Vanderbilt Capital Advisors
PROPER
CASH-FLOW DISCOUNTING FOR PENSION FUND LIABILITIES
Financial
Accounting Standards Board (FASB) Statements 87 and 88 have given rise to a
great deal of confusion over the concept of discounting pension liabilities at
market rates. Until recently,
liabilities were frequently discounted at rates determined solely by actuaries,
but now many pension sponsors use a variety of market rates—long bond rates,
internal rates of return on the corresponding portfolio or duration-matched
rates, among others. Unfortunately, few
sponsors have a systematic, theoretically consistent approach to discounting
liabilities.
Background
The
FASB mandated the use of market rates as a standard in order to increase
comparability, consistency and objectivity of the liability discounting
process. By using market rates,
different actuaries should achieve a higher degree of comparability when
valuing pension liabilities of different firms.
They should also achieve consistency in valuing liability streams over
time. Furthermore, market rates serve as
an anchor in liability valuation. They
help to ensure that actuaries, pension sponsors and investment managers achieve
objectivity in their pension liability measurement. Finally, discounting liabilities at market
rates makes economic sense because there exists a
market for these flows. Thus the use of
market interest rates represents a truly important step in pension fund
management.
If
market interest rates solve all the pension investor's problems, then why is
there still confusion? The confusion
arises because there is no single "market interest rate." Different interest rates reflect differences
in terms to maturity, various forms and sources of risk liquidity and tax
considerations. FAS 87 specifies that,
for liability discounting, pension sponsors may look at currently available and
expected future returns on high-quality, fixed income securities to infer the
appropriate market rate. That narrows
down the specification of interest rates significantly, but does not completely
clear up the question of the appropriate discount rate.
Identifying
Appropriate Discount Rates
Actuaries
use subjective probability estimates on scores of variables (including mortality,
expected inflation and termination rates) in order to estimate expected values
of pension liabilities. The cash flows
estimated by the actuaries are essentially risk-free in the conventional
finance sense, because they are subject only to interest rate risk and
taxes. While taxes are a potentially
important issue with investments, they can generally be ignored in the present
context, because pension benefits are promised on a pre-tax basis and portfolio
income is tax-exempt to the sponsor.
The
task of the pension manager is thus essentially a matter of evaluating a series
of pre-tax, risk-free cash flows. This
can be accomplished in a number of ways.
One method commonly employed for discounting liabilities is to use a
20-year or similar U.S. Treasury bond rate as the discount rate. The argument in favor of this is that
Treasury bonds are close to being risk-free and, furthermore, 20 years may be
close to the weighted average life of the liabilities.
A
problem with this method is that the rate used does not necessarily, and in
most cases will not, correspond to the term of the liability being
discounted. In fact, with a positively
sloped yield curve, the use of a single rate tends significantly to undervalue
the near-term and overvalue the long-term liabilities. The distortion becomes greater, the steeper
the yield curve. In short, the use of
the yield to maturity of a single security as a proxy for the rate to be used
in discounting liabilities can result in serious valuation errors which may, in
turn, distort investment allocation decisions on the asset side.
Pension
liabilities may be discounted at the internal rate of return (IRR) on the
portfolio backing the liabilities. This
has the advantage of being a market rate.
Also, as long as the assets are somehow matched against the liabilities,
the rate represents a logical rate to associate with those liabilities.
The
problem is that most portfolios are subject to more than just interest rate
risk, whereas the liabilities have only interest rate risk. Corporate bonds, for example, have market
risk exposure due to individual company risks.
Many bonds, including Treasury bonds, have call or other features that
push the yields away from what the discount rate on a simple risk-free cash
flow should be. In general, this means
that the discount rate will be higher than it should be, leading to a lower
present value estimate of the pension obligations. This, in turn, leads to potential underfunding and under-hedging of the true pension
liability.
Even
if we were to use the IRR of an immunized portfolio of non-callable Treasury
securities as our discount rate, we would still have a problem. The IRR is naturally sensitive to the timing
of the portfolio's cash flows. To the
extent the timing of the liabilities deviates from these, use of the IRR rate
will distort the liability valuation.
The
shortcomings of the first two alternatives suggest a third alternative:
Discount the liabilities along the Treasury yield curve. Because we are considering only Treasury
issues, there is no credit risk present.
Also, if only "current" or "on-the-run" (OTR)
Treasury issues are considered (as is typically the case), call risk is
eliminated, because the Treasury is currently not issuing callable bonds. By using OTR Treasuries, we have also
minimized liquidity risk, as these are the most liquid bonds traded. Finally, by discounting along the yield
curve, this method associates the maturities of the assets with those of the
liabilities. This, then, would seem to
be an appropriate method for discounting a stream of "riskless"
liabilities. Unfortunately, it fails on
one point.
Discounting
along the yield curve associates the maturities of the assets and
liabilities. As pointed out above,
however, the Treasury bond yield to maturity is an average rate incorporating
the pricing of cash flows from coupon payments as well as the final principal
payment. The liabilities, by contrast,
are represented as a series of individual future cash flows. What we need is a set of rates that
eliminates all but interest rate risk yet corresponds to a series of single
future cash flows. Two alternatives
exist.
STRIPS
STRIPS
(Separate Trading of Registered Interest and Principal of Securities) are
created by separating the coupon and principal payments from a Treasury coupon
bond. These securities thus provide the
only vehicle by which an investor can effectively lock up a single future cash
flow with certainty (i.e., risklessly). They are traded in a very large and liquid
market (though not as liquid as the Treasury coupon market) and provide an
objective, readily accessibly measure for discounting liabilities.
While
STRIPS possess very little liquidity risk, this risk is still priced and
results in a slight increase in the yield demanded by investors. Because we wish to price only interest rate
risk, the incorporation of this liquidity premium in discounting will slightly
understate the value of the liabilities.
The discrepancy, although minor, can be
adjusted for directly by observing STRIPS' bid-ask spreads. These spreads will vary with volatility
levels and technical factors, but an average or normal spread can be closely
approximated. STRIPS rates adjusted to
account for bid-ask spreads would seem to provide an appropriate proxy for the
"riskless" rates we are looking for. However, one concern with the approach remains.
Supply
and demand factors in the STRIPS market cause discrepancies between STRIPS
rates and the theoretical spot rates.
Because of their ability to substitute for T-bills, STRIPS in the short
end of the market tend to trade richer than we would expect. Similarly, STRIPS in the very long (28-30
year) maturity range tend to trade rich.
This is a result of the high demand for these securities by investors
needing their long duration and high interest rate sensitivity. But technical factors play a role in all
markets; witness, for example, the hump in the 20-year area of the Treasury
curve.
Spot
Rates
Another
method of obtaining single-period, risk-free rates is
to use Treasury market information to estimate theoretical "spot"
rates. Based on a hypothetical, pure
discount security, these estimates of the yield-maturity relationships in the
Treasury market are adjusted to take account of callability,
liquidity, tax and other effects. In
theory, these spot rates are precisely what we are after. However, some practical concerns must be
addressed.
The
first concern is objectivity. The theory
behind spot rate estimation is very straightforward, but differences arise in
practical application. Of primary
importance are differences in the methods employed to account for the various
effects we wish to eliminate, particularly the effect of callability. Such differences will naturally lead to
discrepancies between various spot rate estimates and between the resulting
liability valuations. If different
models are theoretically consistent, however, these differences should be
minor.
Another
problem concerning objectivity exists, however.
Because the applied term structure models are proprietary in nature,
they are not readily observable by all market participants.
Were
we able, through divine intervention, to obtain actual spot rates, as opposed
to estimates, we would still have a problem, because these rates are not
actually available in the market. In
theory, we could obtain these rates by perfectly cash-matching
the liability stream. Even if this
perfect match were possible, the associated transaction costs would prove
prohibitive.
In
practice, these spot rates are obtained by matching the key characteristics
(present value, duration, convexity) of the asset and liability streams. Attempts may also be made to control for more
complex, non-parallel, term-structure movements. In any case, the results realized on the
assets will not equal those predicted by the spot rates. Thus spot rates are not truly riskless in the sense that our ability to obtain these
rates depends on our ability to "immunize" the liability stream. If the immunization is set up properly,
however, this problem is a very minor one.
The
Problem with Long Liabilities
We
have concluded that the appropriate method for discounting liabilities is to
use single-payment, riskless rates corresponding to
each respective liability projection. A
problem arises, however, when we consider liabilities beyond 30 years, because
there exists no corresponding asset market with this
maturity.
A
monotonically increasing or decreasing term structure, flattening rapidly in
the long end, would enable us to extrapolate the curve out beyond 30
years.
An
alternative to this solution is suggested by the fact that corporations
(primarily utilities) issue debt out to 40 years. By observing and measuring the risk
characteristics of utilities with less than 30 years to maturity, and
extrapolating these relationships to utilities in the 30 to 40-year area, we may
obtain spot rate estimates. Of course,
this method assumes these relationships are either constant or deviate
systematically across maturities. It
also leaves us with the question of what to do with liabilities beyond 40 years
(though alternative methods of discounting liabilities out this far will have
very little effect on the valuation of the total liability stream). Given this, as well as the above discussion
on term structure flattening in the long end, we would suggest using the
30-year, risk-free single payment for valuing liabilities beyond 30 years.
(*)
M. Livingston, "Flattening of Bond Yield Curves,"
Journal of
Financial Research, Spring 1987, pp. 17-24
Conclusion
In
determining the appropriate rate to use for discounting liabilities, we have
focused on the accumulated portion (ABO) of the pension obligation. Pension obligations that will be incurred in
the future are subject to a great deal of non-interest-rate uncertainty, much
of which can be offset by investments in non-fixed-income securities. But the accumulated portion of the pension
liability is relatively predictable.
Furthermore, the uncertainty that does exist results from uncertainty
associated with the underlying actuarial projections and assumptions, which
cannot be readily hedged in the market.
From a market perspective, then, these cash flows should be considered riskless. The
appropriate method for discounting them (i.e., the method that eliminates all
but interest rate risk from the valuation) is one that uses single-period,
risk-free rates (i.e., rates adjusted for credit, callability,
liquidity and other risk premiums).
While
we have espoused the use of risk-free rates in liability valuation, we have
said nothing about the asset side of the equation. A perfect cash match using non-callable
Treasury securities is the only riskless way to hedge
a set of liabilities. In fact, there are
very few circumstances under which a perfect cash match would be appropriate,
but such a strategy represents the true risk-free posture; any deviations from
it (e.g., immunization, investments in callables, corporates, other investments)
subject the pension plan to additional risk, for which it should be
compensated. In this sense, a perfect
cash match represents the appropriate benchmark for gauging asset allocation
and overall pension fund hedging decisions.