A portfolio approach to the optimal funding of pensions

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1 Economics Letters 69 (000) locte/ econbse A portfolio pproch to the optiml funding of pensions Jysri Dutt, Sndeep Kpur *, J. Michel Orszg b, b Fculty of Economics University of Cmbridge, Cmbridge, UK b Deprtment of Economics, Birkbeck College, London W1P LL, UK Received 4 My 1999; received in revised form 1 Jnury 000; ccepted 7 Mrch 000 Abstrct Fully funded pension systems re dvocted for their higher rte of return, but this return is typiclly risky. Using simple men-vrince model, we find tht mixed funded unfunded systems re desirble in this setting becuse they enble risk diversifiction. 000 Elsevier Science S.A. All rights reserved. Keywords: Pensions; Socil security; Portfolio choice JEL clssifiction: H55; G11 1. Introduction The originl rgument for unfunded pension systems is bsed on the possibility of dynmic inefficiency, or cpitl overccumultion (Dimond, 1965; Smuelson, 1975): individuls my sve too much, nd the rte of return on cpitl be too low reltive to the growth rte of the economy. Unfunded pensions re direct method of redistributing consumption cross genertions nd restoring efficiency. Excessive sving my be prticulr problem in situtions where younger workers cnnot fully insure future risks of income or mortlity (Dimond, 1977). The current cse for funded pensions is mde, mong other things, on the grounds tht the rte of return on investment exceeds income growth (e.g. Aron, 1966; Feldstein, 1974, 1996). Therefore, in the bsence of lbour supply effects nd chnges in the tx regime, investment in funded systems yields higher returns thn n unfunded system. The force of the rte of return rgument is prticulrly strong in countries with negtive popultion growth nd geing popultions. The cost of unfunded pensions flls symmetriclly on younger workers. Miles (1997) evlutes the prcticl relevnce of these rguments, s well s the likely impct of trnsition to funded system in the UK nd comprble countries. *Corresponding uthor. Tel.: ; fx: E-mil ddress: skpur@econ.bbk.c.uk (S. Kpur) / 00/ $ see front mtter 000 Elsevier Science S.A. All rights reserved. PII: S (00)0071-8

2 0 J. Dutt et l. / Economics Letters 69 (000) However, this nlysis focused on the men level of returns nd ignored the vrince nd portfolio effects. Such effects were indeed looked t by Merton (1983) nd Merton et l. (1987) s well s by Dutt et l. (1999). Ernings risks cnnot be diversified directly, nd prtil funding llows the old to hold shres in the humn cpitl of the young. This pper provides simplified tretment for some of these rguments, csting the optiml pension funding choice in men-vrince portfolio choice frmework. The optimum funding solution then is to hedge by holding diversified set of libilities, both funded nd unfunded. Section below looks t this problem. Section 3 extends the bsic men-vrince model to look t wht portfolio shre of bonds nd equities should be held in funded system. In prticulr, the portfolio weights in equities nd bonds might depend on the level of funding. A finl section concludes.. A simple men-vrince model The rte of return to funded pension is r wheres n unfunded pension hs return g where g is the growth rte in ntionl income. We suppose frction w of pension libilities re covered with funded provision nd the reminder is unfunded. Then, the totl pension workers will receive per unit of money contributed is: 1 1 wr 1 (1 w)g. Since both r nd g re rndom vribles, the utility of men pension income is: EU(1 1 wr 1 (1 w)g) (1) Let P wr 1 (1 w)g denote pension income. To obtin the optiml funded/unfunded mix, we mximize with respect to the funded shre, w, obtining: E(U 9(P)(r g)) 5 0 () if 0, w, 1. In the bsence of risk version, U 9 is constnt, nd we obtin the (Aron, 1966) solution tht it is optiml to invest in funded system whenever Er. Eg. However, with risk version, it my be better to hedge by using mixture of funded nd unfunded pensions. To keep the nlysis simple, we focus on men-vrince utility function: g EU(P) 5 EP ] vr(p) (3) where g is risk-version prmeter. We note tht EP wm 1 (1 w)m r g (4) vr(p) 5 w s 1 (1 w) s 1 w(1 w)s (5) r g rg i i rg where m, s re the expecttion nd vrince of ny vrible i nd s the covrince of r nd g. The optiml funded shre is: r g g rg m m 1 g(s s ) w 5]]]]]]] gs rg (6)

3 J. Dutt et l. / Economics Letters 69 (000) Tble 1 Growth rtes nd totl return on equity ( ) Country GDP growth (%) Return on equity Covr Men Vrince Men Vrince s rg mg sg mr sr USA UK Frnce Germny Jpn Dt from own clcultions using 10-yer verges; dt on GDP from Mddison (1991); dt on equity returns from Globl Finncil Dt (1999). How lrge is w for relistic prmeter vlues? In Tble 1, we report the relevnt chrcteristics for five countries. The return on the funded component, r, is pproximted by the rel return on equity. As pension funds re held for reltively long periods, we report these chrcteristics for the period , using 10-yer verges over this intervl for our computtions. Thus the funded prt of pensions (equity) hs high men return nd high risk sset. For risk verse individuls, it is optiml to choose mix of the two. Tble reports optiml vlues obtined from Eq. (6) for the bove prmeter vlues. As the vrince covrince prmeters differ shrply cross countries, so will the optiml funding levels. As Fig. 1 illustrtes, the optiml choice of w vries with the degree of risk-version, here prmetrized by g. It lso vries with s rg, which ffects the possibility of diversifying income risk in the stock mrket. For the US, optiml funding levels re high becuse the men return on equity is high, nd srg is low. For Jpn, funding levels re reltively low becuse s r is lrge nd diversifiction possibilities re limited. 3. Portfolio lloction in funded systems Another considertion is tht unfunded socil security will ffect optiml portfolio lloctions of investors. As n exmple of this, consider country such s Singpore or Mlysi which hs lrgely funded system. In such country, there is no unfunded system to provide risk hedge, forcing Tble Risk-version nd optiml funding Country Risk-version prmeter g g g USA 77.% 38.6% 19.% UK 45.1% 19.3% 6.3% Frnce 0.6% 9.3% 3.5% Germny 63.5% 4.9% 5.5% Jpn 0.1% 0 0

4 04 J. Dutt et l. / Economics Letters 69 (000) Fig. 1. The effect of chnges in g on optiml funding. funded schemes to invest in less risky, lower return ssets. While there my be other fctors such s politicl independence of the investment bord tht re importnt, the level of risk in lterntive vilble ssets is lso crucil considertion. In the bsence of nother low risk lterntive, individuls nd pension funds will hold government bonds which my hve much lower returns thn tht on unfunded pensions. A common rgument for funded pensions is tht they will led to more developed cpitl mrkets. One issue with these rguments is tht the existence of unfunded pensions is n importnt risk hedge through which diversifiction into equities cn tke plce. This model is esily formlized. Ech unit of pension contributions now results in pension of: P wr 1 w(1 )r 1 (1 w)g (7) b where is the frction of the funded pension llocted to equity nd r is the return on bonds. Given b fixed w, the sset lloction problem is to choose optimlly. Using dt comprble to tht in Tble 1, we report long-term rel return on bonds. The dt in Tble 3 suggest tht the bonds hve provided low return in rel terms, nd with considerble vrince. Bsed on these figures, the funded portion of pension systems is better llocted to equities rther thn bonds. In the long run, bonds re probbly dominted by mix of unfunded nd equity ssets. The optiml vlues of bsed on these figures using this dt re shown in Tble 4. Germny, with reltively higher return on bonds, is one exception to the generl rule tht portfolios should be minly invested in equity.

5 Tble 3 Rel return on bonds: Country Return on bonds Men Vr mb sb USA UK Frnce Germny Jpn.0 54 J. Dutt et l. / Economics Letters 69 (000) Clcultions using 10-yer verges (dt from Globl Finncil Dt, 1999). Tble 4 Portfolio lloction in funded systems: shre of equity Country Funding rtio w w w USA 100% 100% 88.7% UK 100% 100% 78.% Frnce 100% 100% 100% Germny 33.7% 33.1% 33.0% Jpn 100% 100% 100% Optiml conditionl on funding level; truncted t 100%. 4. Conclusions This pper hs provided simplified model of why funded pensions should ordinrily be combined with unfunded pensions in order to mximize the combintion of risk nd return. It lso hs provided simple nlyticl frmework for ssessing wht frction of investments in funded system should be funded nd unfunded. This simplifiction comes t cost. There is no generl equilibrium wge or rte of return determintion or creful modelling of issues such s erly retirement nd the government budget constrint. Despite the simplicity though, the messge of pying more ttention to risk-return trdeoffs in socil security policy nlysis is well-worth heeding. References Aron, H.J., The socil insurnce prdox. Cndin Journl of Economics 3, Dimond, P.A., Ntionl debt in neoclssicl growth model. Americn Economic Review 55, Dimond, P.A., A frmework for socil security nlysis. Journl of Public Economics 83, Dutt, J., Kpur, S., Orszg, J.M., How to fund pensions: income uncertinty nd risk-version, Birkbeck Economics Working Pper No

6 06 J. Dutt et l. / Economics Letters 69 (000) Feldstein, M.S., Socil security, induced retirement, nd ggregte cpitl ccumultion. Journl of Politicl Economy 8, Feldstein, M.S., The missing piece in policy nlysis: socil security reform. Americn Economic Review 86, Globl Finncil Dt, 1999; vilble electroniclly t Mddison, A., Dynmic Forces in Cpitlist Development. Oxford University Press, Oxford. Merton, R.C., On the role of socil security s mens for efficient risk shring in n economy where humn cpitl is not trdeble. In: Bodie, Z., Shoven, J. (Eds.), Finncil Aspects of the United Sttes Pension System. University of Chicgo Press. Merton, R.C., Bodie, Z., Mrcus, A., Pension pln integrtion s insurnce ginst socil security risk. In: Bodie, Z., Shoven, J., Wise, D. (Eds.), Issues in Pension Economics. Chicgo University Press. Miles, D., Finncil Mrkets, Ageing, nd Socil Welfre, Inugurl Lecture. Imperil College, University of London. Smuelson, P.A., Optimum socil security in life-cycle growth model. Interntionl Economic Review 16,