Chapter 10 pension scheme asset allocation with taxation arbitrage, risk sharing, and default insurance

Pension Scheme Asset Allocation with Taxation Arbitrage, Risk Sharing,... Th e analysis proceeds on the basis that in the absence of taxation, risk sharing, and default insurance, the as

Pension Scheme Asset Allocation with Taxation Arbitrage, Risk Sharing,

Asset a l l oca ti on is a c rucial decision for pension f unds, a nd t his

chapter analyzes the economic factors that determine this choice Th e analysis proceeds on the basis that in the absence of taxation, risk sharing, and default insurance, the asset allocation between equities and bonds is indeterminate and governed by the risk–return preferences of the trustees and the employer If the employing company and its shareholders are subject

to taxation, there is a tax advantage in a largely bond allocation Risk ing between the employer and the employees oft en means that one group favors a high equity allocation, while the other favors a low equity alloca-tion Underpriced default insurance creates an incentive for a high equity allocation When taxation, risk sharing, and underpriced default insurance are all present, it is concluded that the appropriate asset allocation varies with the circumstances of the scheme, but that a high equity allocation is probably inappropriate for many private sector pension schemes

shar-Th e main determinant of the investment performance of a pension fund is the asset allocation rather than the stock selection (Brinson et al., 1986, 1991; Blake et al., 1999; Ibbotson and Kaplan, 2000) Th is chapter concentrates on the equity-bond decision, but the arguments can be g eneralized to include other asset classes Th ere is a considerable amount of evidence that in com-petitive capital markets, additional risk is compensated by additional expected returns (e.g., the equity risk premium) (Cornell, 1999; Dimson et al., 2002; Siegel, 2002) Th ere is also evidence that time diversifi cation* is not present for equities (Sutcliff e, 2005) Th erefore, in both the long and the short run, there

is a linear trade-off between risk and return, as in the capital asset pricing model (Sharpe, 1964), and equities are not relatively more attractive for long-term investors Th ere is empirical evidence that equities are not a good hedge for pension scheme liabilities, and so there is no particular hedging advantage

in equities over other forms of investment (Sutcliff e, 2005) In these stances (and in the absence of taxation, risk sharing, and default insurance), the asset allocation decision depends on the risk–return preferences of the trustees, in consultation with the employer A h igh equity proportion leads

circum-to a high risk, high expected return outcome; a low equity proportion, on the other hand, gives a low risk, low expected return outcome

Th is chapter relies on higher expected returns from equities being off set by the higher risks, equity having no special hedging merits, and the absence of a r eduction in equity risk for long-run investors It proceeds

-on the premise that, in the absence of taxati-on, risk sharing, and default

* Time diversifi cation occurs when over and under performance tends to c ancel out i n the long run.

insurance, the asset allocation is indeterminate Section 10.1 considers the eff ects of introducing taxation on the asset allocation, Section 10.2 ana-lyzes the consequences of recognizing that risks are shared between the employer and the employees, while Section 10.3 examines the consequences

of introducing default insurance Section 10.4 presents t he implications for the asset allocation of various combinations of taxation, risk sharing, and default insurance Finally, Section 10.5 provides the conclusions

Keywords: Pension f und, a sset a llocation, t ax a rbitrage, r isk

sharing, default insurance, embedded options

10.1 TAXATION ARBITRAGE

Th e taxation eff ect only applies to companies that pay tax on their profi ts, and does not apply when the employer is not subject to corporate taxation, e.g., local authorities, universities, churches, charities, state-owned broadcasters, etc Th erefore, tax arbitrage is not relevant to many large pension schemes.Assuming that the earnings of the pension fund are tax exempt, while contributions to the fund by the employer are tax deductible, and there are no transactions costs; there are two situations in which there is a tax arbitrage gain from switching the investment of a pension fund from equi-ties to bonds Th e fi rst situation was analyzed by Tepper (1981) (see also Bader, 2003; Frank, 2002), while the second was analyzed by Black (1980) (see also Tepper and Affl eck, 1974; Surz, 1981; Black and Dewhurst, 1981; Alexander, 2002; Frank, 2002; Ralfe et al., 2003)

Both m odels a ssume th at th e p ension s cheme will n ot d efault, th e employer owns any surplus on the scheme, and that the pension scheme

is viewed as an integral part of the employer Th e Black m odel assumes

that the capital market equates the gross risk-adjusted returns on bonds

and the equity; i.e., the world assumed by Modigliani and Miller (1958), where the tax deductibility of interest payments creates an incentive for companies to use primarily debt fi nance Th e Tepper model follows Miller

(1977) and assumes that it is net risk-adjusted returns for bonds and

equi-ties that are equal, and so there is no benefi t from companies using debt

fi nance If the marginal investor is tax exempt, for both the Modigliani and Miller worlds, there is no benefi t to using debt fi nance (Frank, 2002).10.1.1 Tepper

In this case, the pension scheme switches from equities to debt, eff ectively lowering the gearing of the employer (which is integrated with the pension scheme) At the same time, the shareholders in the employer borrow money

and invest the proceeds in equities with the same expected returns and tematic risk as shares in the employer Provided the rate of personal taxation on

sys-income from equities (ts) is higher than the rate of personal taxation on income

from bonds (tb), there is a tax benefi t to the shareholders from this strategy.*

Th e two steps of the Tepper strategy will now be described in more detail

1 Th e pension fund is fully invested in equities, which it sells,

invest-ing the proceeds in bonds Let the value of the pension fund be F, the expected g ross return on equities be E[Re], a nd t he ex pected g ross

return on bonds be E[Rb] Th e resulting reduction in the expected

rev-enue of the fund is F(E[Rb] − E[Re]) A change of £1 in the revenue of

the fund is equivalent to a change of only (1 − tc)£1 in the earnings of

the employer because the employer must pay tax at the rate of tc on earnings.† Th erefore, the switch from equities to bonds by the pension fund is equivalent to a reduction in the earnings of the employer of

F(E[Rb] − E[Re])(1 − tc) Such a decrease in net profi ts by the employer is

passed on to the shareholders, who pay tax at the rate ts, so that the net

loss to the shareholders is F(E[Rb] − E[Re])(1 − tc)(1 − ts).‡

2 At the same time as the fund switches from equities to bonds, the

share-holders borrow F(1 − tc) at the expected rate E[Rb] and invest the ceeds in equities with an expected return and systematic risk, which is the same as that of shares in the employer Assuming that the interest payments by the shareholder are tax deductible, the change in the net

pro-revenue of the shareholders is F(1 − tc){E[Re](1 − ts) − E[Rb](1 − tb)}

Th e total net change in the revenues of shareholders from steps A and B

is F(E[Rb] − E[Re]) × (1 − tc)(1 − ts) + F(1 − tc){E[Re](1 − ts) − E[Rb](1 − tb)} = F(1 − tc)

E[Rb](tb − ts) P rovided t hat tb > ts, t he sha reholders g ain t his a mount each year in perpetuity Th e p resent va lue t o t he sha reholders o f t he profi t stream from this tax arbitrage (discounting at the aft er-tax bond

rate (1 − tc)E[Rb] because this gain is riskless) is F(tb − ts)

* Th e values of ts and tb will diff er between individuals, and the appropriate rates are those for the marginal investor In the United Kingdom, the eff ective rate of personal tax on equities will be higher than that on income from bonds where an individual’s total income is less than his/her personal allowances Th is may happen because the individual simply has a low income

or has losses available to off set against other income In such cases, the tax credit on dividends will not be recoverable, whereas any tax credit on income from bonds would be recoverable.

† Th is assumes that the employer has taxable earnings in excess of their pension contributions.

‡ Th is switch from equities to bonds eff ectively lowers the gearing of the employer However in the world of Miller this has no eff ect on the employer’s net cost of capital.

10.1.2 Black

As for Tepper, the pension scheme switches from equities to bonds, eff tively lowering the gearing of the employer (which is assumed to be inte-grated with the pension scheme) In the world of Modigliani and Miller, as the level of debt is increased, the employer gains Th e employer can either benefi t from a lower cost of capital, or restore their initial level of gearing and enjoy a tax gain because interest payments are tax deductible, while payments to shareholders are not Th ese two steps will now be explained

1 Th e pension fund is fully invested in equities, which it sells, investing the proceeds in bonds As for Tepper, the net cost to the employer of

this switch is F(E[Rb] − E[Re])(1 − tc)

2 Th e employer issues debt to raise the sum F(1 − tc), and the interest

on t his debt has a g ross cost t o t he fi rm of F(1 − tc)E[Rb] per y ear, where the fi rm’s bonds are assumed to pay the same rate of interest as the bonds held by the pension fund.* Th e money raised from issuing this debt is used to buy back an equivalent value of the employer’s shares, leading to a reduction in the gross cost of equity capital to the

employer of F(1 − tc)E[Re] per year.† Hence, the reduction in the gross

cost of capital to the employer is F(1 − tc)(E[Re] − E[Rb]) per year.Using t he assumptions of Modigliani a nd Miler, t he reduction in t he gross cost of capital to the employer equals the increased cost of funding the pension scheme caused by its switch from equities to bonds However, there

is a tax gain to the employer, because the interest paid by the company on its new debt is tax deductible, while payments to shareholders are not Th e

overall net gain to the employer from this strategy is F(1 − tc){E[Re] − E[Rb]

(1 − tc)} + F{E[Rb] − E[Re]}(1 − tc) = F(1 − tc)E[Rb])tc per year Th e present value

of this perpetuity (discounted at the aft er-tax riskless rate) is Ftc.‡

*Even if the employer pays a higher rate on the debt it issues (Y) than the fund receives on the bonds

in which it invests (R), the strategy is still worthwhile provided R < Y/(1−tc), Alexander (2002).

† Th is a ssumes t hat t he employer has suffi cient e quity c apital t hat i s av ailable to b e re chased If the employer purchases shares in other companies with the same expected return and systematic risk as its own equity, any taxes on these returns reduce the tax arbitrage gain

pur-It also assumes that there are no transaction costs from issuing the bonds, the purchasers of the bonds require no risk premium for the possibility that the pension fund may switch back

to investing in equities, and no risk premium for their inability to claim the assets of the sion scheme if the employer goes bankrupt, Scholes et al (2001).

pen-‡ Th e aft er-tax rate is used because this is the net cost of riskless capital to the employer Using

the gross discount rate gives a present value of Ftc(1−tc).

Th is analysis shows that for both the Tepper and Black models the larger

is the value of the pension fund (F), the greater is the tax arbitrage gain.*

Th is implies that schemes adopting either the Tepper or Black st rategies should also seek to fund their schemes up to the maximum level permitted

by the tax authorities.†,‡,§

Th e Tepper and Black m odels deal with diff erent worlds Th e Tepper strategy (which applies in the Modigliani and Miller world) produces a

gain with a present value of F(tb − ts), while the Black strategy (which applies

in the Miller world) gives a gain of Ftc.¶ If the corporate tax rate is 30%, the present value of the tax arbitrage gain from the Black strategy will be sub-stantial at 30% of the value of the fund Th erefore, tax arbitrage can pro-vide a powerful reason for company pension schemes to switch the fund

to bonds Th is is illustrated by the example of Boots As well as switching the pension fund into 100% bonds, Boots bought back £300 million of its own shares using available cash Th is is the tax arbitrage strategy of Black, except that the share buyback should have been almost four times larger.**

Th e e stimated p resent va lue o f t he t ax g ain t o B oots f rom t his c apital restructuring is £100 million (Ralfe et al., 2003)

Tax arbitrage generates a gain for the fi rm’s shareholders, while the sion scheme is now less likely to default as it is 100% bonds Th er efore, such

pen-a switch should benefi t both t he employer pen-a nd t he employees, pen-a nd t here should not be any confl ict between these groups in making the asset alloca-tion decision Th e tax arbitrage case for an all-bond portfolio assumes that the risk-minimizing portfolio is all bonds, although this may not be the case

Th e all-bond portfolio may be ineffi cient, and a small proportion of equities

* However, s ubstantially ove rfunding t he s cheme br ings t he r isks of h itting t he I nland Revenue upper limit on the funding ratio (see Section 10.2 ), and pressure to grant substan- tial benefi t improvements out of the large surplus.

† Th omas (1988) fi nds empirical evidence for t he United States that, if the employer’s ginal tax rate or expected future taxable income changes over time, this leads to a change in the level of contributions and the funding ratio in order to maximize the tax benefi ts.

mar-‡ In the United States, when the upper funding ratio is hit, further contributions to the fund are restricted; but there is no requirement to reduce the surplus, as in the United Kingdom Ippolito (1990) shows that this situation provides an incentive for funds to invest in equities

in order to generate an even larger surplus, before the fund is switched to bonds.

§ Th e desire by c ompanies to hold fi nancial slack may also lead to ove rfunding, Myers and Majluf (1984) Datta et a l (1996) found U.S evidence supporting t he hypothesis t hat t he

fi nancial slack motive for overfunding is strengthened when the managers of the employer

do not own shares in the company.

¶ An empirical study of U.S pension schemes by Fr ank (2002) found support for t he Black model, which is consistent with Graham (2000) who presents evidence for the United States

in support of the Modigliani and Miller world, and therefore the Black model.

** Th e size of the Boots share buyback was set on advice from the credit-rating agencies.

may be benefi cial by reducing risk and increasing expected return In these circumstances, pension funds face a t rade-off between the risk minimiza-tion and the tax arbitrage profi ts from holding 100% bonds.*,† Th is could lead to a small diff erence of opinion between the employer and the employ-ees, but t his may be r esolved by t he employer off ering a sha re of t he tax arbitrage gain to the employees to compensate for the increase in risk.10.2 RISK SHARING

Th e risks and rewards from investing the pension fund do not concern solely the employer, but are shared with the employees and pensioners If the employer goes into liquidation, there may be insuffi cient assets to meet the scheme’s liabilities, w ith t he loss fa lling on t he employees and pen-sioners Conversely, if the scheme has a substantial surplus, this may well

be shared between the employer, employees, and pensioners via reduced contributions a nd i ncreased benefi ts I n t hese ways, t he employees a nd pensioners are exposed to the risks of the scheme.‡

Th e sha ring o f defi cits a nd su rpluses be tween t he employer a nd t he employees has been analyzed using option theory by Sharpe (1976) Aft er explaining the Sharpe model, it will be extended by relaxing a number

of the underlying assumptions In constructing his simple model, Sharpe assumes that the employer benefi ts from the full amount of any surplus, but is not liable for any defi ciency.§ He also assumes there is no taxation and

* Making this risk return trade-off requires the scheme to estimate the segment of their liability effi cient frontier that is dominated by the risk-minimizing portfolio.

asset-† U.K pension schemes in aggregate have high equity allocations, and those with corporate employers have not pursued a tax-arbitrage strategy For the Black model, this may be for the reasons mentioned above by S choles et al (2001), or b ecause the employer has insuffi cient taxable profi ts to off set the bond interest payments, or because the employer has insuffi cient share capital to buyback For both the Black and Tepper models the employer must have suf-

fi cient profi ts to off set their contributions to the fund; while if the risk-minimizing portfolio includes an equity component, this may result in a pension fund that is not 100% bonds Th e

Tepper argument for all bonds may not apply because tb is not greater than ts, which has been argued to be the case for the United States by Chen and Reichenstein (1992) Erickson et al (2003), who studied a diff erent form of tax arbitrage in the United States, found that the level

of arbitrage activity could have been about 20 times larger, and concluded that the lack of tax arbitrage is a puzzle A similar puzzle exists for Black and Tepper tax arbitrage.

‡ In reality, there are additional features of the problem, which mean that the employees may bear a substantial share of the cost of a defi cit, without the scheme being wound up A defi cit can lead to the scheme being closed to new members or to additional contributions Benefi ts, other than those already accrued, can be reduced, the retirement age can be increased, the accrual rate reduced, and the employee contribution rate increased In addition, wages may

be frozen, or increased at a lower rate for those in the pension scheme (as did the Financial Services Authority in April 2003).

§ Th ese assumptions will be relaxed below.

no default insurance or compensation.* Th e pension scheme liabilities are

valued at L, while the assets are valued at A, and so the value of any scheme surplus or defi cit is (A − L) Sharpe argues that, in eff ect, the employer has

a long position in a c all option on t he assets of t he f und, w ith a st rike

price of L (i.e., the right to buy the assets in the fund on payment of L)

Th is call option is valued at C Th e employees have t he right to receive their contractual pension benefi ts (i.e., L) and have eff ectively sold a p ut option on the assets of the fund with a strike price of L (i.e., they must sup- ply the assets in the fund for L, on request) Th is put option is valued at P

Th e European style put-call parity means that A = C − P + L.†

By working for the employer, employees receive their pension

entitle-ments (L) and their wages, which have a present value of W Th e

employ-ees have also accepted the obligation to bear any scheme defi cits, and

this is valued by the put premium (P) Sharpe argues that in a tive labor market the sum of these three amounts will be a co nstant (K),‡

competi-and s o L − P + W = K.§ Th er efore, since A = C − P + L; i t f ollows t hat

K = W + A − C Th is means that the fi xed cost of remuneration (K, or

sal-ary plus pension costs) equals the wage cost ( W), plus the assets in the fund (A), less the value of the call option on any surplus in the fund (C)

Black and Scholes (1973) have shown that the value of a E uropean style call or put option depends on six variables—the price of the underlying

asset (A), the strike price of the option (L), the riskless interest rate (r),

dividends (which are zero in this case), the time to expiry of the option

(t), and the volatility of returns on the underlying asset (σ) Sharpe then

argues that, although a h igh equity allocation increases the riskiness of

returns on the pension fund (i.e., σ) thereby increasing C and P; this will

be off set by a co rresponding i ncrease i n either wa ges (W), or assets in the fund (A) Th erefore, a high equity allocation has no eff ect on the total

* It is also implicitly assumed that there are no pension scheme termination costs, e.g., lawyers fees, poor labor relations, etc Th eir presence makes a high equity allocation less attractive.

† Note t hat for Eu ropean style options on non- dividend paying assets, unless A = L (1 + r), where r is the riskless rate of interest between now and expiry, C does not equal P.

‡ If the employer is a public sector organization, it may be constrained by its government ing, and seek to fi x the total cost of employment.

fund-§ Th e empirical evidence on the existence of a trade-off between pension benefi ts and salaries

is m ixed Gu nderson et a l., (1992) re viewed t his e vidence, a nd fou nd fi ve papers, which support a t rade-off , three papers with some evidence for a t rade-off , two papers that fail

to fi nd a trade-off , and three papers that fi nd a positive relationship between pensions and salaries.

cost of employee remuneration to the employer In Sharpe’s view, pension

“funding policy is irrelevant”.*,†,‡,§

Sharpe’s simple model will be elaborated in three diff erent ways First, if total employee remuneration is not fi xed, the asset allocation is no longer irrel-evant Assuming that there is no wages or funding level off set, a high equity allocation increases the volatility of the underlying asset, and this increases the value of the put and call options Given the assumptions of Sharpe about how defi cits and surpluses are shared, investment risk for the employer is a bet with the characteristics of “heads I win, tails you lose.” Th erefore, a high equity allocation makes the employees worse off , and the employer better off ¶

Second, if total remuneration is not fi xed and the employer bears a

pro-portion of defi cits (d), while the employees receive a sha re (1 − s) of any

surplus, the situation becomes more complex.**,††,‡‡,§§ If there is no off setting,

then employees’ total remuneration rises to K = L − P(1 − d) + C((1 − s) + W,

* It also follows from the theory of option pricing that by reducing the funding ratio, the value

of the put option is increased, while the value of the call option is reduced.

† Th e funding ratio is also indeterminate as an increase in L will be off set by an increase in

P and a reduction in C.

‡ In this case, the asset allocation is the chosen point on the effi cient frontier If a number of asset classes is under consideration (e.g bonds, index-linked gilts, property, U.K equities, overseas equities, etc.) an asset–liability study is needed to determine the effi cient frontier.

§ Sharpe’s model deals only with active members who can renegotiate their wages as the scheme’s asset allocation is altered Deferred members and pensioners have no such sanction against an employer whose pension fund adopts a high equity allocation However, pensioners come before active members in the priority order for compensation on a w inding up, and so the greater is the liability to p ensioners, the greater is the increase in risk borne by a ctive members when the fund has a h igh equity allocation Th erefore, although the problem is more complicated than presented by S harpe, even for m ature schemes, the Sharpe model may be a re asonable approximation.

¶ Th is outcome is mentioned by Sherris (1992).

** Th e variables d a nd s a re i n t he z ero–one r ange a nd a re a ssumed for t he mome nt to b e

known for certain.

†† Discretionary benefi ts a re a me thod of s haring s urpluses b etween t he e mployer a nd t he employees.

‡‡ It will be assumed for simplicity that the same values of s and d apply to both active members

and pensioners However, given the priority order on a winding-up in the Pensions Act 1995 (and the recently proposed government amendments), active members bear much more of the default risk than do current pensioners Th erefore, pensioners have a greater appetite for

a high equity allocation than active members Benefi t increases may be directed at a ctive members, current pensioners, deferred pensioners, or all three groups.

§§ Until 2003, when a scheme was wound up the employer only needed to ensure the funding level was up to t he MFR, and this may correspond to a f unding ratio that is well below 100% In consequence, the employees could suff er from any such under-funding From June 11, 2003 the U.K government required employers to fully fund schemes on a winding-

up, Department for Work and Pensions (2003) Th i s increased d.

while the cost to the employer increases to K = W + A − Cs + Pd Whether

a high equity allocation in this situation is benefi cial to t he employees

or the employer depends on the way in which K changes as the volatility

of returns on the fund (σ) changes Th is depends on the sign of ∂K/∂σ =

∂(L + W)/∂σ + (1 − s)(∂C/∂σ) − (1 − d)(∂P/∂σ), wh ere ∂ C/∂σ a nd ∂ P/∂σ are, b y d efi nition, t he va lues o f v ega (v) f or t he c all a nd p ut o ptions,

respectively

Using the Black-Scholes model, vega is a positive number which is the

same for both the put and call options, and is given by v = A√t.exp(−D2/2)/(2π)0.5 where D = [ln(A/L) + (r + 0.5σ2)t]/σ√t Since the values of r, t, A, L, and

σ are the same for both the call and put options, and total remuneration is

fully responsive, i.e., ∂(L + W)/∂σ = 0, then ∂K/∂σ = v(d − s) Provided that

d > s, a high equity allocation increases σ, which increases K, making the

employees better off and the employer worse off When s > d, a high equity allocation leads to a r eduction in K, and so t he employer gains, and the

employees lose For example, if the employing company is close to fi nancial distress, with a net asset value near zero, it may be in the interests of the shareholders of this company to have a high equity allocation If equities

do well, the net asset value of the company increases because the value of the pension fund has increased If equities do badly, the funding ratio of the scheme deteriorates, leading to a n increase i n t he contribution rate and the likely liquidation of the employer In this case, all the outstanding obligations of the employer fall on the creditors of the company, including the obligations to the pension scheme, Alexander (2002)

Th erefore, when total remuneration is not fi xed, surpluses and defi cits are shared between the employer and the employers on a simple propor-tionate basis, the Black-Scholes option-pricing model applies, and there are

no tax arbitrage eff ects: (1) the interests of the employer and the employees concerning a high equity allocation are directly opposed* and (2) whether

* Confl ict between t he employer and t he employees over t he investment policy of t he f und

is only important if neither party can make this decision acting alone Th e requirement by the Pensions Act 1995 for me mber-nominated trustees from 1997 may have increased the infl uence of employees on the asset allocation decision However, whether or not one group controls t his decision depends on t he r ules of e ach scheme, a nd some schemes a llow t he employer to set the contribution rate Useem and Hess (2001) analyzed the asset allocation decisions of 2 53 of t he l argest U.S pu blic p ension s chemes i n 1992 Th ey fou nd t hat t he equity proportion was negatively related to investment restrictions, and positively related to the existence of independent performance evaluation and the number of trustees However, the proportion of t rustees elected by t he members had no si gnifi cant eff ect on t he equity proportions.

it i s t he employer or t he employees who favor a h igh equity a llocation

depends on the relative magnitudes of d and s.*

Over the past two decades, many pension schemes have granted stantial benefi t improvements, but no data are available on the cost of these improvements, as a proportion of the surplus However, there is informa-tion on the way in which surpluses are shared when schemes breach the revenue limit Schemes whose funding ratio breaches the upper limit of 105% set by the Inland Revenue for the retention of their tax-exempt sta-tus, must reduce their surplus For a 14-year period (1987–2001), the pro-portion of such required reductions in surplus received by members was 34.4% If schemes share surpluses in the same proportion as reductions in

sub-surplus required by the inland revenue, then s = 0.656.† For well-funded schemes w ith a la rge and successful employer who is committed to t he

scheme, the value of d will be close to unity Th erefore, it is probable that

d > s , and a h igh equity a llocation favors the employees at the expense

of the employer.‡ However, if the employees receive a very small share of

any surpluses, or the employer may well default, then it is likely that s > d

and the employees will be opposed to a high equity allocation, while the employer will support a high equity allocation

A further complication of the second variant of the Sharpe model arises when there is a partial off set, i.e., total remuneration responds to a change

in the values of C and P, but by less than the full amount because of a tial off set against wages or the funding level In which case ∂(L + W)/∂σ ≠ 0

par-In consequence, assuming that the degree of partial off set is the same for both surpluses and defi cits, the gains and losses are reduced in size by the partial off set, but the result that the employees favor a high equity alloca-

tion when d > s (and vice versa) is unaff ected.

In the fi nal variation of the Sharpe model, it is again assumed that total

remuneration (K) is fi xed, while defi cits and surpluses are shared in some

* Ippolito (1985) shows that, if the labor force is unionized and the company has a s tial investment in specialized capital equipment, the union may seek to i ncrease wages by threatening to s trike Th e employer can counter this threat by d eliberately under-funding the pension scheme Th e employees now bear some of t he risks of a s trike, which may lead

ubstan-to the closure of t he company and default on t he pension scheme Cooper and Ross (2001) argue that, if the fi rm faces a binding borrowing constraint, it can eff ectively borrow from the pension fund by under-funding the pension scheme.

† Inland Revenue Web site.

‡ Th e value of d may also be close to unity if there is some actual or implicit guarantee (e.g.,

the government) in the event of a defi cit on winding up Th is situation will be considered in

Section 10.3 on default insurance.

way, and any gains or losses to the employees and employer from a high equity allocation are off set by changes in wages or the level of funding In such circumstances, the asset allocation again becomes irrelevant.

Th e various situations analyzed earlier are summarized in Table 10.1 In each case, a high equity allocation is a zero sum game Following the rule changes of June 11, 2003, solvent employers cannot wind up a scheme with-out funding any defi cit In consequence, there is a strong probability that

the employer will not wind up the scheme in a defi cit situation (so that d is close to unity), surpluses are shared (possibly s = 2/1/4) and total remunera- tion (K) is variable In these circumstances, d > s and the employees favor

a high equity allocation, while the employer favors bonds Th is is because

a high equity al location now off ers t he em ployees a “ heads I w in, t ails you lose” bet If equities perform well, the employees receive substantial benefi t improvements, while if equities perform badly, the costs are very largely met by the employer However, because they bear most of the risk

of defi cits, but receive only a proportion of the surpluses, employers favor the risk-minimizing portfolio When total remuneration is fi xed, the asset

allocation is unaff ected by the values of d and s If total remuneration can

vary, the funding decision only requires the estimation of the relative size

of two parameters, d and s It does not require the valuation of the implicit

put and call options, the degree of partial off set, or the value of vega.Two generalizations of the various Sharpe models will now be consid-ered Th e fi rst involves t he implicit assumption concerning diversifi able risk A h igh equity a llocation i ncreases t he volatility of t he a ssets, a nd this increased risk is shared in diff erent ways between the employees and the employer It has been assumed so fa r t hat t hese changes in risk are

TABLE 10.1 Summary of the Various Combinations of Total Remuneration and Risk Sharing

Th e Sharpe Model and Its Th r ee Variants