What about the theoretical optimal asset allocation ...

What about the theoretical optimal asset allocation policy of pension funds in practice? The case of the United States.

Najat El Mekkaoui de Freitas1 Katarzyna Romaniuk2

Abstract: The literature deals with determining the theoretical optimal asset allocation policies of different types of pension funds. In a parallel way, it also focuses on describing the investment strategies chosen by pension funds in practice. Yet no contribution puts these two aspects together, in order to respond to the important question: whether pension funds do, or do not, follow the principle of optimality when determining the asset allocation strategy to adopt in practice. The purpose of this paper is to propose a response to this question, basing on the United States pension industry. The paper first develops a simple model allowing to define and compare the optimal asset allocation policies of defined contribution and defined benefit pension funds. It then analyzes the evolution of the investment strategies followed by different types of pension funds in the United States. The main conclusion of the paper is that the principle of optimality played an increasing role in the definition of the investment strategies in the American pension industry. Yet some pension funds, and specifically the defined benefit ones, seem to still follow a strategy too defensive to be compatible with the optimality principle.

JEL classification: G23; G11; C61. Key words: pension funds, defined benefit, defined contribution, stochastic dynamic programming, optimality principle, theoretical and empirical asset allocation. 1 University Paris-Dauphine, EURIsCO, Place du Maréchal de Lattre de Tassigny, 75775 Paris cedex 16. E-mail address: [email protected] 2 University of Paris 1 Panthéon-Sorbonne, PRISM-OSES, 1, rue Victor Cousin, 75005 Paris. E-mail address: [email protected]

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When determining their asset allocation, pension funds face some specific constraints, which standard investment funds do not have to observe. The main reason lies in the heavy regulation applicable to the functioning of pension funds. Their investment possibilities are for example quantitatively or qualitatively limited in many OECD and Latin American countries. In the United States, the principle of the “Prudent Person Rule” applies: No explicit quantitative limits for given asset classes are specified and caution in the management defines the basic rule. When preventing actuarial deficits in defined benefit funds, some rules concerning the funding of future liabilities have to be observed. In the United States, these rules are defined in the Employee Retirement Income Security Act (ERISA) of 1974. The characteristics of the chosen asset allocation will also crucially depend on the type of pension fund: The definition of the promised pension importantly impacts on the form of the optimal asset allocation strategy. This strategy differs for defined contribution (DC) funds – which offer a pension equal to the fund final asset value – and for defined benefit (DB) funds – which promise a pension depending mainly on the final wage and the number of years of service. As emphasized by Blake (1998) and Boulier et al. (2001), the investment decision of a defined contribution pension fund is strongly similar to an individual saving decision, while the defined benefit management issue is in fact an assetliability one. The literature deals with the theoretical optimal asset allocation policies of different types of pension funds or, separately, with their empirical investment strategies. The purpose of this paper is to put these two aspects together, in order to evaluate the degree of compatibility between the asset allocation policies of pension funds in practice and their theoretical optimal investment strategies. The analysis is conducted in the framework of the United States pension industry. The definition and the comparison of the theoretical optimal asset allocation policies of defined contribution and defined benefit pension funds define the purpose of the second section. The framework is stochastic, in continuous time. We consider a manager maximizing the expected utility of the final wealth. The control variable is defined as the proportion of wealth to invest in the risky asset.

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The described framework goes back to Merton (1971) – using stochastic dynamic programming in solving the optimization program - and Cox and Huang (1989, 1991) – who opt for the martingale approach. This framework is often used in papers focusing on the optimal investment strategy of pension funds. The contribution by Sundaresan and Zapatero (1997) initiates the analysis of the optimal asset allocation of DB funds. The authors emphasize that, when compared to the case of a standard fund, the optimal investment strategy of a DB fund incorporates a preference independent liability-hedge fund. Yet the framework considered is simplified by the assumption that the risky financial asset and wages (which determine the value of the liabilities) are perfectly correlated, which makes correlation disappear from the liability-hedge term. Rudolf and Ziemba (2004) relax this simplifying assumption. Furthermore, they introduce a state variable influencing the parameters of the risky asset and the liability processes. As a consequence, a new term is present in the optimal asset allocation policy, preference dependent and hedging against variations in the state variable. Yen and Hsu Ku (2003) extend the analysis by Rudolf and Ziemba (2004) by studying the consequences of the taking into account of a proportion only of the liability value in the objective function. As to DC funds, the first branch of the literature is based on the general model by Menoncin (2002), applied to the pension fund asset allocation issue in the contributions by Battocchio et al. (2003), Menoncin and Scaillet (2003) and Battocchio and Menoncin (2004). While Battocchio and Menoncin (2004) analyze the accumulation phase only, Battocchio et al. (2003) and Menoncin and Scaillet (2003) generalize this approach by treating both the accumulation and decumulation phases in a unique setting. Furthermore, they analyze the implications of a stochastic death time of the participant. When compared to the framework proposed by Menoncin (2002), the contribution by Cairns et al. (2006) innovates by using a salary-related numeraire as argument of the utility function, which models the fact that the participant would like to preserve his standard of living after retirement. The problem of a fund subject to a minimum stochastic guarantee to be met at retirement is analyzed in the contributions by Boulier et al. (2001) and Deelstra et al. (2003). While Boulier et al. (2001) assume deterministic contributions to the fund and a

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Vasicek specification of interest rates, Deelstra et al. (2003) extend this analysis by the introduction of stochastic contributions and a more general specification of the interest rate structure. The model by Menoncin and Scaillet (2003) appears as the most general and complete. In particular, it can be applied to both defined benefit and defined contribution funds. As contributions and pensions are being set as stochastic variables, by equating the diffusion term of pensions (respectively contributions) to zero, the framework becomes the one of a DB (respectively DC) plan. Yet this distinction is questionable when the salary is assumed to be stochastic. The DB pension cannot be then considered as deterministic, because it depends in general on the level of the final salary. Moreover, contributions generally take the form of a proportion of salary, in either the DC or the DB plan: As a consequence, they are also stochastic. Furthermore, the contribution by Menoncin and Scaillet (2003) does not analyze the differences between the optimal policies of the two types of schemes. These issues are raised in the contribution by Romaniuk (2005), which develops a general, theoretical framework in which the optimal investment strategies of different types of pension funds can be first defined, and then compared in a unique setting. The model developed in this paper uses some elements of the framework proposed by Romaniuk (2005). Yet this paper modifies the former analysis, because of the different focus of this paper, which is the determining of the importance attributed to the optimality principle in the definition of the investment strategies in practice. Specifically, this paper focuses on the basic framework in which defined contribution and defined benefit funds evolve, in order to allow clear – theoretical and then empirical comparisons between these two types of funds. After solving the optimization programs characteristic of defined contribution and defined benefit funds with the stochastic dynamic programming method, we conclude that the optimal proportion of wealth to invest in the risky asset of defined benefit funds has an additional term, covering against the variations in their liabilities, a term which is absent from the optimal proportion of defined contribution funds. The conclusion is that defined benefit funds should invest a larger part of their wealth in the risky asset, when following the optimality principle.

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The third section of the paper analyzes the investment allocation actually followed by different types of pension funds – public and private, defined contribution and defined benefit. The conclusion is that the optimality principle has played an increasing role for pension funds in the United States. One notes the total reversal of the investment strategy form of public pension funds. Though it seems that, for defined benefit funds, the optimality principle is still not the determining factor for their asset allocation decisions: Their investment strategies are still more cautious than the ones of defined contribution funds, which is contrary to the recommendations of the proposed theoretical model. The paper is organized as follows. The first section presents the main specificities of pension plans. The theoretical model of the optimal asset allocation of defined contribution and defined benefit funds is presented in the second section. The third one analyzes the empirical asset allocation of different types of pension funds in the United States, in order to evaluate their degree of compatibility with the optimality principle. The last section concludes the paper.

1. Specificities of defined contribution and defined benefit plans

In many countries, pension funds are the most important pillar of pension plans. A pension fund represents an institution which collects and invests the contributions from employees and/or employer(s) in order to finance the retirement pension for the beneficiaries or participants of pension plans. A pension plan is an employee benefit plan established by an employer in the public and in the private sector or by an employee organization (such as a union), or both, that provides retirement income. There are two major types of retirement plans : defined benefit and defined contribution plans. A defined benefit plan promises a specified monthly benefit at retirement. This promised benefit represents an exact amount and is calculated through a plan formula that considers such factors as salary and service. The benefits in most traditional defined

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benefit plans are protected by federal insurance provided through the Pension Benefit Guarantee Corporation (PBGC). A defined contribution plan, on the other hand, does not promise a specific amount of benefits at retirement. In these plans, the employee or the employer (or both) contribute to the employee's individual account under the plan. The employee will ultimately receive the balance in his account, which is based on contributions plus or minus investment gains or losses. The value of the account will fluctuate due to changes in the value of investments. Defined contribution plans include, for example, 401(k) plans, 403(b) plans, employee stock ownership plans, and profit-sharing plans. Most private sector pension plans are covered by the Employee Retirement Income Security Act (ERISA) of 1974. ERISA provides protections for participants and beneficiaries in employee benefit plans, including providing access to plan information.

1.1 Funding

By definition, DC plans are fully funded. In DB plans, there is underfunding (resp. overfunding) when the fund is worth less (resp. more) than the present value of promised benefits. Funding requirements for DB plans were introduced in 1974 by ERISA and were based initially on the Projected Benefit Obligation (PBO) and the requirement for uniform contribution rates over a worker’s career. The assumption that rights will be indexed up to retirement, as in normal final salary schemes, defines the Projected Benefit Obligation (PBO), whose characteristic is the taking into account of the projected benefit rises. In 1986 and 1987, the funding requirements were modified, considering an increase in contribution rates with age and based on the Accumulated Benefit Obligation (ABO) rather than PBO. ABO rules define "pension-fund liabilities as the present value of pension benefit owed to employees under the benefit formula omitting any projections of salary, discounted at a nominal rate of interest" (Davis, 1995). The ABO has become the most used principle in the recent years.

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1.2 Insurance

The PBGC, a federal corporation created by ERISA, insures the beneficiaries against the risk of the pension fund bankruptcy. The insurance is compulsory and is financed by insurance premiums. The premium is payed by the sponsor and is an increasing function of underfunding. In 2005, the flat rate premium equals $19 per participant in singleemployer plans and $2,60 in the multi-employer ones. The PBGC currently protects the pensions of 44,1 million American workers and retirees in 30330 private single-employer and multi-employer defined benefit pension plans. The PBGC estimates that underfunding reached $450 billion in 2003-2005 in singleemployer DB pension plans and $200 billion in the multi-employer ones. A large part of underfunding is concentrated in the sector of the old economy, in particular in the metal, automobile and airlines sectors, characterized by large and generous DB pension plans. This situation is also due to the recent decline in stock markets, and historically low interest rates.

1.3 Investment

Pension fund investments in the US are subject to a prudent man rule. Although there is no explicit definition of a "prudent man", the rule is interpreted as requiring a sensible asset diversification. According to the Department of Labour, the trustee must act "in the sole benefit of the beneficiaries", which means to select investment with "the care, skill, prudence and diligence under the circumstances then prevailing that a prudent man acting in the like capacity and familiar with such matters would use in the conduct of an enterprise of a like character and with like aims". Courts have a restrictive view of what a prudent man is, the prudent man being a prudent expert. The only quantitative limit is a 10% ceiling on self-investment, to protect against the positive correlation of the sponsor's and the pension fund's insolvency.

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2. Determining of the optimal asset allocation policies of defined contribution and defined benefit funds

It is assumed that the manager of the pension fund chooses the asset allocation that is optimal from the participant’s (or employee’s) point of view. The employer (or the firm) does not intervene in the determining of the investment strategy.

2.1. Optimization programs of defined contribution and defined benefit funds

2.1.1. Constraints

First, the argument of the utility function has to be strictly positive at the initial date. In order to take into account the flow of future contributions, the initial fund capital is augmented by the expectation of the discounted value of future contributions (Merton, 1990). The argument of the utility function at the retirement date must be positive. Finally, the last constraint is composed of the variable dynamics.

2.1.2. Defined contribution fund

The pension is defined as the pension fund asset value A at the retirement date. The program takes the standard form, proposed by Merton (1971). At date t, inferior to the retirement date T, the program writes : MaxEt [U ( A(T ) )] with Et : expectation, conditional on the information available in t; U: utility function; A: fund asset value. The program corresponds to the one characteristic of an individual saving decision.

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2.1.3. Defined benefit fund

The pension is now equal to the value, at the retirement date, of the liabilities of the fund, denoted by L. Though the manager is not able to influence the value of the liabilities, which evolve independently of the asset allocation decisions. The proportion of wealth to invest in the risky asset defines the control variable of the manager, which means that the manager can influence the final value of the assets A only. In the United States, the employer is responsible for the possible deficit of a defined benefit fund, and at the same time benefits from the possible surplus. This means that the participant is certain to obtain exactly the liability value at the date of retirement, independently of the fund asset value at this date. As a consequence, the participant is indifferent as to the investment strategy of the fund. This situation could become dangerous for the employer who guarantees the payment of a possible deficit. In order to neutralize the risk of an inappropriate allocation, which would be the result of the participant’s indifference, the employer will take the responsibility of defining the optimization program. The program of the employer writes: MaxEt [U ( A(T ) )] under the solvency constraint A(T)≥L(T), incorporated by the employer because of his responsibility for the possible deficit.

As

proposed

by

Basak

(2002),

the

following

program

is

used :

MaxEt [U ( A(T ) − L(T ) )] . This second form of the optimization program renders the solvency constraint implicit: By conducting the optimal investment strategy resulting from this last program, it is guaranteed that the final asset value will lie above the final liability value. In the United States, defined benefit funds are insured by the Pension Benefit Guarantee Corporation. This organization receives an insurance premium from the firm against the guarantee of the payment of 85% of the possible deficit of the pension fund. If such a deficit occurs, the firm is nonetheless responsible up to 30% of its net value. How does this guarantee influence the optimal investment strategy of the pension fund ? As this guarantee is only partial (because concerning only a fraction of the deficit) and as the responsibility of the firm is involved in case of a deficit, the employer 9

incorporates the solvency constraint in his optimization program. Thus, in the model developed, the guarantee of the PBGC does not impact on the form of the optimal investment policy.

2.2. The model 2.2.1. Assumptions The manager of the pension fund can invest in the risky or the riskless asset. The riskless asset, denoted by η, earns the constant riskless interest rate r and evolves with the following dynamics :

dη (t ) = rdt η (t ) The risky asset, denoted by S, can be interpreted as the market portfolio. It follows a geometric Brownian motion (GBM) : dS (t ) = µ S dt + σ S dB S (t ) S (t ) with

µ S : expectation of the instantaneous return of S, constant; σ S : volatility of the instantaneous return, constant; B S : standard Brownian motion.

The defined benefit fund faces a specific constraint : It has to generate at least the final value of the liabilities L. A contribution is continuously brought to the asset value of the defined benefit and the defined contribution funds. This contribution is defined as a constant proportion ζ of the employee’s wage. The dynamics of the liabilities L and of the wage Y take the form of GBMs : dL(t ) = µ L dt + σ L dB L (t ) L(t ) dY (t ) = µ Y dt + σ Y dB Y (t ) Y (t )

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where

µ L and µ Y denote the expectations of the instantaneous returns of L and Y respectively, σ L and σ Y the volatilities of these returns, µ L , µ Y , σ L and σ Y being constant, and B L and B Y standard Brownian motions. The instantaneous correlations between the Wiener processes are defined as follows : dB S (t )dB L (t ) = ρ SL dt dB S (t )dB Y (t ) = ρ SY dt dB L (t )dB Y (t ) = ρ LY dt with − 1 ≤ ρ ≤ 1 .

The financial market is assumed to meet the standard assumptions, in particular the completeness one. 2.2.2. The investor’s program The utility function of the participant, assumed increasing and concave, takes the form U (t , X (t )) , where X (T ) = A(T ) in the case of a defined contribution fund, and

X (T ) = A(T ) − L(T ) in a defined benefit fund. The dynamics of the variable X can be formulated under the following, general form: dX (t ) = µ X (t )dt + σ X (t )dB(t ) X (t ) with µ X (t ) the drift, σ X (t ) the volatility, vector of dimensions (1×3), and B a

dB S    Brownian motion of dimension 3, defined as dB ≡ dBY  . dB L   

The optimization program of the manager writes: Max xS Et [U ( X (T )] dX (t ) = µ X (t )dt + σ X (t )dB(t ) X (t ) X (0) > 0

s.c.

X (T ) ≥ 0

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with x S : proportion of X invested in the risky asset.

The investment horizon, equal to the retirement date, is assumed to be known at the initial date. The date of death is considered to be certain.

2.3. Definition of the optimal asset allocation

Two methods can be used to solve the kind of optimization programs defined above : stochastic dynamic programming and the martingale approach. We opt for the first of these methods. A contribution process being brought continuously to the pension fund assets, the wealth of the fund does not have the self-financing property. As a consequence, applying stochastic dynamic programming appears as more adapted, because dealing with this kind of variables does not lead to serious difficulties when using this method. 2.3.1. Solution in the general case In what follows, the dependence with respect to time t will be omitted for ease of exposition, except in the case when a risk of confusion exists. Let us define the indirect utility function J, increasing and strictly concave, by the following equation: J (t , X (t )) ≡ max xS Et [U ( X (T ))]

The optimality equation of Hamilton-Jacobi-Bellman takes the form: max xS DJ = 0 where D denotes the Dynkin operator, the Dynkin of J being defined as follows: DJ = J t + J X Xµ X +

1 J XX X 2σ X2 2

where J X denotes the partial derivative of J with respect to X, J XX the second derivative with respect to X.

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2.3.2. Solving the optimization program Let us consider directly the case where X = A − L , corresponding to the situation of a defined benefit fund. The solution for a defined contribution fund is then easily obtained by assuming that the liability variable takes the zero value. The assets A are invested in the risky asset S and in the riskless asset η. They are defined as follows: A = X S S +η with X S : number of assets S acquired. Thus X = X S S +η − L The variable X is invested in the risky asset S with the proportion x S ≡ riskless asset η with the proportion xη ≡ proportion x L ≡

η X

XSS , in the X

and (negatively) in the liabilities L with the

L . The following identity is met: x S + xη − x L = 1 . X

The dynamics of the variable X write: dX dS dη Y dY dL = xS + xη +ζ − xL η X S X Y L

The term ζ

Y dY represents the contribution process. As already mentioned, the X Y

contributions take the form of a proportion ζ of the wage. They accumulate continuously to the pension fund assets. As soon as they are integrated to the assets, these contributions are invested in both assets S and η. By replacing the dynamics of the variables η, S, L and Y, and using the identity x S + xη − x L = 1 , one obtains:

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dX  Y Y  =  x S (µ S − r ) + r + ζ µ Y − x L (µ L − r ) dt + x S σ S dB S + ζ σ Y dB Y − x Lσ L dB L X X X  

Thus the Dynkin of J takes the form:

Y   µ Y − x L (µ L − r ) DJ = J t + J X X  x S (µ S − r ) + r + ζ X   2    Y  2 2 ( ) σ ζ σ x +   S S  Y  + ( x Lσ L ) 1  X   + J XX X 2   2 Y Y   + 2 x S σ S ρ SY ζ σ Y − x S σ S ρ SL x Lσ L − ζ σ Y ρ LY x Lσ L  X X   

By deriving with respect to x S , one obtains the first order condition for an optimum:

xS = −

µS − r σ σ Y ρ SY Y + x L ρ SL L −ζ 2 σS J XX X σ S X σS JX

2.3.3. Result interpretation 2.3.3.1. Defined contribution fund In the case of a defined contribution fund, X (T ) = A(T ) . The variable L takes the zero value. The optimal strategy thus takes the form :

xS = −

µS − r σ Y ρ SY Y −ζ 2 J XX X σ S X σS JX

As X = A , one can rewrite :

xS = −

σ J A µS − r Y − ζ ρ SY Y 2 J AA A σ S A σS

The optimal strategy is thus composed of two elements : -

the standard speculative fund, preference-dependent, first derived by

Merton (1971) ; Of the usual mean-variance form, this term is defined as a function of the reciprocal of the relative risk aversion coefficient (with respect to the indirect utility function) and of the Sharpe ratio.

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-

a hedge fund covering against variations in the wage, preference-

independent, resulting from the accumulation of the contribution process. By adding this term, the fund manager conducts an investment policy in which the proportion to invest in the risky asset considers the evolution of a variable determining for the contribution process – the wage. The characteristics of this variable (its standard deviation, correlation with the risky financial asset and level) are taken into account, in order to determine the proportion to invest in the risky asset which will optimally cover against the wage variations. 2.3.3.2. Defined benefit fund The optimal proportion to invest in the risky asset writes : xS = −

µS − r σ σ Y −ζ ρ SY Y + x L ρ SL L 2 J XX X σ S X σS σS JX

The proportion x S is calculated with respect to the variable X. Let us denote by x S ' the proportion of the fund assets A to invest in the risky asset, with x S ' = x S

X . A

The proportion x S ' then writes : xS ' = −

µS − r σ σ Y L − ζ ρ SY Y + ρ SL L 2 J XX A σ S A σS σS A JX

The optimal investment strategy is composed of three elements : -

the speculative fund;

-

the contribution hedge fund ;

-

a new element : a hedge fund covering against variations in the liabilities,

preference-independent. Let us now compare the optimal investment strategies of defined contribution and defined benefit funds.

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One first notes that both strategies contain the standard speculative fund. The formulations of this term for the cases of defined contribution and defined benefit funds can be considered as comparable.3 The contribution hedge fund defines the second element of the investment strategies. Its formulations are identical for defined contribution and defined benefit funds. The main difference between the two strategies concerns the existence of a liability hedge fund in the case of a defined benefit fund only. What is the precise definition of this liability hedge fund ? In the United States, in the majority of cases, the liabilities of a defined benefit fund depend on the final wage.4 One can then write : L(T ) = γY (T ) γ denoting the multiple of the final wage defining the pension of a defined benefit fund. By integrating the dynamics of the wage variable, one rewrites the liability hedge term in the following way :

σ γY σ L ρ SL L = ρ SY Y A σS A σS As emphasized by Rudolf and Ziemba (2004), this term depends on the financial health of the fund. The higher the ratio

γY A

, and thus the worse the fund financial health,

the higher the value of this hedge portfolio. The optimal investment strategy will thus write : xS ' = −

σ µS − r σ Y γY − ζ ρ SY Y + ρ SY Y 2 J XX A σ S A A σS σS JX

When going from a defined contribution to a defined benefit fund, one thus needs to add a term hedging against variations in the liabilities to the optimal proportion to invest 3

The derivatives of the function J are calculated with respect to the variable A in a defined contribution fund, and with respect to the variable X in an defined benefit fund. A utility function of the CARA type (constant absolute risk aversion) leads to the equivalence of the two formulations, while a function of the CRRA type (constant relative risk aversion) can lead to a divergence between the results for the two kinds of funds. 4 The pension of some defined benefit funds is defined as the sum of a predetermined amount for each participation year. The liabilities then lose their stochastic property. As a consequence, the liability hedge term does not appear in the optimal investment strategy.

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in the risky asset. As

γY A

and

σY are positive, this proportion increases when adding the σS

liability hedge fund if ρ SY is positive. The assumption of a positive correlation between the risky financial asset and the wage seems a realistic one. Sundaresan and Zapatero (1997) even assumed a correlation coefficient of 1. To conclude, the optimal proportion to invest in the risky asset is higher in a defined benefit fund, when compared to the one characteristic of a defined contribution fund, because it contains an additional term, covering against variations in the liabilities.

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3. The asset allocation policies in practice

Let us now focus on the practice of the asset allocation policies of pension funds in the United States, the purpose being the determining of the basic characteristics of the investment strategies conducted by these funds, but also the analysis of their possible accordance with the theory. In this framework, some questions need to be answered. The first one is without doubt the following: Can we consider that American pension funds do in general follow investment strategies compatible with the optimality criterion ? The second subsection deals with a comparison of the investment strategies chosen by public and private pension funds. The third one jointly analyzes the asset allocation policies of defined contribution and defined benefit pension funds.

3.1. An overview of pension funds assets and investment strategies in OECD countries

In most OECD countries reviewed, the economic size of pension funds has increased. As a percentage of GDP, the highest accumulation of assets is observed for the United States, the United-Kingdom and the Netherlands, with respectively 63%, 66.4%, and 105.1% of GDP (table 1).

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Table 1 : Pension funds assets in OECD countries (% of GDP) 1981

1991

2001

United States

24.3

46.9

63.0

United Kingdom

22.4

54.7

66.4

Canada

16.8

31.4

48.2

Denmark

--

15.4

23.8

Germany

1.8

2.9

3.3

Italy

--

4.0

4.4

49.9

73.5

105.1

Portugal

--

2.3

11.3

Spain

--

--

8.2

Netherlands

Source : OECD (2003), Financial Assets of Institutional Investors

The investment strategies, defined as the relative proportions of equities and bonds in the pension fund assets, can be very different when considering different countries. As table 2 shows, these strategies go from the ones giving an overwhelming weight to equities, to the ones where bonds represent the highest proportion. Table 2 : Asset structure of pension funds in 2002 Country United Kingdom Canada United States Switzerland Netherlands Germany Spain

Proportion of equities5 65,2 61,5 57,2 41,7 37 23,9 23,9

Source : OECD, Financial Market Trends, N°88, March 2005

5

Mutual funds are included in this proportion.

19

Proportion of bonds 19,2 27,4 13,9 26,8 44 41,4 58,1

The important question is now the precise definition of the optimal investment strategy, to which the strategies actually observed will be compared. The theoretical model shows that the optimal proportion to invest in the risky asset depends on the risk aversion of the participant, the relative return of the market portfolio, the characteristics of the variables, the variations of which the investor will cover against.6 This proportion also varies with the participant’s age: Younger participants will tend to invest heavily in risky assets, while participants approaching the retirement date will opt for a large proportion of riskless assets. One can clearly see the difficulty (or even the impossibility) to determine the optimal strategy. Let us further note that the proportions given in table 2 represent a mean of all pension funds, and also a mean of strategies adopted by younger and older participants, and more or less risk averse. In practice different strategies are considered as a benchmark: for example, the policy of « your age in bonds » (Booth, 2004) or 60% in equities and 40% in bonds and money market funds (Kim and Wong, 1997). When going back to the table 2, one easily observes that the given countries can be classified in two main groups: The United Kingdom, Canada, the United States and Switzerland invest more heavily in equities (in comparison with bonds), while in the Netherlands, Germany and Spain bonds have a higher proportion than equities. We consider this first group of countries as the one following the optimality criterion. In the second group, the caution criterion appears as determining for the investment strategy form. The United States thus belong to the group of countries whose pension funds follow an investment strategy that can be considered as in general compatible with the optimality criterion.

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The risk aversion of the participant is represented by the term

portfolio by

−

JX J XX X

, the relative return of the market

µS − r . The investor covers against variations of the salary Y. σ S2 20

3.2. Asset allocation policies of private and public pension funds7

Sarney (2000) studies the asset allocation of public pension funds, and proceeds to a comparison to the investment strategy of private pension funds. He concludes that, during the nineties, public pension funds operated a transition from an investment in bonds to an investment in equities. The proportion of the aggregated assets of public pension funds invested in equities has nearly tripled since the beginning of the eighties. In 1999, this proportion was estimated at 67%.8,9 This strategy is comparable to the one of five of the biggest private pension funds. Healey and Rozenov (2004) also conclude that the differences between the investment strategies of public and private pension funds have nearly disappeared nowadays. Let us now proceed to an analysis of American data, which will allow to illustrate these evolutions.

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Data used for the figures of the subsections 3.2 and 3.3 are available in the “Flow of Funds Accounts of the United States”, published by the Board of Governors of the Federal Reserve System. 8 This number constitutes an aggregate of data concerning all public pension funds. Though it is not representative of the investment policy of all public pension funds taken separately. For example, funds of smaller sizes invest less in equities than bigger funds. 9 This investment in equities can be decomposed in domestic equities for 80% and foreign for 20%.

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3.2.1. Evolution of the asset allocation of private pension funds

Figure 1 : Asset allocation of private pension funds 1975-2004 0.5

0.45

0.4 0.35 Corporate equities Mutual fund shares

Proportion

0.3

Corporate and foreign bonds Treasury securities

0.25

Agency- and GSE-backed securities Time and savings deposits

0.2

Unallocated insurance contracts 0.15 0.1

0.05

20 03

20 01

19 99

19 97

19 95

19 93

19 91

19 89

19 87

19 85

19 83

19 81

19 79

19 77

19 75

0

Year

Some general characteristics of the asset allocation of private pension funds in the last three decades can be observed in figure 1. First, the proportion of equities oscillates around 43% approximately. A decrease is to note in the period of the financial market crisis, the year 2002 being characteristic of the smallest proportion. Second, the proportion of mutual fund shares records a pronounced growth, going from 2% to 27%. Concerning bonds, a decrease can be seen, from 17% to 8%. The proportions of treasury securities, of agency- and GSE-backed securities and of time and savings deposits first increase, and then decrease, the 2004 proportions being situated between 2 and 5%. From 1985 on, private pension funds begin to invest in unallocated insurance contracts: After a sharp increase in this proportion, reaching 14% in 1987, a downward trend is to note, the 2004 proportion being around 8%. As a consequence, one can conclude to an increasing weight of risky assets in the private pension fund portfolios, due to a pronounced growth in the investment in mutual funds shares.

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3.2.2. Evolution of the asset allocation of public pension funds

Figure 2 : Asset allocation of public pension funds 1975-2004 0.7

0.6

Proportion

0.5

Corporate equities Mutual fund shares

0.4

Corporate and foreign bonds Treasury securities 0.3

Agency- and GSE-backed securities

0.2

0.1

20 03

20 01

19 99

19 97

19 95

19 93

19 91

19 89

19 87

19 85

19 83

19 81

19 79

19 77

19 75

0

Year

As figure 2 shows, the situation is quite different for public pension funds. One first notes the heavy increase in the proportion of equities, going from 24% to more than 60%. Second, the proportion of mutual fund shares also increases, from 0% to 9%. Concerning the proportion of bonds, a pronounced decrease is recorded, going from 58% to less than 10%. The proportion of treasury securities first increases, and then decreases, the variations being situated between 5% and 25% approximately, the 2004 proportion being 7%. The proportion of agency and GSE-backed securities oscillates around the approximate mean of 8%, the 2004 proportion being 8%. One can thus conclude to a total reversal of the investment policy form of public pension funds. These funds initially invested heavily in bonds. They nowadays give the highest proportion to equities and mutual fund shares.

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3.2.3. Comparison between private and public pension funds Figures 3 and 4 illustrate the asset allocation policies of private and public pension funds in 2004 :

Figure 3 : Asset allocation of private pension funds in 2004 Other assets 9% Unallocated insurance contracts 8% Money market fund shares 2% Time and savings deposits 3%

Corporate equities 38%

Agency- and GSE-backed securities 5% Treasury securities 2% Corporate and foreign bonds 7%

Mutual fund shares 26%

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Figure 4 : Asset allocation of public pension funds in 2004

Agency- and GSE-backed Other assets 4% securities 8% Treasury securities 6% Corporate and foreign bonds 7%

Mutual fund shares 9% Corporate equities 66%

In 2004, private pension funds invest 64% of their wealth in equities and mutual funds shares, 19% in corporate and foreign bonds, treasury securities, agency and GSE-backed securities, time and savings deposits and money market fund shares, while these proportions are 75% - 21% for public funds. As a consequence, one clearly sees that the asset allocation policies of public pension funds joined the ones conducted by private pension funds. One important difference should nonetheless be underlined : Private funds invest more heavily in mutual fund shares than public funds. To conclude, the optimality criterion has played an increasing role in the investment decisions of American pension funds, public pension funds having even totally reversed their investment principles.

Going back to the model presented in the first section, let us note that the optimization programs of public and private pension funds coincide. Thus the results found when analyzing the theoretical optimal asset allocation policies apply to both public and private pension funds.

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Thus the theoretical model does not provide a differentiation between these two types of funds. Yet a differentiation between defined benefit and defined contribution pension funds is provided. It will be useful for the analysis of the next subsection, dealing with a comparison of the strategies of defined benefit and defined contribution funds.

3.3. Asset allocation policies of defined benefit and defined contribution pension funds

Healey and Rozenov (2004) study the evolution of the investment policies of the 200 biggest defined benefit pension funds during the nineties. They conclude that the value of held assets doubled in this period and that the proportion invested in equities increased, while the proportion invested in fixed-income assets and monetary assets recorded an opposite evolution.10 As a consequence, the asset allocation strategy of defined benefit funds is today comparable to the one of defined contribution funds. The description of the practice of the determining of investment policies in defined benefit funds would rather lead us to predict unsuitable strategies. As Pozen (2004) explains, in the majority of defined benefit funds, the proportions to invest in equities and bonds are determined by trusties, in spite of their frequent lack of experience in the investment preparing retirement income. Their decisions are mainly based on reports of actuarial firms, whose recommendations as to the optimal investment policy result from analyses of the past performance of different asset classes. What can data tell us about the practice of the management of defined benefit and defined contribution pension funds in the private sector?11

10

The authors also emphasize an increase in the proportion of global equities. Data concerning DB and DC funds available in the Flow of Funds Accounts refer to the private sector only. 11

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3.3.1. Evolution of the asset allocation of defined benefit pension funds Figure 5 : Asset allocation of defined benefit pension funds 1985-2004 0.6

0.5

Proportion

0.4 Corporate equities Mutual fund shares Corporate and foreign bonds Treasury securities

0.3

Agency- and GSE-backed securities Time and savings deposits Unallocated insurance contracts 0.2

0.1

19 85 19 86 19 87 19 88 19 89 19 90 19 91 19 92 19 93 19 94 19 95 19 96 19 97 19 98 19 99 20 00 20 01 20 02 20 03 20 04

0

Year

Figure 5 plots the evolution of the asset allocation policy of defined benefit funds in the two last decades. One fist observes the growing trend in the proportion of equities, from 40% to 50% approximately. The financial market crisis leads to a sharp decrease in this proportion, 2002 recording its minimum. Second, the proportion of mutual fund shares increases heavily, going from 1% to 11%. Concerning bonds, a light increase can be observed (12% defining its approximate mean), with a peak during the financial market crisis. The proportion of treasury securities decreases sharply (from 12% to 4%). The proportion of agency- and GSE-backed securities can be considered as relatively stable, varying around the mean of 10% approximately. The proportion of time and savings deposits shows similar patters, the approximate mean being 6%. Finally, the proportion of unallocated insurance contracts decreases from 10% to 5%. To conclude, one notes an upward trend in the proportions of equities and mutual fund shares. These proportions constitute together 58% of the wealth in 1999. This upward evolution in the proportion of equities is temporarily stopped by the consequences of the financial market crisis. 27

3.3.2. Evolution of the asset allocation of defined contribution pension funds Figure 6 : Asset allocation of defined contribution pension funds 1985-2004 0.5

0.45

0.4 0.35 Corporate equities Mutual fund shares Corporate and foreign bonds

Proportion

0.3

Treasury securities Agency- and GSE-backed securities

0.25

Time and savings deposits Money market fund shares

0.2

Unallocated insurance contracts 0.15 0.1

0.05

19 85 19 86 19 87 19 88 19 89 19 90 19 91 19 92 19 93 19 94 19 95 19 96 19 97 19 98 19 99 20 00 20 01 20 02 20 03 20 04

0

Year

As figure 6 shows, the asset allocation policy of defined contribution funds in the period 1985-2004 is characterized by a relative constancy in the proportion of equities (40% approximately), a decrease being recorded during the financial market crisis. The proportion of mutual fund shares increases very strongly, going from 2% to 37%. The proportion of bonds decreases from 8% to 3%. The proportions of treasury securities and agency- and GSE-backed securities also decrease, going approximately from 5% to 2%, and 4% to 2% respectively. The proportion of time and savings deposits decreases from 8% to 2%, while the proportion of money market fund shares appears as relatively stable, even showing an upward trend, going from to 2% to 4% approximately. Finally, the proportion of unallocated insurance contracts first increases, and then decreases, varying between 11% and 19%. One concludes to a pronounced upward trend in the proportion of risky assets (equities and mutual fund shares taken together), due to the exceptional growth in the investment in mutual funds shares. 28

3.3.3. Comparison between defined benefit and defined contribution pension funds Figures 7 and 8 show the investment strategies chosen by defined benefit and defined contribution funds in 2004 : Figure 7 : Asset allocation of defined benefit pension funds in 2004

Other assets 9% Unallocated insurance contracts 5% Time and savings deposits 7%

Corporate equities 40%

Agency- and GSE-backed securities 11%

Treasury securities 3%

Corporate and foreign bonds 14%

Mutual fund shares 11%

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Figure 8 : Asset allocation of defined contribution pension funds in 2004 Unallocated insurance contracts 10% Money market fund shares 3%

Other assets 8%

Time and savings deposits 1%

Corporate equities 36%

Agency- and GSE-backed securities 2% Treasury securities 1% Corporate and foreign bonds 3%

Mutual fund shares 36%

In 2004, defined benefit funds invest 51% of their wealth in equities and mutual fund shares, 35% in corporate and foreign bonds, treasury securities, agency and GSE-backed securities, time and savings deposits and money market fund shares. The proportions 72% - 10% are characteristic of defined contribution funds. The investment strategy of defined benefit funds has thus approached the one conducted by defined contribution funds. The assets of defined benefit funds are nonetheless still less invested in risky assets that the ones of defined contribution funds. One can thus conclude that the strategy chosen by defined benefit funds is today more determined by the optimality criterion than in the past. Though the caution criterion still plays an important role, which can be seen when observing the high proportion attributed to less risky assets. The actual investment strategy of defined benefit funds is still far from the optimal one. As was demonstrated in the theoretical model, the optimal proportion to invest in the risky asset of a defined benefit fund exceeds the one of a defined contribution fund, because of the presence of a liability hedge term. In practice, defined benefit funds still opt for less risky strategies, in order to generate a final asset value allowing them to finance the promised pensions. Yet the optimality 30

criterion rather suggests the acquisition of a heavier proportion of risky assets, the purpose being to hedge against variations in their liabilities. It would thus be advisable for defined benefit funds to forget defensive strategies, and to focus on strategies more compatible with the optimality criterion.

Let us emphasize that our conclusion is contrary to the recommendations prevailing in the recent years.12 The financial problems that DB funds face for several years, due to the decline in stock prices during the financial market crash between 2000 and 2002 and historically low interest rates, led many economists to conclude that DB funds chose an inadequate asset allocation in the past. These economists emphasized that the difficult financial status of DB funds results from an insufficient focus on matching assets to liabilities. They recommended that DB funds, when aiming a better asset-liability matching, invest more in bonds, as these financial assets provide a hedge against the two main risks influencing the value of the liabilities: inflation and interest rate variations. As an argument for the appropriateness of this strategy, the case of Boots, a British company, is put forward: This enterprise decided to invest 100% of its DB plan assets in long-term bonds. Yet this issue does not appear as a simple one. In practice, many pension fund managers are reluctant to investing a higher proportion of their assets in bonds, because these assets offer a relatively low yield, unable not only to meet the fund liabilities, but also to close the current financial gaps. The justification for this advised shift to bonds refers to the properties of liabilities, which are subject to the inflation and interest rate risks. As the liabilities of a defined benefit fund depend on future wages, whose evolution itself depends on inflation, a hedge against the inflation risk appears as advisable. The DB fund manager also has the obligation to generate an asset value at least equal to the present value of the liabilities. The interest rate defines the discounting variable of these liabilities, and as such constitutes a variable whose variations must be covered against by the manager. Proponents of this shift to a more pronounced investment in bonds emphasize that bonds

12

See for example the IMF Global Financial Stability Report (2004) and Tuer and Woodman (2005).

31

have a similar nature to liabilities, and as such provide a hedge against the inflation and interest rate risks. This reasoning does not seem appealing to us. First, the definition of contributions as a percentage of the wage already provides a certain cover against variations in the wage. Furthermore, investing in bonds allows a hedge against inflation in the case of specific bonds only – the inflation-indexed ones. Another dimension is to note: It seems that the fact that pension funds invest a large part of their wealth in bonds has already exerted a downward pressure on the interest rates; Increasing this proportion would even worsen the situation. One another issue remains: An increased demand for high-quality bonds would face an insufficient supply.13 Second, referring to our model, the liabilities as well as the contributions are defined as a function of the wage, which leads to an investment policy taking into account the specific nature of DB funds, by adding hedge funds against variations of the key variables influencing its liabilities. As a consequence, the investment in risky assets is constructed in a way guaranteeing a match with the liability structure. As to the argument of a need of covering against interest rate variations, the interest rate being understood as the discounting variable of the liabilities, this interest rate impacts in a similar way on both the asset and the liability sides. By definition, the present value of these variables is defined as the conditional expectation of their future value, discounted at the risk-free rate under the risk-neutral probability measure. To sum up, we provide the following conclusion, opposite to the one of a large part of the literature: The optimal strategy of DB funds incorporates a larger proportion of risky assets than actually observed in practice. We think that, instead of operating a shift towards a higher proportion of bonds, which is a strategy often advised in the recent years, DB funds should rather invest more in riskier assets. The proportion of risky assets proposed in our model guarantees an asset-liability matching, as it incorporates hedges against variations of variables influencing the liability value.

13

The OECD Newsletter from December 2005 evaluates the future gap between supply and demand.

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4. Conclusion

The purpose of this paper was to analyze jointly theoretical optimal asset allocation policies of different types of pension funds and their empirical investment strategies in the framework of the United States pension industry, in order to evaluate whether the allocation policies actually chosen by pension funds follow the optimality principle. A simple theoretical model was first presented and optimal investment strategies of defined contribution and defined benefit funds were derived in this framework. The conclusion is that an additional term appears in the optimal investment strategy of a defined benefit fund, which covers against variations in the liability value. The proportion of wealth invested in the risky asset should thus be higher in defined benefit than in defined contribution funds. The paper then analyzed the empirical investment strategies conducted by pension funds in the United States in the two - three last decades. After an analysis of the evolution of the investment strategies of private and public pension funds, one concludes to an increasing role of the optimality principle for both types of funds. Yet the weight of equities has always been relatively high in private pension funds, while public pension funds proceeded to a total reversal of their asset allocation policies: They first invested largely in bonds and now largely invest in equities. The optimality principle thus played an increasing role in both types of pension funds, yet the increase was rather sharp for public funds, as they went from almost no role to an important one. The analysis of the investment strategies conducted by defined contribution and defined benefit pension funds reveals that both have invested more and more in risky assets: The optimality principle has played an increasing role. Yet the investment strategy of defined benefit funds is still more cautious than the one of defined contribution funds: The proportion of wealth invested in risky assets is smaller in defined benefit funds. This is contrary to the recommendations of the theoretical model presented in the first section, where it was shown that defined benefit funds should invest more in risky assets than defined contribution funds, because of the presence of a liability hedge term in their investment strategy. The main conclusion of the paper is that the actual asset allocation

33

policies of defined benefit funds cannot be considered as being determined by the optimality criterion. Defined benefit funds could thus gain from forgetting defensive investment techniques, and taking more into account the optimality principle when deciding about the asset allocation policies to adopt.

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