities. Each year, an ALM study identifies the optimal strategic asset allocation for a specific pension fund as a result of multiple future scenarios. By the use of the multi-manager principle, several multi-managers are assigned to manage a single asset class. These multi-managers have unique individual skills, with the opportunity to realize higher returns due to enhanced active management on operational level. Combined, this should enhance higher returns on the strategic level. Moreover, this approach provides better governance, diversification and lower cost.

Recently, the composition of asset classes in the strategic asset allocation has been expanded. Due to efforts hedging liability risk and the upcoming of several new asset classes, strategic asset allocation has become a more complex problem. Therefore it is important to review both the traditional11 _{and the new asset classes with respect to their risk-return trade-off and their liability}

hedging capabilities. The following section evaluates the implementation methods and the characteristics of the asset classes involved in the strategic asset allocation of TKPI.

3. DATA

TKP Investments manages pension funds for multiple employers, therefore to keep the scope of the paper within limits this research will focus on a single pension fund managed by TKPI. For that reason, data and results presented are of the single pension fund considered. General models and conclusions can apply for other pension funds managed by TKPI in addition. To evaluate performance of the funding ratio with respect to current regulations, the time period of data collection has to be restricted to the period that the new regulations were introduced at TKPI. Since 2005 TKPI follows the regulations of the FTK and suitable daily data for assets and liabilities is available from 2006 onwards. Therefore this research covers a period of 36 months; from January 2006 up to and including December 2008.

3.1 Correlation

For liability hedging strategies, it is important to consider the co-movement of asset-class returns with the returns on liabilities. An asset-class is favourable for liability hedging when returns are highly correlated with return on liabilities. Correlation only describes the co-movement of the factors; the idiosyncratic risk is not considered. Therefore concerning the choice for an asset-class in the strategic asset allocation; a pension fund should be aware of the risk-return characteristics of the highly correlated asset-class. An overview of the correlation coefficients of an asset-class with nominal liabilities is presented in table 1.

TABLE 1

Correlation coefficients Assets with Liabilities

ASSET CLASS 2006 2007 2008 STOCKS - 0.06 - 0.28 - 0.14 BONDS 0.80 0.74 0.71 CASH 0.10 - 0.08 - 0.03 REAL ESTATE 0.05 - 0.03 - 0.15 ALTERNATIVES - 0.02 - 0.02 - 0.15 INFLATION LINKED BONDS 0.81 0.80 0.61

SWAP OVERLAY 0.78 0.80 0.85

Note: These correlations are based on daily movements; monthly correlation is less accurate since the sample size is lower. Appendix B shows more detailed information for correlation coefficients, including results based on monthly data.

favourable for hedging liability risk. The remaining asset classes show correlations which are negative or close to zero, which indicates that there is none to little co-movement of those assets with liabilities. With the correlation coefficients of asset classes with liabilities determined; it is important to review the asset classes to identify the fundamentals for hedging liability risk and possible other characteristics.

3.2 Asset Classes

3.1.1. Return Characteristics

To meet the requirements of the FTK, the nominal liabilities are valued using the nominal zero coupon yield provided by the DNB12_{. The liability return is the percentage change of the market}

value of the liabilities in a specific time period:

t t t t L

L

L

L

R

=

+1

−

₍₁₎

In which the return on liabilities t L

R

is determined by the market values measured on a daily basis t. The changes in market values include actuarial changes which are carried out on occasion13_{. The return of the asset classes is also determined from the change in market values of}

the assets. A geometric return is appropriate due to the principle of compounding; since dividends and coupons are reinvested within asset classes. Over a time period; e.g. a month, a quarter or a year, the total compounded return of an asset class is:

(

1

)

1

1

−

⎟

⎠

⎞

⎜

⎝

⎛

₊

=

∏

= T t t A T A

R

R

(

1

)

1

1

−

⎟

⎠

⎞

⎜

⎝

⎛

₊

=

∏

= T t t L T L

R

R

(2)

In which

R

T_A is the return of the asset-class over the time period T, and

R

t_Ais the return of the asset class on a daily basis t. Similarly,

R

T_Lis the return of the liabilities over the same time

12

For this pension fund the liabilities have an approximate duration of 16 years. This means that a 16 year nominal zero coupon interest rate is a fairly good measure for the discount rate in valuing liabilities.

13 _{For example unexpected changes in mortality rates, structure of active and inactive members.}

period, determined as a function of the daily return on liabilities

R .

_Lt Given the returns for both assets and liabilities from equation (1) and (2), the associated risk is determined by the standard deviations:

(

)

)

1

(

1 2

−

−

=

∑

=

n

n

R

R

T t T A t A t A

σ

With, t

n

A T A

σ

σ

=

(

)

)

1

(

1 2

−

−

=

∑

=

n

n

R

R

T t T L t L t L

σ

With, t

n

L T L

σ

σ

=

(3) In which t A

σ

is the risk of an asset-class and t L

σ

the risk of liabilities over a single trading day t. These are functions of the daily returns on assets

R

t_A and liabilities

R

_Lt , the average returns on assets

R

TA and liabilities

T L

R

over the time period measured. The terms

σ

T_A and

σ

_LT are the standard deviations of the asset-class and the liabilities over the entire time period. Table 2 summarizes the results from equation (1) to (3) for the pension fund over the years 2006-2008, measured on a yearly basis14_{. These results will serve as input variables for the models presented}

in the methodology section in this paper:

TABLE 2 Returns and volatilities

2006 2007 2008

Return Risk Return Risk Return Risk

LIABILITIES - 2.97% 9.63% - 2.21% 8.21% + 26.76% 18.48% STOCKS + 14.81% 10.31% + 2.02% 12.95% - 41.28% 30.89% BONDS - 0,18% 2.42% + 0.75% 2.66% + 0.63% 5.88% CASH + 2.83% 0.13% + 3.75% 0.25% + 0.88% 0.95% REAL ESTATE + 16.89% 3.15% + 5.98% 3.65% - 1.26% 3.43% ALTERNATIVES - 17.58% 20.14% + 18.96% 14.03% - 35.28% 21.79% INFLATION LINKED BONDS - 1.97% 5.53% + 0.97% 5.32% + 1.89% 10.29%

PORTFOLIO TOTAL 7.43% 5.11% 2.80% 5.52% - 13.53% 14.10%

3.2.2. Stocks

Stocks are one of the traditional asset classes in which pension funds invest. Since around the ‘90s, stocks cover a major part in the strategic asset allocation. An important reason for including stocks is the risk premium over other assets such as bonds, hence increasing profitability. Furthermore, Bodie and Al. (2005) provide several possible correct reasons why pension funds adopt a considerable amount of equities. First, it is believed that a successful policy of investment in equities might allow it to pay extra benefits to employees as if it were a defined contribution plan and is therefore worth taking the risk. Second, management believes that through superior market timing and security selection it is possible to create value in excess of management fees and expenses. The price of the higher expected returns is the increase in risk. However, in the long run stocks tend to mean revert and become less risky; which is favourable to the long-term investment policy of a pension fund. Campbell and Viceira (2005) find that annualized standard deviation of real stock returns drop from 16 to 10% after 10 years, and below 8% after 25 years. The decision about the weight of stocks in the strategic asset allocation deals with the question how much risk a pension fund wants to bear to increase the expected return on assets.

With respect to liability driven investing, stock portfolios are instruments to increase profitability instead of hedging liabilities. Leibowitz (1995) finds an implied stock market duration of 2.19 years in a sample of S&P 500 returns, explaining that stock returns have a low sensitivity towards interest rate changes. Furthermore, variation of stock returns is only for a small part explained by interest rate changes; many factors other than interest rate changes affect the variation in stock returns (Waring, 2004a). This also explains the somewhat negative correlation with liabilities; therefore stocks are not suitable for liability hedging strategies. The choice of including stocks in the strategic asset allocation is a part of the aggressive approach. However, including stocks in a liability driven portfolio is believed to hedge the risk of salary inflation, which is a cause of the increase in real liabilities (Black, 1989). Other empirical studies have shown that stocks have been negatively correlated with inflation in the past with a low R-squared, therefore offering only a limited hedge against inflation risk (Bodie, Kane and Marcus 2005).

international stock funds for asset allocation within a pension fund. For the pension fund considered all the stock funds in the strategic portfolio are hedged to the euro.

3.5.2 Bonds

Bonds are also one of the traditional asset classes and serve as a fixed income component in the strategic asset allocation. For liability driven investment strategies, bonds prove to have considerable liability hedging characteristics. When interest rates change; bonds and liabilities face similar returns, this also explains their high correlation. This co-movement allows for conservative strategies such as duration matching. However, the approximate duration of the bond portfolio in the strategic asset allocation of the pension fund considered is 6 years as opposed to approximate liability duration of 16 years; resulting in a duration mismatch. Even though a high correlation, liabilities prove to have a larger sensitivity to interest rate movements as bonds do. Therefore bonds do not completely hedge the liabilities. Currently, pension funds adopt strategies to increase bond duration and therefore decrease the duration mismatch. These strategies include adopting long-duration bonds or increase duration by the use of a swap overlay, which are discussed further in this section.

Moreover, passively managed bond funds have considerable lower transaction costs and management fees than an actively managed stock fund. Therefore in duration matching policy an investment of 100% in bonds would minimize the cost of guaranteeing the defined benefits (Bodie et al. 2005). If in this policy duration is fully matched, it would also minimize the chance of underfunding.

3.5.3 Cash

3.5.4 Alternatives

The popularity of including alternative assets in the strategic asset allocation has grown considerably over the past decade. Alternative assets increase diversification across asset classes in a Markowitz framework and therefore a reduction of portfolio risk is expected. The alternative asset classes included in the strategic asset allocation of the pension fund considered are real estate, absolute return strategies, commodities and hedge funds. For liability hedging purposes, Swinkels (2004) investigates the use of alternative assets in a pension fund facing the requirements of the FTK. He finds that only commodities provide a partial hedge of liabilities, while other alternative asset classes are more correlated with the equity market. The prices of commodities are directly related to consumer prices, this indicates that investing in commodities can hedge against inflation. Nijman and Swinkels (2003) find that for an inflation-protected pension fund; investing in commodities can reduce funding ratio risk substantially. Real estate has traditionally been regarded to have inflation hedging capabilities also. However, Brounen, Porras Prado and Verbeek (2007) find that real estate investments provide return enhancement properties as opposed to inflation hedging properties. Furthermore, investing in real estate can have relatively high returns as compared to stocks and other alternative asset classes. Together with absolute return strategies and hedge funds, real estate therefore is appropriate for an aggressive approach on liability driven investing. Swinkels and de Groot (2007) find that excess returns of alternative asset classes above liabilities range between 2 and 3%, with an optimal allocation between 15 and 30%.

3.5.5 Inflation linked bonds

risks independently of another. With a combination of inflation linked and conventional bonds, a pension fund can match both durations of the liability stream.

Especially for funds with indexation strategies inflation linked bonds provide a good liability hedge. The value of the liabilities is adjusted in real terms; with a decomposition of interest rates, inflation linked bonds completely hedge the value of the real liabilities and the inflation component. This explains the high correlation of inflation linked bonds with liabilities; on the long-run this asset class is considered having less risk than cash when in a portfolio with liabilities (Campbell and Viceira 2002). A problem with using inflation linked bonds to hedge liabilities is that in cases where inflation linked bonds have lower nominal returns than those of liabilities; funding ratio will decline. This is an important argument to consider when determining the amount inflation linked bonds in the strategic asset allocation.

3.5.6 Interest rate SWAPS

Interest rate swaps usually have very long durations15; therefore an interest rate swap used as an overlay is a very strong instrument for hedging interest rate risk. Vertical shifts in the nominal yield curve will cause the present value of the liabilities to change in the opposite direction. In general, the duration of liabilities is considerably higher than those of assets. Therefore a fall in the yield causes the present value of the liabilities to increase with a larger amount than the increase of the value of assets. This will have a negative effect on the funding ratio. By the use of a swap overlay the duration of an asset portfolio is extended without changing the strategic asset allocation. This allows a pension fund to match the duration of an asset portfolio with those of the liabilities. In that case; a fall in the yield causes the present value of the assets to increase equally with the present value of the liabilities, with the value of the funding ratio being unaffected. A pension fund can choose to enter in a plain vanilla interest rate swap; in which the notional value is agreed with the counterparty and cash flows are exchanged over a fixed period of time. Figure 2 below illustrates the cash flows of a swap overlay on bonds in a liability driven investment strategy. A floating interest is exchanged with a fixed interest on some notional. The floating leg is treated as a loan where a floating interest is paid, which has a very small duration close to zero. The fixed leg on the other hand, is treated as a long position in a bond portfolio with duration which is usually longer than the duration of bonds. The swap value is determined by the value of the fixed leg minus the value of the floating leg. Consider a fall in interest rates; this will

cause the present value of both bonds and liabilities to increase. In addition, the value of the swap increases due to the positive duration. Without the swap, the mismatch will cause the present value of the liabilities to increase more than the present value of the bond portfolio; resulting in a decrease of the funding ratio. Including the swap to the bond portfolio will increase duration and therefore is a useful tool for matching strategies.

FIGURE 2

Plain vanilla interest rate swap

With respect to strategic asset allocation, the decision of using swaps depends on the amount of overlay a pension fund wishes to consider to hedge liability risk. The percentage overlay is a ratio of the notional value of the swap and the value of the assets. Consider for example the portfolio in table 3:

TABLE 3 Example Interest Rate SWAP

ASSETS WEIGHT DURATION LIABILITIES WEIGHT DURATION

STOCKS 40% 2.5 BONDS 60% 5 SWAP OVERLAY 0% - FIXED LEG 60% 11 FLOATING LEG -60% 0 ASSETS 100% 10.6 LIABILITIES - 100% 16

with the fixed leg treated as a bond portfolio in which fixed interest is received and the floating leg as a portfolio in which floating interest is paid. As an overlay, the value of the floating leg is not sensitive to interest movements, while the weight of the fixed leg is the determinant of extending duration of the bond portfolio by 11 years. Consider for example a decrease of 1% in interest rates, value of the liabilities increase by 16%. The fixed leg of the swap adds 11% to the 5% increase on bonds, matching the change in value of the liabilities. While the swap has zero weight in the strategic asset allocation, it has considerable weight as an overlay.

Surplus duration is defined as the duration of assets minus the duration of liabilities16_{, and}

measures the interest rate sensitivity of the surplus. When interest rate risk is not being hedged, duration of the surplus would be negative; resulting in fall in value when interest rates decrease. Too much hedging, on the other hand, will cause the duration of the surplus being positive; resulting in an increase in value when interest rates fall. Therefore, volatility due to interest changes in the surplus can be eliminated by allocating the swap in such a way that surplus duration is zero. A problem by using this hedging instrument is that the duration of all the assets have to be matched to get a surplus duration of zero. Although duration of fixed income securities is fairly stable and predictable, equity duration is quite unpredictable and volatile over time.

−

3.3 Actual Portfolio

Table 4 presents the actual asset allocation for the pension fund considered as of the first of October 2008. An overview and explanation of asset classes available for strategic asset allocation of a pension fund managed by TKPI is presented in appendix A.

TABLE 4

Strategic Asset Allocation as of October 2008

PORTFOLIO WEIGHTS

STOCKS 34,8% CASH 0,2%

World Equity Fund hedged into euro 28,5% Money Market Fund 0,0%

Futures 0,7% Treasury 3,2%

European Equity Fund hedged into

euro 3,2% Futures Treasury -3,0%

Futures 0,2% SWAP 0,0%

Emerging Markets 2,2%

BONDS 32,8% ALTERNATIVES 21,2%

Fixed Income PLUS Fund 15,0% Unlisted Real Estate 12,5% Fixed Income Index Fund 2,1% Listed Real Estate 1,0% Fixed Income Index Extra Long Fund 13,5% Socially Responsible Investment Fund 0,1%

Futures Fixed Income 2,1% Commodities 4,4%

Global Hedge fund 3,2%

INFLATION LINKED BONDS 11,0%

TOTAL 100,0%

The weights of the asset classes sum to 100% and determine the total asset value of the pension fund. These weights are determined from the results of an ALM study which is performed each year for each fund. The ALM studies are based on scenario analysis in which a wide range of forecasts is made by using various macroeconomic scenarios with certain asset allocations. Eventually, the pension board of the employer decides the strategic asset allocation which has the most favourable contribution, indexation and risk-return prospects. Each asset class has a benchmark, usually an index to measure outperformance as opposed to the market. These benchmarks are also in appendix A.

entered to rebalance the weights of the actual asset allocation in the case that the difference as opposed to strategic asset allocation is too large.

With respect to determining the returns of the actual portfolio in the pension fund, it is very important to treat the geometric portfolio return in the right way. Geometric portfolio return is not equal to a weighted average of the asset-class geometric return, but the geometric return of the weighted average17_: 1 1 1 − ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ₊ =

∏

∑

= n t i t i i T P R R

ω

(5)

In which daily portfolio return is determined as a weighted average of asset class returns

R

_it with the sum of the weights constrained to Σ

ω

_i = 1. The geometric daily portfolio return determines the return of the actual portfolio

R

T_P over time T. If a swap overlay is included as an overlay instrument, equation (4) is extended by including the weight

z

_oand return t

o

R

on the swap value

:

1 1 1 − ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ _{+ +} =

∏

∑

= n t i t o o t i i T P R z R R

ω

(6)

With the value of the swap is determined as the difference in value between the fixed leg and the floating leg; the daily return

R

_ot on the swap is the change of this difference. The swap value in the portfolio can become either positive or negative; therefore the swap weight

z

_o in the portfolio can also have negative values. The constraint towards the weights of the asset classes changes to Σ

ω

_i

= 1 – z.

3.4 Funding Ratio

The funding ratio consists of two elements; the value of the total portfolio assets and the value of the liabilities. The nominal funding ratio is the value of the total assets divided by the nominal value of the liabilities18_:

n n n

L

A

F

=

(7)

The data required calculating the returns on asset classes; the strategic portfolio and the return on liabilities are internally available at TKPI. These include the weights of the asset classes, daily returns on asset classes and day-to-day market and real values of liabilities; which are the independent variables. With the funding ratio being the dependent variable, an approach of varying the inputs can explain the relationship between the return and risk of the funding ratio and the combination of inputs used. Results based on daily data gives very small outcomes; therefore it does not give a clear overview of risk-return characteristics over time. For this reason data measurement is done daily and presented as being compounded over a year.

To build up the solvency position of a pension fund, the return on assets should be higher than the return on liabilities. The difference between the return on portfolio assets and liabilities is the excess return on liabilities. If excess return is positive; solvency, hence funding ratio will increase. When excess return is negative, the opposite happens. An overview of the excess returns in the sample period is presented in table 5:

TABLE 5

Funding ratio and Excess Returns

2006 2007 2008 FUNDING RATIO T=0 120% 133% 139% T=1 133% 139% 94% PORTFOLIO RETURN + 7.43% + 2.80% - 13.53% LIABILITY RETURN - 2.97% - 2.21% + 26.76% EXCESS RETURN 10.40% 5.01% - 40.29%

The observations in table 5 justify the argument that portfolio return should exceed liability return to have an increase in the funding ratio for a better solvency position. In the period of 2006-2007 there is a positive excess return; resulting in an increase of the funding ratio, while the funding ratio suffers a major decline in 2008 due to the very negative excess return.

18 _{The same equation applies for the real funding ratio, in which the value of the nominal liabilities is being}

3.5 Specific Questions

The strategic asset allocation decision explains most of the variation in the returns of the strategic portfolio. In addition, it is determined by the trade-off between the aggressive and conservative approach towards liability driven investing. With the funding ratio as the regulatory measure for solvency of the pension fund; the effect of the strategic decisions on the risk and return of the funding ratio determines the performance of the pension fund. Since asset classes have different purposes for liability driven investing, the following specific questions will be assumed:

(I) What is the performance attribution in terms of actual funding ratio risk and return, for an asset class used in an aggressive approach on liability driven investing?

(II) What is the performance attribution in terms of actual funding ratio risk and return, for an asset class used in a conservative approach on liability driven investing?

(III) What will be the risk and return of the funding ratio, if the swap overlay would be increased or decreased?

(IV) What will be the risk and the return of the funding ratio, if the strategic asset allocation is based on only a conservative approach or only an aggressive approach on liability driven investing?

4. METHODOLOGY

Performance measurement of liability driven investment strategies is either surplus or funding ratio oriented19_{. Important is to distinguish the methods which are applicable for measuring past}

performance with the methods used in forecasting. In this paper, historical information will provide the input for evaluating performance attribution for the strategic decisions.

4.1 Funding Ratio Return

The method used in this research to measure performance of a pension fund is the funding ratio return R_F presented by Leibowitz et al. (1994):

L L P t t t t t t F

_R

R

R

F

F

L

A

L

A

R

+

−

=

−

=

−

=

− − −

1

1

1

1 1 1 (8)

This equation measures the percentage change of the funding ratio over a time period t, defined as a function of the final funding ratio

F

_t divided by the initial funding ratio

F

_t−1 . From the definition it can also be shown that funding ratio return is a function of the actual portfolio return

P

R and liability returnR_L

,

which fits better to the data available and therefore will be used in this research.

Funding ratio return has considerable appeal above surplus return provided by Sharpe and Tint (1990) for performance measurement. Surplus return is the change in surplus over time relative to the initial asset value, thus depending on the initial value of the surplus and the assets20. This means that surplus return depends on the initial value of the funding ratio. Contrary to that; funding ratio return is unaffected by the initial value of the funding ratio and identical for all plans which have the same asset and liability returns; regardless of their initial funding status. Table 6 gives an example of this argument; three scenarios with different initial funding ratios are presented, given that asset return is 21% and return on liabilities is 10% over the time period:

19 _{Surplus oriented: Shape and Tint (1990), Ezra (1991), Waring (2004a,b) and Bazdarich (2006); Funding}

ratio oriented: Leibowitz et al. (1994), Ponds and Quix (2002)

TABLE 6

A comparison of surplus return and funding ratio return (Values in millions of euros) 1: A = L Assets Liabilities Surplus Funding Ratio

Initial Value t-1 1400 1400 0 100 % Final Value t 1694 1540 154 110 % Return + 21% + 10% 11% + 10 % 2: A > L Initial Value t-1 1400 1000 400 140 % Final Value t 1694 1100 594 154 % Return + 21% + 10% 13.9% + 10 % 3: A < L Initial Value t-1 800 1000 - 200 80 % Final Value t 968 1100 - 132 88 % Return + 21% + 10% + 8.5% + 10 %

Note: Funding ratio return is determined from equation (8), surplus return is determined as the final surplus minus the initial surplus, divided by the initial value of assets.

The return on assets exceed the return on liabilities, funding ratio therefore will increase. For all three scenarios, funding ratio has increased by 10% regardless of the initial funding status. Surplus return on the other hand, is positively related with the initial value of the funding ratio. Therefore funding ratio return is a more universal performance measure used to compare pension plans with different initial funding ratios. This not only allows comparing between pension plans, also between time periods within pension plans. In addition, performance attribution of asset classes can be determined regardless of initial funding ratios. However, funding ratio return is not applicable for return optimization, since it is based on geometric returns. Nevertheless, Bodie, Kane and Marcus (2005) consider geometric average to have considerable appeal to measure past performance. It represents the constant rate of return we would have needed to earn in each time period to match actual performance over some past investment period. For these reasons funding ratio return is a good measure for past performance of the pension fund.

4.2 Return Models

measured is being left out. This portfolio is the benchmark for the actual portfolio, in which the difference in funding ratio return is the performance attribution for including the asset class.

4.2.1 Adjusted Portfolio

First, the return of the adjusted portfolio is needed to serve as an input for equation (8) to determine the funding ratio return of the adjusted portfolio; the liability return is given and identical for all models. To create the adjusted portfolio an asset class is being excluded from the actual portfolio, therefore the weights of the remaining asset classes have to be adjusted to maintain the constraint Σ

ω

_i

= 1 – z.

The return for an adjusted portfolio

R

_Bt in which a single asset class is being left out is determined by the following equation:

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

+

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

−

−

−

×

⎟

⎠

⎞

⎜

⎝

⎛

₋

=

∑

= t o j t j j n i t i i t B

zR

z

z

R

R

R

ω

ω

ω

1

1

1 (9) In which,

∑

= n i t i i

R

1

ω

=

Weighted return of all asset classes in the actual portfolio

j

ω

= Weight of the asset class left out

z

= Weight of the swap overlay

t j

R = Return of the asset class left out

t o

R

= Return of the swap overlay

The first expression is the weighted return of all asset classes minus the weighted return of the asset class which is being left out. This expression then is then multiplied by

_⎟

⎟

To determine an adjusted portfolio in which a range of asset classes are being left out, equation (9) changes to the following equation:

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

+

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

−

−

−

×

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

−

=

∑

∑

∑

= = t o j n j t j j n i t i i t B

_z

zR

z

R

R

R

ω

ω

ω

1

1

1 1 (10)

For a range of asset classes, the first expression changes that the weighted sum asset classes considered is deducted. The sum of the weights of these asset classes is also deducted in the denominator of the second expression. Equation (9) and (10) are used to determine the return of various alternative portfolios in which specific asset classes or ranges of asset classes are left out. In addition, the swap overlay is being considered in creating alternative portfolios. These alternative portfolios are similar to the actual portfolio which has all asset classes included, only the face value of the swap overlay is being changed. This face value determines the amount of overlay, which is from zero to complete overlay on assets. The model for determining an adjusted portfolio with a swap overlay other than realized is:

t o n i t i i t B

z

R

z

z

R

R

₂ 1 2 1

1

1

+

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

−

−

×

⎟

⎠

⎞

⎜

⎝

⎛

=

∑

=

ω

(11) In which, 1

z = Actual weight of the swap value

2

z = Adjusted weight of the swap value

This allows putting more or less emphasis on the swap overlay in the portfolio. The swap overlay reduces the duration mismatch of the assets in the portfolio. For 2006, the duration match due to the inclusion of bonds is 22%21_{. From 2007 onwards, this duration is slightly increased to 26%}

due to the adding long duration bonds in the portfolio. Since the weight of the swap overlay varies daily, the adjusted weight z₂included is a factor of the actual weightz₁.

4.2.2 Performance Attribution

The difference between the funding ratio return of the actual portfolio and the funding ratio return of the adjusted portfolio is the performance attribution for including the asset class in the actual portfolio. To determine this difference, the second step is to use the outcome of equation (9) or (10) as an input for equation (8) to determine the funding ratio return of the adjusted portfolio. The difference in funding ratio return over a specific time period is then:

= − = ΔR_F R_FP R_FB

_⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

+

+

−

−

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

+

+

−

∏

∏

= = T t L L t B T t L L t P

R

R

R

R

R

R

1 1

1

1

1

1

(12) In which, FP

R = Funding ratio return of the actual portfolio

FB

R = Funding ratio return of the adjusted portfolio

Portfolio returns are compounded over time T which is the total amount of trading days in a year. Performance attribution ΔR_F presents is the excess return received for including the asset class, as opposed to not including the asset class in the strategic asset allocation. For the swap overlay, the performance attribution is the excess return of the actual duration matching strategy, as opposed to alternative strategies.

4.2.3 Marginal Funding Ratio Return

A limitation of the preceding approach is that among assets in the strategic asset allocation decision portfolio weights differ substantially; therefore the performance attribution on funding ratio return is greater for an asset class which has a larger weight

ω

_j attached. For that reason it is important to consider the marginal funding ratio return (MR_F ), which is the percentage change in funding ratio return as a result of a 1% increase in the weight of a specific asset class in the adjusted portfolio.

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

+

+

−

=

∏

= T t L L t J FJ

_R

R

R

R

1

1

1

With, t o t j t J z R zR R =(1− ) + (13) FJ

R

= Funding ratio return of asset class J

J

R

= Return of the portfolio consisting of only the considered asset class J

The marginal funding ratio return for an asset class considered can be presented as a linear approximation between this portfolio and its adjusted portfolio:

100

FB FJ F

R

R

MR

=

−

(14)

In whichMR_Fis the difference between the funding ratio return of a portfolio consisting of only the asset class considered

R

_FJ, and the adjusted portfolio R_FA in which the considered asset class is being left out, divided by the total percentage. The outcome of this equation identifies the slope of the performance attribution on funding ratio returnΔR_F, measured on an interval in which the asset class measured has a weight between 0 and 100% in the strategic portfolio.

To illustrate this, figure 3 shows two examples for performance attribution of an asset class. First, figure 3a illustrates the slope MR_F for an asset class which has a positive effect on the funding ratio return; second, figure 3b illustrates an asset class which has a negative effect:

FIGURE 3

Marginal Funding Ratio Return

The y-axis presents the funding ratio return as opposed to the actual portfolio, either higher or lower. On the x-axis the respective weight of the asset class considered is presented in a range of 0-100% with the intercept being the weight in the actual portfolio. The y-intercept is the funding ratio return of the adjusted portfolio, since the weight of the considered asset class is zero. From equation (12); performance attributionΔR_F is determined as R_FP −R_FB on the y-axis. Marginal funding ratio return can be seen as a reversed process; in which the asset class considered is added again by steps of 1% to the adjusted portfolio. This process slopes towards the actual weight at the x-intercept and ends in an opposed return of the 100% asset class portfolio

R

_FJ. In figure 3a the adjusted portfolio has a lower funding ratio return than the actual portfolio, therefore the asset class considered has a positive performance attribution, hence a positive sloping line. The steeper the slope, the stronger the effect of a 1% increase in weight of the asset class considered. Figure 3b shows the opposite effect, when there is a negative performance attribution, resulting in a downward sloping line.

4.2.4 Alternative Approaches

In addition, portfolio returns are determined which are based on either a complete conservative approach or a complete aggressive approach. The conservative approach is a fixed income portfolio consisting of conventional bonds, inflation linked bonds and the swap overlay. The aggressive approach consists is an equity portfolio consisting of all the stock funds available. To determine the funding ratio return of these alternative approaches the returns of the fixed income and equity portfolio are used in a compounded version of equation (8):

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

+

+

−

=

∏

= T t L L t FI FI F

R

R

R

R

1 ) ( ) (

1

1

And,

⎟

⎟

_⎠

⎞

⎜

⎜

⎝

⎛

⎟

⎟

⎠

⎞

⎜

⎜

⎝

⎛

+

+

−

=

∏

= T t L L t EQ EQ F

R

R

R

R

1 ) ( ) (

1

1

In which,

Return on fixed income: t

o t fi t FI z R zR R_{( )} =(1− ) + Return on equity: R₍t_EQ)

4.3 Risk Models

Beside the measures for the value of the funding ratio, the stability reflected by risk is also an important issue. The method used for the risk of the funding ratio is from Ponds and Quix (2002a), who define short-term funding ratio risk as the standard deviation of funding ratio return:

[

]

(

A L L F F

)

L t F R R R 2 1 1 2 2 2 2 2 − + + ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ + =

σ

σ

σ

σ

With; t

n

F T F

σ

σ

=

(15) In which, t F

σ

= Funding ratio risk (daily)

T F

σ

= Funding ratio risk (over a time period with trading days n)

2 A

σ

= Variance of asset returns

2 L

σ

= Variance of liability returns

F

R = Funding ratio return

L

R = Return on liabilities

For the alternative portfolios defined in the previous section the risk is determined by using equation (15). The attribution of the specific asset considered on the risk of the actual funding ratio is measured by the difference between risk of the actual portfolio and the alternative portfolio: T FB T FP T F

σ

σ

σ

=

−

Δ

(16)

5. RESULTS 5.1 Actual Statistics

The actual risk-return characteristics for the pension fund considered in the years 2006-2008 are summarized in Table 7. These statistics represent the performance of the strategic asset allocation and are the essential statistics which will be compared to the statistics of the adjusted portfolios.

TABLE 7

Actual Risk-Return Characteristics

2006 2007 2008

Return Risk Return Risk Return Risk

Strategic Portfolio + 7.43% 9.97% + 2.80% 11.06% - 13.53% 14.10%

Liabilities -2.97% 9.63% -2.21% 8.21% + 26.76% 18.48%

Funding Ratio + 10.72% 10.34% + 5.12% 9.78% - 31.79% 22.20%

The funding ratio return is positive in 2006 and 2007 and negative in 2008 due to the bear market. This is mainly explained by the excess return of the strategic portfolio over liabilities; positive portfolio returns and decreasing values of liabilities caused the funding ratio to rise by 10.72 and 5.12% respectively in 2006 and 2007. In addition, risk of the strategic portfolio is larger than the risk of the liabilities; which results in a risk premium. This risk premium shows that it rewards on average to bear excess risk over liabilities by investing a part of the portfolio aggressively. On the other hand, negative returns of the strategic portfolio and a considerable rise in the value of the liabilities caused a funding ratio return of -31.79% in 2008. Risk of the liabilities is considerably larger than the risk of the strategic portfolio, which indicates there is a penalty for not completely hedging the liabilities.

5.2 Performance Attribution

The performance attribution of the asset classes considered on the risk and return of the funding ratio are presented in table 8. These results present the total performance attribution of the asset class, and therefore asset classes which have larger weights in the strategic asset allocation also have a relatively larger performance attribution. As a reference, average weights of these asset classes are presented in appendix D.

TABLE 8

Funding ratio return and risk 2006-2008

Asset Class 2006 2007 2008 Aggressive Δ RF Δ σ RF Δ RF Δ σ RF Δ RF Δ σ RF World Hedged + 2.62% + 0.45% - 0.18% + 1.09% - 9.27% + 2.20% Europe Hedged + 1.34% + 0.14% + 0.12% + 0.27% - 0.68% + 0.21% Emerging Markets - 0.10% + 0.02% + 0.33% + 0.10% - 0.76% + 0.19% Total Equity + 5.60% +0.24% - 1.63% + 1.19% - 12.75% + 2.59% Real Estate + 1.18% - 0.35% + 0.28% - 0.24% + 2.12% - 0.79% Conservative

Fixed Income Plus - 1.58% - 0.37% - 0.61% - 0.46% + 1.35% - 0.77% Fixed Income Index - 1.84% - 0.33% - 0.81% - 0.78% + 0.70% - 0.20% Fixed Income Extra Long - - + 0.21% - 0.09% + 2.45% -0.89%

Total Fixed Income - 4.93% - 1.23% - 0.28% -1.87% + 7.25% - 2.76%

Inflation Linked Bonds - 0.38% - 0.06% - 0.16% - 0.17% + 1.85% - 0.57% Commodities - 1.05% + 0.08% + 1.37% - 0.12% - 1.00% + 0.18% Note: For total equity and fixed income, futures transactions which occurred in the time period is included in the results, for the results of the individual asset classes it is not.

Δ RF = Performance attribution on funding ratio return of the considered asset class. Determined by

equation (11)

Δ σ RF = Performance attribution funding ratio risk of the considered asset class. Determined by

equation (16)

Risk attribution for including an equity class is positive in all cases. Therefore regardless of economic circumstances, including equity in the strategic asset allocation increases funding ratio risk. This is not only the result of stocks being riskier than other asset classes, but also the inadequate liability hedging potential. This increase in risk by including an equity fund in the portfolio requires a funding ratio risk premium. In addition, this should result in higher funding ratio returns and therefore including stock funds should have a positive performance attribution. In 2006 and 2007, returns on equity are 14.81 and 2.02%22_{; therefore a positive performance}

attribution is expected.