October 24, 2013
To Actuarial Standards Board ASOP #4 Committee
c/o Mr. Gordon Enderle
Dear Gordon,
To summarize our discussion earlier this week, you called me in reference to my May 2013
ASOP 4 comment letter, in which I said ASOP 4 should omit the proposed definition of marketconsistent present value. The ASOP #4 2nd Exposure Draft contains the following definition and
supplemental discussion of market-consistent present value:
2.14 Market-Consistent Present Value—An actuarial present value that is consistent with the
price at which benefits that are expected to be paid in the future would trade in an open market
between a knowledgeable seller and a knowledgeable buyer. The existence of a deep and liquid
market for pension cash flows or for entire pension plans is not a prerequisite for this present
value measurement.
3.11 Market-Consistent Present Values—If the actuary calculates a market-consistent present
value, the actuary should do the following:
a. select assumptions based on the actuary’s observation of the estimates inherent in financial
market data as described in ASOP Nos. 27 and 35, depending on the purpose of the
measurement; and
b. reflect benefits earned as of the measurement date.
In addition, the actuary may consider how benefit payment default risk or the financial health of
the plan sponsor affects the calculation.
Gordon, your question relates to the fact that the committee only proposes to define market-consistent
present value, and not to require its use. Therefore, you asked me my opinion of whether the definition
should remain in ASOP 4 as proposed.
My opinion is: No, it should not remain, for the following reasons.
1. The definition of market-consistent present value is based on an error, and is fundamentally
misleading.
2. Correction of the preceding error points to a different value as being the theoretically correct
“market consistent present value”.
3. The ASB should not create definitions that are not empirically supported, without any effort
having been made to test the validity of the definition empirically.
These points are discussed in more detail below.
1. The definition of market-consistent present value is based on an error, and is fundamentally
misleading.
The error, as pointed out in my ASOP #4 comment letter, is that the hypothesis of market participants
placing a consensus value on the pension liabilities which is lower than indicated by current financial
economics teachings, does not lead to an arbitrage opportunity. (The argument that a pricing deviation
leads to an arbitrage opportunity underlies virtually all of financial economics.) My ASOP #4 comment
letter shows that there is no arbitrage opportunity in the case of a conglomerated pension liability,
because there is no perfect hedge available in the market for the plan sponsor, minus its pension
liabilities.
The diagram above illustrates this point. An investor who subscribes to current financial economics
tenets may recognize that the market places a value on Company A’s pension liabilities which is less in
absolute value than the price of a risk-free bond with the same cash flows. He may then attempt to gain
an arbitrage profit by selling short Company A, which he perceives as overvalued, due to the pension
liability valuation. Indeed, if Company A's pension liability were available as a stand-alone security (with
the same valuation), he could execute the arbitrage by shorting Company A’s pension liability
(equivalent to buying a bond at a bargain price) and shorting a risk-free bond with the same cash flows.
However, Company A’s pension liability is not available as a stand-alone security. In order to execute the
arbitrage, the investor must also find a perfect hedge for the rest of Company A (shaded in blue, labeled
SWOP – Sponsor without pension). The perfect hedge (SWOPH, or Sponsor without pension hedge) does
not, however exist; hence, there is only a pretend arbitrage opportunity, not a genuine one. Imperfect
hedges exist, but not as a riskless arbitrage.
Other more sophisticated no arbitrage arguments also fail. For example, financial economists might
assert that the combination of the 2nd Fundamental Theorem of Asset Pricing, plus the assertion that all
cash flows can be securitized, leads to a valuation of the pension liability using a market risk-free rate.
However, the assertion that all cash flows can be securitized is not a theorem, and is not in fact true. In
this case, the cash flows of the conglomerated pension liability have the characteristic that a different
market pricing does not trigger an arbitrage opportunity; in the case of a security, pricing not in
accordance with the 2nd Fundamental Theorem of Asset Pricing always produces a “buy low, sell high”
arbitrage opportunity. Thus, this essential characteristic of a conglomerated pension liability cannot be
translated to a security.
2. Correction of the preceding error points to a different value as being the theoretically correct
“market consistent present value”.
One of the fundamental assumptions of financial economics is that plan sponsors update their opinions
based on relevant information using Bayes’ Theorem. A key insight of 20th century financial economics is
that care must be taken to decide whether information is relevant or not. In particular, information (that
is acted upon by the investor) would cause an arbitrage opportunity for a counterparty at the investor’s
expense cannot be relevant. For example, in the case of stock options that are correctly valued using the
Black-Scholes formula, the stock’s expected return is not relevant.
In the case of conglomerated pension liabilities, the following attributes are relevant because they affect
the expected future cash flows of a company in connection with an equity or company valuation model
based on free cash flows or discounted dividends (the most common types of fundamental company
valuation):
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Pension plan funded status
Pension plan asset investment allocation
Factors affecting future benefit accruals, such as projected salary increases
Time horizon of invested pension plan assets
Also, these attributes are not ‘out of bounds’ due to the creation of a genuine arbitrage opportunity.
I am working on a paper which will propose a two-step model to derive a theoretically correct discount
rate for pension liabilities:
1. Using the formula below, derive a preliminary discount rate:
MVA + PVFC = EFL.
MVA is the market value of pension assets and PVFC is the present value of future contributions
discounted at the company’s borrowing rate (or a high quality bond rate). EFL, expected full
liability, is similar to M. Burton Waring’s concept of Full Economic Liability, but the discount rate
in this case is solved for. EFL cash flows represent projected benefits for current and future
pension plan participants.
2. Because market participants are risk averse, apply a risk penalty (a deduction) to the preliminary
discount rate derived above if the pension plan assets include risky investments. The risk penalty
would take into account the estimated time horizon of pension plan assets vs. the market time
horizon, the beta of the pension asset account and the funded status of the EFL.
The above described model is a better candidate for the term “market consistent value” because the
attributes of pension plans listed above which are incorrectly excluded as ‘out-of-bounds’ by current
financial economics are actually in-bounds; they should be reflected in an estimate of how much the
market believes pension liabilities are worth.
3. The ASB should not create definitions that are not empirically supported, without any effort
having been made to test the validity of the definition empirically.
The practitioners of financial economics lack a tradition of using empirical testing to validate
proclamations of what things are worth. One reason for this is that the field of Behavioral Finance has
shown that real people do not behave precisely as “REM” – rational economic man. So, any empirical
results that have been obtained are explained away by behavioral finance, and thus become the subject
matter of behavioral finance, rather than financial economics per se.
This approach is a mistake in my opinion. Financial economics should not be viewed as exempt from
empirical testing. The error discussed in this letter would likely have been spotted earlier had empirical
testing been applied to financial economics. Also, there is significant evidence supporting at least the
weak form of the efficient market hypothesis. If it is the case that actual human behavior is wildly
different from that of ‘REM’, published empirical studies which show this may cause behavior to become
more rational (similar to investment anomalies disappearing once they were publicized).
Thank you for the opportunity to expand on my earlier comments.
Sincerely,
Daniel P. Moore, FSA, EA, MAAA, FCA, MSPA
[email protected]
(312) 566-1269