How Pension Funds Lost In Market Boom

In one of the happiest reports to come out of Detroit lately, General Motors proclaimed Tuesday that its U.S. pension funds are now "fully funded on an economic basis." Less noticed was GM's admission that, in accounting terms, it is still a few cents—well, $3 billion—shy of the mark.

Wait a minute. If GM's pension plans were $9.3 billion in the hole when the year began, and if the company, to its credit, shoveled in $10.4 billion more during the year, how come its pension deficit wasn't wiped out in full?

We'll get to that, but the real news here is broader than GM. According to experts, most pension funds actually lost ground, . . . even though, as you may recall, it was a rather good year for stocks and bonds.

True, pension-fund assets did have a banner year. But as is sometimes overlooked, pension funds also have liabilities (their obligations to retirees). And at most funds, liabilities grew at a rate that put asset growth to shame. At the margin, that means more companies' pension plans will be "underfunded." And down the road, assuming no reversal in the trend, more companies will have to pony up more cash.

What's to blame? The sharp decline in interest rates that brought joy to everyone else. As rates fall, pension funds have to set aside more money today to pay off a fixed obligation tomorrow. In accounting-speak, this "discounted present value" of their liabilities rises.

By now, maybe you sense that pension liabilities swing more, in either direction, than assets. How come? In a phrase, most funds are "mismatched," meaning their liabilities are longer-lived than their investments. The longer an obligation, the more its present value reacts to changes in rates. And at a typical pension fund, even though the average obligation is 15 years away, the average duration of its bond portfolio is roughly five years.

If this seems to defy common sense, it does. No sensible family puts its grocery money (a short-term obligation) into common stocks (a long-term asset). Ordinary Joes and Janes grasp the principle of "matching" without even thinking about it.

But fund managers—the pros—insist on shorter, un-matching bond portfolios for a simple, stupefying reason. They are graded—usually by consultants— according to how they perform against standard (and shorter-term) bond indexes. Thus, rather than invest to keep up with liabilities, managers are investing so as to avoid lagging behind the popular index in any year.

Source: Roger Lowenstein, "How Pension Funds Lost in Market Boom," The Wall Street Journal, February 1, 1996. Excerpted by permission of The Wall Street Journal, © 1996 Dow Jones & Company, Inc. All Rights Reserved Worldwide.

Several points are worth highlighting. First, duration matching balances the difference between the accumulated value of the coupon payments (reinvestment rate risk) and the sale value of the bond (price risk). That is, when interest rates fall, the coupons grow less than in the base case, but the gain on the sale of the bond offsets this. When interest rates rise, the resale value of the bond falls, but the coupons more than make up for this loss because they are reinvested at the higher rate. Figure 16.9 illustrates this case. The solid curve traces out the accumulated value of the bonds if interest rates remain at 8%. The dashed curve shows that value if interest rates happen to increase. The initial impact is a capital loss, but this loss eventually is offset by the now-faster growth rate of reinvested funds. At the five-year horizon date, the two effects just cancel, leaving the company able to satisfy its obligation with the accumulated proceeds from the bond. The nearby box (page 507) discusses this trade-off between price and reinvestment rate risk, suggesting how duration can be used to tailor a fixed-income portfolio to the horizon of the investor.

We can also analyze immunization in terms of present as opposed to future values. Table 16.7A shows the initial balance sheet for the insurance company's GIC account. Both assets and the obligation have market values of $10,000, so that the plan is just fully funded. Tables 16.7B and C show that whether the interest rate increases or decreases, the value of the bonds funding the GIC and the present value of the company's obligation change by virtually identical amounts. Regardless of the interest rate change, the plan remains fully funded, with the surplus in Table 16.7B and C just about zero. The duration-matching strategy has ensured that both assets and liabilities react equally to interest rate fluctuations.

PART IV Fixed-Income Securities

Figure 16.9 Growth of invested funds. The solid colored curve represents the growth of portfolio value at the original interest rate. If interest rates increase at time t*, the portfolio value initially falls but increases thereafter at the faster rate represented by the broken curve. At time D (duration) the curves cross.

PART IV Fixed-Income Securities

Table 16.7 Market Value Balance Sheet



A. Interest rate = 8%

Bonds $10,000



B. Interest rate = 7%

Bonds $10,476.65



C. Interest rate = 9%

Bonds $9,551.41



Value of bonds = 800 x Annuity factory 6) + 10,000 x PV factor(r,6) 14,693.28

Value of obligation = + ^ 5 = 14,693.28 x PV factor(r,5)


Value of bonds = 800 x Annuity factory 6) + 10,000 x PV factor(r,6) 14,693.28

Value of obligation = + ^ 5 = 14,693.28 x PV factor(r,5)


Figure 16.10 is a graph of the present values of the bond and the single-payment obligation as a function of the interest rate. At the current rate of 8%, the values are equal, and the obligation is fully funded by the bond. Moreover, the two present value curves are tangent at y = 8%. As interest rates change, the change in value of both the asset and the obligation is equal, so the obligation remains fully funded. For greater changes in the interest rate, however, the present value curves diverge. This reflects the fact that the fund actually shows a small surplus in Table 16.6 at market interest rates other than 8%.

If the obligation was immunized, why is there any surplus in the fund? The answer is convexity. Figure 16.10 shows that the coupon bond has greater convexity than the obligation it funds. Hence, when rates move substantially, the bond value exceeds the present value of the obligation by a noticeable amount. Another way to think about it is that although the duration of the bond is indeed equal to 5 years at a yield to maturity of 8%, it rises to 5.02 years when its yield falls to 7% and drops to 4.97 years at y = 9%; that is, the bond and the obligation were not duration-matched across the interest rate shift.


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