September 28, 2009
International Accounting Standards Board
30 Cannon Street
London EC4M 6XH
United Kingdom
To whom it may concern:
My comment concerns Question 1, quoted in its entirety below:
The exposure draft proposes defining fair value as ‘the price that would be received to sell an asset or
paid to transfer a liability in an orderly transaction between market participants at the measurement
date’ (an exit price) (see paragraph 1 of the draft IFRS and paragraphs BC15-BC18 of the Basis for
Conclusions). This definition is relevant only when fair value is used in IFRSs.
Is this definition appropriate? Why or why not? If not, what would be a better definition, and why?
I believe that the ED does not provide an appropriate definition of fair value in all cases:

The definition in paragraph 11 is an appropriate fair value definition for all instruments
that have a fair value.

In effect, the ED does not define fair value in paragraph 1, but rather in paragraph 15;
i.e., the exit price in the most advantageous market.

The paragraph 1 definition retains what paragraph BC15 describes as the ‘core principle’
of fair value; the concept of an orderly transaction; i.e., not forced or distressed. A similar
concept is also found in the older paragraph BC16 fair value definition: an exchange between
‘knowledgeable, willing parties”.

In the case of RFP Model Liabilities (defined below), the paragraph 15 fair value (exit
price) definition does not retain the core principle of knowledgeable, willing parties engaging in
an orderly transaction, because there is no evidence available that the exit price as defined is a
price that a rational liability holder would pay.
RFP Model Liabilities are:

Level 3 liabilities (i.e., having only Level 3 inputs) that are either:

transacted under the RFP Model (defined below); or

liabilities with a low nonperformance risk that are never (or almost never) transacted.
RFP Model Defined
The RFP transaction model is a simplified model of how liabilities with a low nonperformance risk are
settled in the real world. The liability holder seeks to transfer (or settle) its liability at the lowest cost
possible. At the same time, the liability holder seeks to minimize its potential residual liability that
would result from a potential future financial failure of the counterparty. Therefore, the liability holder
will only consider a settlement transaction with a counterparty of sufficient financial strength (i.e., with
a low probability of default.)
1
In this letter, paragraph numbers refer to the Fair Value Exposure Draft (ED), or to the Fair Value
Basis for Conclusions (with prefix BC).
In the RFP Model, the liability holder issues a request for proposal to the n strongest providers of
settlement contracts (the RFP group). The number n is chosen to include all ties with the nth strongest,
so that all providers outside the RFP group are strictly financially weaker than all the RFP group
members. The liability holder supplies identical data to each RFP group member, sufficient for each
member to generate a bid of the amount it is willing to accept to settle the liability.
At an appointed time, bids from the RFP group members are submitted to the liability holder. The
liability holder accepts the lowest bid and transacts the settlement with the lowest bidder, provided the
bid is less than or equal to the liability holder’s pre-determined rational price maximum. If the lowest
bid exceeds the liability holder’s rational price maximum, there is no settlement.
Liabilities with a low nonperformance risk that are never (or almost never) transacted are included in
the term ‘RFP Model Liabilities’ because the liability holder shares the same motivations to minimize
the cost, and to avoid potential residual liability resulting from the counterparty’s future financial
failure. Thus, any settlement transaction process for such an instrument would involve a mechanism to
restrict the group of potential counterparties to include only those with the lowest probability of default.
Also, the process would need a method for determining which of the bids represented the most
favorable arrangement for the liability holder. Therefore, if such liabilities were transacted, the
transaction model would have these key elements in common with the RFP model.
RFP Model Liability Example: US Pension Liabilities
During the last decade, the US stock market has had an annual dollar volume exceeding its market
capitalization; i.e., an average share of stock changed hands more than once each year.2 Pension
liabilities, on the other hand, had a probability of perhaps 0.1% of being settled during any year. 3 Thus,
the ratio of trading velocity of US pension liabilities to US stocks is approximately 1 in 1,000 or less.
This ratio supports the position that pension liabilities should be classified as Level 3.
Also, actual US pension liability settlement transactions are well described by the RFP model.
Therefore, US pension liabilities are an example of RFP Model Liabilities.
Group annuity contract prices for US pension liabilities have historically been closely related to 10 and
30-year swap rates. Thus, it appears likely that a US pension liability exit price corresponding to
IASB’s operational fair value definition would be a rate based on these swap rates, based on the
duration of the plan’s liabilities. This conclusion could then lead to a change in the discount rate basis
used to value pension liabilities, from the current AA bond yield curve to swap rates, which are
generally lower (thus producing higher calculated pension liabilities). The two steps IASB could take
leading to this potential change are:
1. Concluding that the exit price, and thus fair value of US pension liabilities are based on
swap rates; and
2. Deciding to value pension liabilities at fair value.
Step #1 (in particular the Fair Value ED) is the more appropriate point to object to this change, because
once the fair value of a liability has been defined, there appears to be few arguments for an exception
for pension liabilities if all other instruments are to be valued at fair value.
2
http://www.cross-currents.net/charts.htm
Moore, Daniel P., ‘The Market Value of Pension Liabilities’, Contingencies, March/April 2008,
http://www.contingencies.org/marapr08/commentary.pdf
3
2
Law of One Price
To retain the core principle of an orderly transaction between knowledgeable, willing parties (and to be
consistent with axiomatic economic theory), the fair value operational definition must provide evidence
of the rationality of the liability holder’s decision to transact at the exit value price. For Level 1
instruments, such evidence is provided by the law of one price (LOOP). LOOP is a theorem for Level 1
instruments, summarized as follows:
It is widely accepted that a reasonable economic model should be free of arbitrage opportunities. In a
free trading environment where short selling is allowed, the existence of two instruments representing
the same cash flows that are priced differently produces an arbitrage opportunity. That is, an arbitrageur
can make an immediate, low-risk profit by selling short the more expensive instrument and buying the
lower priced instrument. Therefore, any two instruments having the same cash flows, both available in
a free trading environment, must be traded at the same price.
This argument is of logical type modus tollens (i.e., proof by contradiction) with the following
syllogism:
A implies B
~B
Therefore,
~A
The existence of two differently priced instruments with identical cash flows in a free
trading environment implies the existence of an arbitrage opportunity.
Reasonable economic models are free of arbitrage opportunities.
Therefore, any two instruments with identical cash flows in a free trading environment
must have the same price; otherwise the economic model is unreasonable.
The first main point of this letter is that for RFP Model Liabilities, the first premise in the above
syllogism is shown to be false in the theorem in Appendix A to this letter. That is, arbitrage
opportunities do not result from two liability holders (with identical liabilities) insisting on two
different maximum transaction prices, nor do they result from bidders submitting different bids. For
concreteness, the language in the Theorem uses pension liabilities, but the logic of the theorem
concerns only the fact that the liability in question is transacted under the RFP Model.
As a result, LOOP does not apply to RFP Model Liabilities. What, then, would constitute evidence that
a liability holder’s maximum acceptable settlement price is rational, from the liability holder’s point of
view? The answer to this question given by financial economics (and this comment letter) is that a
decision to settle an RFP Model Liability at a certain price is rational if the liability holder’s expected
utility is not diminished as a result of the settlement. In other words, the RFP Model Liability holder’s
rational settlement price maximum is the price that makes his expected utility immediately after
settlement equal to his expected utility immediately before settlement.
However, the Fair Value ED, in essence, simply asserts that LOOP does apply to all instruments,
including RFP Model Liabilities, thus contravening the expected utility maximization principle. This is
the second main point of this letter: the Fair Value ED fails to comply with the core principle of an
orderly transaction between knowledgeable, willing parties because it is in conflict with the principle
that a rational market participant will seek to maximize his expected utility. Instead, the Fair Value ED
espouses the Strong Law of One Price (SLOOP), discussed and rebutted further below.
3
Analysis of SLOOP
Below are statements of three versions of the law of one price. The first statement follows from the
science of financial economics, which has historically dealt with freely traded financial instruments.
1. (Weak): The price of any two freely traded instruments which represent the same cash flows
must trade for the same price.
2. (Medium): The market-based entry price (i.e., the unique rational price a market participant
would pay or receive to purchase or settle) for any financial instrument (including an RFP
Model Liability) is the same as the price of a reference security in a freely traded market.
3. (Strong): The unique rational price for all market participants for any financial instrument
(including an RFP Model Liability) is the same as given in #2, including the rational settlement
price maximum for a pension plan sponsor.
As explained in the preceding section, version #3 above (i.e., SLOOP) does not have a theoretical
derivation, because the theorem in Appendix A shows that arbitrage opportunities do not result from
price differences in an RFP Model setting. Additionally, SLOOP does not have an empirical derivation,
as the hallmark of Level 3 instruments is a lack of observable inputs.
The Fair Value ED does not state that it is based on SLOOP; however, the conclusions contained in the
ED are the same as if it were based on SLOOP, and, the ED’s conclusions imply SLOOP. Therefore, a
rebuttal of SLOOP is essentially a rebuttal of this aspect of the ED.
One possible derivation of SLOOP is to begin with positive financial economics4 – i.e., the study of
trades that are made involving money. As explained above, a key theorem of positive financial
economics is LOOP. Then, unreasonably expand positive financial economics to include what could
logically be called ‘negative financial economics’ – i.e., the study of trades that aren’t made. Hold your
nose, and simply assert that the price preferences of the market participants in this negative case are the
same as in the positive case. Ignore the fact that in the negative financial economics case, the common
sense interpretation is that transactions do not occur because buyers and sellers, as groups, have
different price preferences; in particular, the sellers’ price preferences are higher than the buyers’ price
preferences.
If SLOOP is not assumed, it becomes clear that financial economics explains why pension liabilities
are not traded. Plan sponsors have a rational price maximum for the pension liabilities, which is almost
always lower than the market-based entry price. No logical inconsistency results from the situation
where plan sponsors' rational price maximum is lower than the price the market participants would
charge for settlement, resulting in no settlement transactions. The absence of settlement transactions is
evidence that the plan sponsors' rational price maximum is lower that the market-based entry price.
SLOOP is on one hand a simple scope error; a principle that applies as a theorem for freely traded
instruments is blindly applied to RFP Model Liabilities as a sweeping generalization. In terms of a
theoretical settlement transaction, the notion embodies the petitio principii fallacy; the notion begs the
question that the transaction will occur, regardless of whether the transaction price exceeds the plan
sponsor's rational price maximum.
There are no scholarly articles or textbooks demonstrating or deriving SLOOP for RFP Model
4
Sharpe, William F., Macro-Investment Analysis, http://stanford.edu/~wfsharpe/mia/mia.htm
4
Liabilities. No number of expert opinions can make up for this lack of support. In fact, RFP Model
Liabilities simply haven’t yet been studied within the field of financial economics to any significant
degree. If they had been studied, the RFP Model Theorem in Appendix A – an elementary result would have been previously proven.
SLOOP meets all the criteria to be called junk science. Despite the claims of many experts that SLOOP
is valid economics, it is not axiomatically derived (in fact, it violates the principle that market
participants are rational and act on the basis of self-interest.) It’s not possible to achieve transparency
through junk science.
Informational cascade
Why do many experts subscribe to SLOOP? There is an informational cascade resulting from the
conflation of LOOP with SLOOP, and the fact that the concept of Level 3 liabilities was never put into
writing until FAS 157 in 2006. SLOOP is conflated with LOOP; also, the no-arbitrage condition is
conflated with SLOOP. Without ever proving it, financial experts have convinced themselves that
because an arbitrage possibility results from mispricing in a free trading environment, it must also
result in a more structured environment such as the RFP Model. Even the terms ‘mispricing’ and
‘pricing’ (as used in ED paragraph 14) have a specialized meaning based on concepts from the free
trading model of financial economics – ‘pricing’ is clearly not used by IASB to describe the liability
holder’s perspective of what they are willing to pay.
Additionally, the notion that all financial instruments (including Level 3 instruments) have a fair value
follows from SLOOP. And, the push for fair value has a momentum on its own.
The fair value Basis for Conclusions has very little to say about the theoretical underpinnings of
SLOOP. Even the sentence ‘Exit value is the value the market would assign if pension liabilities were
freely traded.’ is nonsense – the barrier to free trading of such instruments is explained above in the
RFP Model Liability section.
Another observation is that SLOOP is simply bad philosophy. SLOOP proponents believe in the
ontological reality of something called fair value, which differs from the amount that rational liability
holders are willing to pay to settle that liability. They believe that a Level 3 liability is merely hidden
by an epistemological shroud, which must be penetrated to achieve transparency. The reality is that fair
value is entirely epistemological; when it exists, it exists in a meeting of the minds of market
participants on both sides of the transaction.
Plan Sponsor Expected Utility Maximization Model – Background
This section and the following section discuss parameters in the simplified expected utility
maximization model illustrated in the attached Excel workbook. The goal of these two sections is to
illustrate that different pension plan sponsors have different rational price maximums and
corresponding discount rates – referred to below as maximum rational price settlement discount
rates.
In the workbook:

(1) Pension plan sponsor’s expected utility =  v t E(ut (wt )) ,
t1
Where:
5

v = 1/(1+IRR);
IRR is the plan sponsor’s internal rate of return, calculated here as rf + β( rm – rf) (from the CAPM
model, where rm is the stock market expected return and rf is the risk-free rate.)
ut(wt) = wt – wt2 / (2Mt)
for wt  Mt
= Mt / 2
for wt  Mt
is the plan sponsor’s truncated quadratic utility function for each duration t.
The truncated quadratic utility parameter Mt equals the plan sponsor’s wealth at time t if the return on
corporate wealth (excluding pension plan assets) and the pension plan assets are both in accordance
with a constant value of  = ps for the standard normal distribution underlying the lognormal
distributions of corporate wealth and pension plan assets. Illustrated in the workbook are utility
functions with ps = 0.6 (higher risk aversion) and ps = 0.9 (lower risk aversion). The truncated
quadratic utility parameter Mt is also the level of wealth at which utility is saturated; the plan sponsor
has no additional utility for wealth in excess of this amount. The more risk averse plan sponsor has
utility saturation at the 60th percentile return on assets, and the less risk averse plan sponsor has utility
saturation at the 90th percentile return on assets.
This model has the ability to reflect two key aspects of the settlement of pension liabilities:
 The opportunity cost of committing assets outside the plan to settle pension liabilities (this
tends to decrease the plan sponsor's expected utility from settlement); and
 The reduction in risk brought about by settling the pension liabilities (this tends to increase the
plan sponsor's expected utility from settlement).
The plan sponsor’s  would normally be empirically derived; it is estimated in this example. Although
the plan sponsor’s β will be reduced to βX as a result of any significant pension liability settlement, the
same discount rate is used in equation (1) after settlement as before settlement. This is because all of
the plan sponsor’s risk aversion is assumed to be fully represented by the duration t utility functions ut
– thus changing the discount rate in (1) would be double counting.
In describing the rationale for using a sum of discount-weighted expected utilities as the overall
expected utility, the plan sponsor's stakeholders can be substituted for the plan sponsor:
 The plan sponsor is concerned about the expected utility of its wealth at all future durations
 The plan sponsor's IRR is an appropriate discount rate for expected utility at a future date, as
this is the inherent discount rate in valuing the plan sponsor.
 The use of IRR to discount the expected utility allows recognition of the risk reduction
equivalent value to the plan sponsor of a plan settlement.
 As with other utility functions:
 Utility is a function of total wealth, including the pension plan funded status; and
 The sum of discount-weighted expected utilities operator provides a preference ordering.
The pension plan sponsor’s total wealth includes the pension plan funded status. For the purpose of
valuing the pension liability as a component of total wealth from the plan sponsor’s viewpoint (to
calculate utility), the workbook uses the following optional ‘internal’ discount rates, to illustrate two
optional plan sponsor viewpoints:

Risk / opportunity cost-neutral internal discount rate: Equation (2) solves to the
6
settlement price maximum discount rate q for a plan sponsor who is unconcerned about the
opportunity cost and risk reduction resulting from settling pension liabilities:
(2)
EFEL + PV(surplus) = PFVC + MVA
In (2), EFEL (expected full economic liability) equals the present value of future benefits and
expenses (PVFB + PVFE) (a deterministic calculation using the solved-for discount rate q).
PV(surplus) is the present value of surplus assets over EFEL – this term is significant only for
very well funded plans. Present value of future sponsor contributions (PVFC) is a partially riskadjusted present value of future contributions. That is, it estimates the effect of applying the full
expected asset return distribution (rather than a single expected return). The surplus in
PV(surplus) and the contributions in PVFC are discounted at a low-risk or risk-free rate.

Constant internal discount rate based on external accounting standard: A constant
rate of either 6% or 4% is used, illustrating the effect of a lowering of the discount rate under a
new accounting standard.
Plan Sponsor Expected Utility Maximization Model – Excel Workbook
The attached Excel workbook illustrates the calculation of the discount rate p that preserves the plan
sponsor’s expected utility. In this example:
 The plan sponsor is a corporation that pays no dividends. Its wealth w (excluding the pension
liability) is initially $1 (or $10) million.
 Excluding the pension plan, the plan sponsor would have a β of 1.0 – the plan sponsor's β
including the pension plan is estimated in cell C36 of sheet Current.
 The pension liability in this case is for a single payment of $1 million to be made at time 20
years. There are no expenses or taxes. The plan sponsor will fund the liability with an
immediate (time 0 years) contribution, plus a time 20 years contribution (if needed). The plan
sponsor will fund any shortfall or recoup any excess in the pension plan at time 20 years.
 The pension asset portfolio has β, expected return, and standard deviation of return as shown in
the chart below:
Investment
β
Expected Return
Standard Deviation of
Scenario
Return
1
0.5
7.0%
13.8465%
2
0.0
4.0%
0.0%



The stock market has an expected return of 10% and a standard deviation of return of 20%. The
risk-free rate is 4% with 0% standard deviation.
The stock market return, the plan sponsor's wealth w, and the plan asset return are all distributed
according to the lognormal distribution.
To limit the size of this illustrative-only workbook, the expected utility is summed over only 40
years.
The workbook contains 3 tabs:
 Navigation; providing a map of the calculated values in the following three tabs;
 Current; showing the plan sponsor's current situation at time zero and expected situation
through time 40 years; the risk / opportunity cost-neutral internal discount rate q is calculated in
cell C19, and the plan sponsor’s expected utility is displayed in cell F26.
 Settlement; calculates the plan sponsor’s expected utility after settlement of entire pension
7
liability at discount rate p.
8
The following charts display the settlement discount rate corresponding to the plan sponsor’s
rational price maximum for various scenarios, as calculated in the workbook:
$1 Million Initial Plan Sponsor Wealth; Risk / Opportunity Cost-Neutral Internal Discount Rate
Initial Plan
Assets
Investment Scenario 1 (7% EROA)
Investment Scenario 2
(4% EROA)
q (Eqn. 2)
ps = 0.6
ps = 0.9
ps = 0.6
ps = 0.9
$0
4.00%
6.07%
7.79%
6.07%
7.79%
$100,000
4.93%
5.93%
7.33%
5.66%
6.84%
$200,000
6.07%
5.72%
6.77%
5.22%
5.96%
$300,000
7.55%
5.48%
6.15%
4.75%
5.15%
$10 Million Initial Plan Sponsor Wealth; Risk / Opportunity Cost-Neutral Internal Discount
Rate
Initial Plan
Assets
Investment Scenario 1 (7% EROA)
Investment Scenario 2
(4% EROA)
q (Eqn. 2)
ps = 0.6
ps = 0.9
ps = 0.6
ps = 0.9
$0
4.00%
6.80%
8.85%
6.80%
8.85%
$100,000
4.93%
6.33%
7.80%
6.06%
7.34%
$200,000
6.07%
5.90%
6.91%
5.40%
6.17%
$300,000
7.55%
5.49%
6.14%
4.81%
5.21%
$1 Million Initial Plan Sponsor Wealth; 6% Internal Discount Rate
Initial Plan
Assets
Investment Scenario 1 (7% EROA)
Investment Scenario 2
(4% EROA)
ps = 0.6
ps = 0.9
ps = 0.6
ps = 0.9
$0
7.03%
8.85%
7.03%
8.85%
$100,000
6.46%
7.80%
6.51%
7.65%
$200,000
5.88%
6.83%
5.96%
6.59%
$300,000
5.31%
5.93%
5.41%
5.65%
$10 Million Initial Plan Sponsor Wealth; 6% Internal Discount Rate
Initial Plan
Assets
Investment Scenario 1 (7% EROA)
Investment Scenario 2
(4% EROA)
ps = 0.6
ps = 0.9
ps = 0.6
ps = 0.9
$0
7.77%
9.87%
7.77%
9.87%
$100,000
6.84%
8.21%
6.88%
8.08%
$200,000
6.04%
6.95%
6.11%
6.74%
$300,000
5.34%
5.94%
5.44%
5.68%
9
$1 Million Initial Plan Sponsor Wealth; 4% Internal Discount Rate
Initial Plan
Assets
Investment Scenario 1 (7% EROA)
Investment Scenario 2
(4% EROA)
ps = 0.6
ps = 0.9
ps = 0.6
ps = 0.9
$0
6.07%
7.79%
6.07%
7.79%
$100,000
5.62%
6.97%
5.66%
6.84%
$200,000
5.15%
6.17%
5.22%
5.96%
$300,000
4.66%
5.40%
4.75%
5.15%
$10 Million Initial Plan Sponsor Wealth; 4% Internal Discount Rate
Initial Plan
Assets
Investment Scenario 1 (7% EROA)
Investment Scenario 2
(4% EROA)
ps = 0.6
ps = 0.9
ps = 0.6
ps = 0.9
$0
6.80%
8.85%
6.80%
8.85%
$100,000
6.02%
7.46%
6.06%
7.34%
$200,000
5.34%
6.36%
5.40%
6.17%
$300,000
4.73%
5.45%
4.81%
5.21%
Key conclusions based on the foregoing results:
 The plan sponsor in this example has two decisions: First, whether to settle the pension liability
in its entirety at time 0, or if not, how much to fund at time 0. (The next funding opportunity in
this example is at time 20).
 In most cases presented here, the plan sponsor would maximize their expected utility by settling
the entire pension liability at least equal to their maximum rational price settlement discount
rate (ranging from below 4% to over 6%), provided that rate is available. If that rate is not
available, the plan sponsor would maximize their expected utility by essentially fully funding
the plan.
 The maximum rational price settlement discount rates shown in the chart for lower funding
levels show a decreasing pattern with increasing funded level. This is explained by the
opportunity cost of using corporate resources for pension settlement. The opportunity cost is
highest with a low funded level, as indicated by a high maximum rational price settlement
discount rate.
 The level of risk aversion, the size of the pension plan relative to the plan sponsor, the plan’s
investment allocation, and the plan sponsor’s internal discount rate also affect the plan
sponsor’s maximum rational price settlement discount rate. Thus, different plan sponsors have
different maximum rational price settlement discount rates.
Noteworthy points about the workbook, and the model and its application to discount rate rules:
 The slope of the discount rate p as a function of funded status is exaggerated in this simple
example because of the terminal funding in the example.
 The workbook illustrates a constant-Ф approach to projecting asset returns (based on a
lognormal distribution), enabling the computations to reflect variations from the mean return,
without requiring stochastic processing. Choosing an integer n (n = 15 in the workbook), you
calculate n equally probability-spaced representative constant-Ф arrays; i.e., at each time t, the
10

cumulative distribution function of the cumulative product Πt(Y - μ )/ σ is a constant Фi = (2i –
1)/2n, for i = 1 to n. As n increases, the sample mean (arithmetic average) of the n cumulative
products approaches the expected cumulative product using the arithmetic mean of the
underlying continuous distribution, and the sample variance approaches the predicted
underlying variance.
As a constant-Ф example, for the stock market return in the workbook, Ф1 = 0.0333, the first
two years of experience are -22.25% the first year, and -5.63% the second year. For Ф15 =
0.9667, the first two years of stock market experience are returns of 50.65% followed by
24.12%. The sample means of the first two years’ experience for Ф1 through Ф15 are 9.85% for
both years one and two (vs. 10.0% arithmetic average of the underlying continuous
distribution).
Recommendation
For the reasons stated above, my recommendation is that the scope exclusion be added to omit a fair
value definition for all RFP Model Liabilities. Instead, the term exit price is available to be used.
The opinions in this letter are entirely my own, and not those of any entity of which I am a member. I
would be interested in participating in the US Fair Value Roundtable.
Sincerely,
Daniel P. Moore, FSA, EA, MAAA
1610 N. Larrabee Street
Chicago, IL 60614
Phone: (312) 440-0131
danpmoore@gmail.com
Attachments: Appendix A (follows below)
IASB pension example.xls
11
Appendix A: RFP Model Theorem
Theorem: In the RFP Model, if two pension plan sponsors with identical plans hold out for
different asking prices to settle them, the difference in these asking prices does not lead to an
arbitrage opportunity. Also, differences in bid prices among bidders to settle the plan do not lead
to arbitrage opportunities.
Explanation of RFP (request for proposal) Model:
A sponsors Pension Plan A; A's asking price to settle their pension liability is $100.
B sponsors Pension Plan B; B's asking price to settle their pension liability is $110.
(Note that actual numbers are used to clarify the presentation, instead of using variables with the order
assigned.)
A series of auctions is held; the lowest bidder wins and a pension settlement is transacted at that price if
the low bid is less than or equal to the asking price. If the lowest bid is greater than the pension plan
sponsor's asking price, there is no sale.
A and B each define the same group of bidders as the n most financially stable annuity providers. The
market participants in the bidder group know that Plans A and B are identical, so they bid the same
amount for each.
A and B keep their asking prices secret, because revealing their asking prices could result in an upward
adjustment in the bid of what would have been the low bidder. However, they may hold practice
auctions and reveal the bid amounts to the other bidders.
Bidders each have a bid minimum representing their cost and minimum acceptable profit margin. A and
B will not bid less than their own asking price for each others' plans. An additional case is included: A
is included in the bidder group for B and makes the low bid (or not). A case is not needed for B to bid
on A, because B will bid $110 or more, while A will ask $100.
There are no changes in bids in subsequent auctions, except if a participant has engaged in a
transaction, in an attempt to make an arbitrage profit:
 If a participant bought an annuity and paid $X, they can bid on selling an annuity for the same
plan (or an identical plan) for $X or more. (So, if A buys an annuity from La, A will be included
in the bidder group to sell an annuity to La – likewise B.)
 If the participant sold an annuity and accepted $X, the participant can try to buy an annuity for
the plan (or an identical plan) with asking price $X or less.
 In other words, all market participants can try for an arbitrage profit, but they won't accept an
arbitrage loss.
The asking price for a plan is monotonically decreasing in this model, because it only changes upon a
sale, and the new plan sponsor will ask to pay no more than they received.
The low bid for a plan is monotonically increasing, because it only changes after a sale, and all other
bidders' bids (including the former plan sponsor who just paid the low bid amount) will be greater than
or equal to the low bid amount.
Therefore, if at any point, the asking price is less than the low bid, there will be no future transactions
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for this plan. If the asking price is equal to the low bid, then all future transactions (if any) will be at
that asking price.
The three cases below show that, given these rules, after at most two auctions (one for each plan):
 the asking price for the sponsor of each plan will be less than or equal to the lowest possible
bid, and
 if the plan has changed hands, the highest possible asking price will equal the price the current
plan sponsor received to settle it.
These two statements are referred in the cases below as 'the condition'. Note that a dollar amount for
the low bid is used in the cases below to clarify the presentation (instead of using variables with the
order assigned.)
Therefore, there is no arbitrage possible in this model, despite A and B having different asking prices.
Please note: Say the winning bidder L among the group of n bidders chooses to issue an RFP to a larger
group of m (> n) bidders, and secures a lower bid (from a bidder L2 outside the original group of n)
than the amount L was paid. This set of transactions does not represent an arbitrage for L because L2 is
a weaker annuity provider than L; thus the probability of payment of the cash flows is not the same
between L and L2.
Proof by cases:
Auctions
A bid
A ask
B ask
Others
low bid
Overall
low bid
Results
Case 1: $95 low bid
1. A auction
100
2. B auction
110
95
95
La sells annuity to A for 95; La will
ask <= 95 to buy an annuity from
bidders.
95
95
Lb sells annuity to B for 95; Lb will
ask <= 95 to buy an annuity from
bidders.
A & B will both bid $95 or more. All other bidders will not change their bids; they will bid 95 or
more. The condition is met.
Case 2a: A is included in the bidders to sell B an annuity and is the low bidder at $100; others' low bid
is $105.
1. A auction
2. B auction
100
100
110
105
105
No sale
105
100
A sells annuity to B for 100; A will
ask 100 or less to buy an annuity for
Plans A & B; B will bid 100 or more.
A now sponsors both Plan A & B; asking price for each is <= 100. Others low bid will be 105. B's bid
>= 100. The condition is met.
Case 2b: Same as Case 2a, but let B go first.
1. B auction
100
110
105
100
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A sells annuity to B for 100; A will
ask 100 or less to buy an annuity for
Plans A & B; B will bid 100 or more.
A now sponsors both Plan A & B; asking price for each is <= 100. Others low bid will be 105. B's bid
>= 100. The condition is met.
Case 2c: A is not included in the bidders to sell B an annuity; low bid is $105.
1. B auction
110
105
105
Lb sells annuity to B for 105; Lb will
ask 105 or less to buy an annuity for
Plan B; B will bid 105 or more.
A will ask 100 for Plan A but all bids are 105 or more. The condition is met for Plan A.
Lb will ask 105 or less to buy an annuity for Plan B. Others low bid will be 105 or more. B's bid >=
105. The condition is met for Plan B.
Case 3a: A is included in the bidders to sell B an annuity and is the low bidder at $100; others' low bid
is $115.
1. A auction
2. B auction
100
100
110
115
115
No sale
115
100
A sells annuity to B for 100; A will
ask 100 or less to buy an annuity for
Plans A & B; B will bid 100 or more.
A now sponsors both Plan A & B; asking price for each is <= 100. Others low bid will be 115. B's bid
>= 100. The condition is met.
Case 3b: A is not included in the bidders to sell B an annuity; others' low bid is $115.
1. A auction
2. B auction
100
110
115
115
No sale
115
115
No sale.
A will ask 100 to buy an annuity for Plan A but all bids are 115 or more. The condition is met.
B will ask 110 to buy an annuity for Plan B but all bids are 115 or more. The condition is met.
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