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Working Paper Series

An Experimental Analysis of Contingent
Capital Triggering Mechanisms

WP 11-01R

Douglas Davis
Virginia Commonwealth University
Oleg Korenok
Virginia Commonwealth University
Edward Simpson Prescott
Federal Reserve Bank of Richmond

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An Experimental Analysis of Contingent Capital Triggering Mechanisms
Douglas Davis, Virginia Commonwealth University
Oleg Korenok, Virginia Commonwealth University
Edward Simpson Prescott, Federal Reserve Bank of Richmond†
October 4, 2011
Working Paper No. 11-01R
Abstract
Abstract: This paper reports an experiment that evaluates three regimes for triggering the
conversion of contingent capital bonds into equity: (a) a “regulator” regime, where socially
motivated regulators make conversion decisions based on observed prices, (b) a “fixed trigger”
regime where a price threshold triggers a mandatory conversion, and (c) a “prediction market”
regime where we supplement the regulator’s information set with the results of a prediction
market that elicits traders’ perceived likelihood of a conversion. Consistent with theory, we
observe informational and allocative inefficiencies as well as numerous errors in conversion
decisions in both the regulator and fixed trigger regimes. Contrary to theory, however, we also
observe inefficiencies and frequent conversion errors in the prediction market regime. Although
the fixed trigger and prediction market regimes are more informationally efficient than the
regulator regime, allocative efficiencies remain low and conversion error rates high in all three
regimes.
Keywords: bank regulation; experiments; contingent capital
JEL codes: C92; G14; G28
_____________________________________________________
* The authors would like to thank Asen Ivanov, Edward Millner, Robert Reilly, and seminar participants at the
Federal Reserve Bank of Richmond, the 2011 LeeX International Conference on Theoretical and Experimental
Macroeconomics, the 2011 SAET conference in Faro Portugal, and the School of Business at Virginia
Commonwealth University for their useful comments. The usual disclaimer applies. Financial assistance from the
National Science Foundation (SES 1024357), the Federal Reserve Bank of Richmond, and the Virginia
Commonwealth University Summer Research Grants Program is gratefully acknowledged.
†

The views expressed in this paper do not necessarily reflect those of the Federal Reserve Bank of Richmond or the
Federal Reserve System.

1

1. Introduction
In the aftermath of the 2008 global financial crisis, economists and policymakers have devoted
considerable attention to improving financial regulation. A primary focus of attention has been
on developing policies to ensure that banks have equity cushions sufficient to maintain solvency
in times of financial distress, in this way reducing the chance of collapse and taxpayer-funded
bailout. One innovative proposal that has received particular attention involves having banks
carry on their balance sheets a new class of subordinated debt that converts to equity in times of
financial distress.1 These “contingent capital” bonds offer a number of important advantages, the
most prominent of which is that they allow banks to convert debt into equity on pre-specified
terms in times of financial distress — precisely when raising equity is most difficult.2 These
advantages were of sufficient appeal in the U.S. for Congress to mandate a study of the
characteristics of contingent capital in the Dodd-Frank Wall Street Reform and Consumer
Protection Act of 2010 and in the U.K. for the Independent Commission on Banking to
recommend that banks use loss-absorbing debt like contingent capital in their capital structure.
Perhaps the most important and controversial issue for implementing contingent capital is
determining what trigger to use for conversion. The two most prominent options are (i) leaving
the conversion decision at the discretion of a regulatory authority, or (ii) using some marketbased performance measure, such as a bank equity price, as a basis for a mandatory trigger.3
Some government agencies have indicated a preference for leaving conversion at the discretion

1

Most of the proposed regulatory changes to capital requirements have focused on making them higher and
procyclical. Indeed, some commentators argue that capital requirements should be much higher (e.g., Admati,
DeMarzo, Hellwig and Pfleiderer, 2010). Contingent capital is not an alternative to raising capital requirements, but
is instead a complement. Higher capital requirements certainly make a bank less likely to encounter financial
distress, but at a cost. A variety of theories in corporate finance suggest that equity is an expensive source of funds
(e.g., Myers and Maljuf (1984)) and in any case debt is an important part of a bank’s financial structure. Further,
unless capital requirements are extremely high, a bank could still find itself in a situation of financial distress and in
that case, contingent capital would still be valuable.
2
Another alleged benefit of contingent capital is that it gives incentives for managers to avoid excessive risk-taking
(Calomoris and Herring, 2011) because equity owners are punished, at least when conversion substantially dilutes
existing equity. Proposals to include contingent capital bonds on banks’ balance sheets are not without critics. For
example Acherya, Cooley, Richardson and Walter (2009) argue that contingent capital fails to eliminate financial
institutions’ incentives to take excessive risks because it fails to fully account for a bank’s large volumes of other
government-guaranteed assets, such as deposits and other non-contingent debt. Hart and Zingales (2010) argue that
requiring banks to carry substantial contingent capital bonds on their balance sheets will delay the timing of defaults
and thus delay needed managerial reorganizations. This list is not exhaustive. For example Admati, DeMarzo,
Hellwig and Pfleiderer (2010) also articulate pertinent reservations.
3
A third option is to rely on accounting measures. A problem with this option is that these measures often lag the
actual condition of a bank.

1

of a bank regulator.4 A group of academics, however, strongly advocate the use of a market price
trigger (e.g., Flannery, 2009; McDonald, 2010; and Calomiris and Herring, 2011). These
commentators argue that the political pressure imposed on discretionary regulators would make
it harder for them to commit to convert when a bank was in trouble and would create harmful
uncertainty as to when a conversion will occur.
Only recently has any bank issued contingent capital, so there is no empirical evidence to
even analyze how it might work in practice.5 Nevertheless, recent theoretical analysis suggests
that basing contingent capital on a market-price trigger will not work. Bond, Goldstein and
Prescott (2010) (‘BGP’) and Birchler and Facchinetti (2007) show that equilibrium need not
exist in a rational expectations model where a regulator uses prices to decide whether to take
actions that feedback to the value of the bank. They interpret nonexistence as indicating that
prices need not efficiently transmit information, which will lead to errors in when the regulator
takes an action. However, BGP also show that if there is a prediction market for whether the
regulator intervenes then an equilibrium exists.
The potential for informational inefficiency, however, is not purely a consequence of
leaving the conversion decision to a discretionary regulator. Sundaresan and Wang (2011) (‘SW’)
show under quite general conditions that if conversion automatically occurs when the price of
equity drops below some number, then no unique price exists for equity. They interpret this
inability to price equity as a significant problem for implementing contingent capital.
This paper provides an additional source of information on the effectiveness of
contingent capital with a market price trigger. We generate data with laboratory asset market
experiments where the fundamental values of the traded security are affected by a contingentcapital like conversion. We examine the three regimes just discussed: a “regulator” regime,
where an imperfectly informed, but socially motivated regulator makes conversion decisions6; a
“fixed trigger” regime where crossing a publicly known price threshold triggers a mandatory
conversion; and a “prediction market” regime where we supplement the information available to
agents (both regulators and traders) with traders’ perceptions of the likelihood of a conversion. In
4

For example, Sundaresan and Wang (2011) report that the Canadian Office of the Superintendent of Financial
Institutions prefers regulator discretion as a conversion trigger.
5
Sundaresan and Wang (2011) report four issuances of contingent capital bonds, all since the recent financial crisis.
6
It should be noted that our experiment with a discretionary regulator is not designed to study a regulator’s
commitment problem, but instead how the regulator reacting to the price influences the information content of the
prices as well as whether the regulator can effectively use the prices to decide when to intervene.

2

each regime we consider cases where the conversion transfers value from holders of contingent
capital bonds to equity owners (“value-increasing conversions” for equity owners), as well as the
case where the reverse occurs and conversion transfers value away from equity owners to holders
of contingent capital bonds (“value-decreasing conversions” for equity owners).7
Our experimental results indicate that concerns about the potential for informational
inefficiencies are well founded and merit prominent consideration in the debate over the
appropriate conversion trigger. Relative to a base condition where no capital conversions occur,
placing the conversion decision in the hands of a regulator results in sizable informational
efficiency losses in the sense that prices fail to closely track the underlying asset value. As a
consequence, markets with regulators generate both considerable allocative (trading) efficiency
losses and numerous errant conversion actions. Trading inefficiencies and conversion errors
occur not only when the conversion is value-increasing for equity owners (as predicted by BGP)
but also when it is value-decreasing (not predicted by BGP). In a fixed-trigger regime,
informational efficiency improves to some extent, particularly in the case of a value-decreasing
conversion. Nevertheless, use of a fixed trigger fails to improve allocative efficiency or reduce
the overall incidence of conversion errors. Similarly, supplementing the information available to
agents with results of a prediction market also improves informational efficiency, but again fails
to either improve trading efficiency or reduce the overall incidence of conversion errors.
We do observe, however, that both the fixed trigger and prediction market regimes
narrow considerably the range of fundamental realizations where conversion errors occur. This
range is narrower than the ranges identified as theoretically problematic. Thus either the
prediction market, or an operationally much simpler fixed trigger may effectively reduce the
problem of informational inefficiency observed in the regulator markets.
Prior to continuing, we observe that the use of experimental methods to examine the
potential effects of regulatory proposals offers some important advantages. Laboratory
experiments are far less costly than naturally occurring social experiments. Further, only in the
laboratory can the investigator observe directly the relationship between fundamentals and asset
7

Both value-increasing and value-decreasing conversion scenarios are quite possible and depend on the bond-toequity conversion ratio. For example, suppose that a contingent capital bond, valued at $10 converts to ½ a share of
equity when the share price falls to $5.00. Upon conversion, the bank retires $10 of debt at a very low cost in terms
of equity dilution, thus raising equity value. An identical conversion, but with a bond-to-equity conversion ratio of 4
would retire the same $10 of debt at a far higher equity dilution cost, thus reducing equity value for incumbent
equity holders.

3

prices, a relationship that is inherently unobservable in natural contexts. Indeed, in contingent
capital proposals it is the unobservability of fundamentals that partly drives recommendations
that regulators use asset prices as a reflection of value. Our ability to set fundamentals and then
observe trading prices allows us to assess directly the information loss in prices associated with
the possibility of intervention, as well as the extent to which regulators in the various regimes
err. The low cost and additional control of laboratory experimentation make it an ideal test bed
for evaluating potential effects of regulatory proposals, and that is our primary objective here.8
The remainder of this paper is organized as follows. Section 2 reviews theoretical predictions in
the context of our experimental design. Section 3 describes the experiment design and
procedures. Section 4 presents experimental results. Finally, the paper concludes.

2. Market-Based Conversion Policies
2.1 A Regulator Regime. To understand the theory that finds potential for informational
inefficiencies and to motivate our experimental design, consider the problem of a monitor who
uses the price of a firm’s equity as an indication of the firm’s underlying fundamental value.9
Suppose that a firm’s fundamental value is randomly drawn from a uniformly distributed range
of values between $2.00 and $8.00, and that this fundamental realization  is known
(collectively) by traders. Unlike the traders, the monitor cannot see the underlying fundamental,
but can only observe transactions prices. The monitor acts out of concern for social welfare, and
conversion is desirable socially only if the (unaided) fundamental value of the firm is below a
critical value ˆ  $5.00 .
We consider two conversion scenarios. The first is a value-increasing scenario in which
the bond-to-equity conversion ratio is set at a level high enough that contingent capital bond
holders transfer =$2.00 of value per share to incumbent equity owners, making the postconversion equity value +. The second is a value-decreasing scenario in which the bond-toequity conversion ratio is set sufficiently low that the conversion transfers =$2.00 of share

8

Laboratory experiments have been used to evaluate market institutions and regulatory structures in a variety of
contexts, including markets for gastroenterology fellowships (Niederle and Roth, 2005), pollution emission trading
schemes (e.g, Cason, Gangadharan and Duke, 2003), markets for water irrigation rights (Cummings, Holt and
Laury, 2004) and the design of radio-spectrum auctions (e.g., Plott and Salmon, 2004).
9
In what follows, except for the label of the regulator treatment, we will use the more neutral terms “monitor” and
“firm” instead of “regulator” and “bank.”

4

value away from incumbent equity owners to contingent capital bondholders. Consequently the
post-conversion equity value becomes -.10
We focus first on the value-increasing scenario. The informational problem is most easily
seen with a fundamental realization relatively close to but below the critical ˆ  $5.00
conversion cutoff. For specificity, let  = $3.50. In this case conversion is socially warranted,
and, if done, would leave incumbent equity holders with an asset worth  +  = $5.50. The
traders could trade the asset at $5.50 under the assumption of conversion, but what if  = $5.50?
In that case conversion is not warranted, but the price would also be $5.50. What should the
monitor infer about the fundamental if he sees that price? What should traders assume the
monitor will do? Figure 1 illustrates. At prices below $3.00 the monitor can unambiguously infer
that conversion is desirable, since it must be the case that  <$3.00 no matter what traders
assume that the monitor will do. Similarly, at prices above $7.00 the monitor can conclude that
conversion is not desirable, since it must be the case that >$5.00. However, at prices between
$3.00 and $7.00, it is not clear what the monitor should infer about the fundamental and what
traders should infer about what the monitor will do. Clearly, the price schedule illustrated in
Figure 1 cannot be an equilibrium. Furthermore, it can be shown that no price schedule exists
that is an equilibrium.11
In contrast, the possibility of a value-decreasing conversion does not undermine the
monotonic relationship between fundamentals and prices. Figure 2 illustrates. When conversion
reduces firm value, trading prices represent an upper rather than a lower bound on the ex post
asset value. Thus, any   ˆ should induce all traders to discount the value of an impending
conversion and price the asset at P(-). For example, if =$3.50, price is bound by the value
without a conversion, $3.50, and the value with a conversion, $1.50. Since the monitor can infer
that an intervention is warranted in either case, no ambiguity arises. Similarly, for any   ˆ
10

Most attention regarding bond to equity conversion rules focuses on value-decreasing conversions, under the
argument that a punitive conversion will provide a firm with correct risk management incentives. Nevertheless, the
value-increasing scenario is more than a theoretical concern. A value-increasing conversion arises any time
incumbent equity holders expect a bailout. BGP provide a variety of additional instances of such value-increasing
corrective actions.
11
The formal proof of nonexistence is simple. No price schedule with P(1)=P(2), for 1≠2 is an equilibrium
because the monitor would intervene with the same probability for these two states, which means their prices would
differ. No price schedule with a unique price for each value of  is an equilibrium either because then the monitor
could figure out the fundamental from the price and would intervene only for
unique price for each value of , which is a contradiction.

5

 ˆ . But then, there would not be a

individuals have no reason to suspect that a conversion will occur and the price remains P().
Notice finally that no prices in the range between P(ˆ) and P (ˆ   ) ($3.00 to $5.00 in Figure
2) should be observed. For any fundamental realization above $5.00, traders have no reason to
believe that a conversion will occur, and assets should trade at prices close to the market
fundamental (without conversion). For any fundamental realization below $5.00, traders should
anticipate and fully discount the value of the conversion.12
2.2 A Fixed-Trigger Regime. A natural proposal for eliminating the informational
ambiguity that the presence of an active monitor can create is to replace the monitor’s discretion
with a fixed price rule that triggers a mandatory intervention; the traders do not need to guess
how the monitor will respond. As SW establish, however, in the case of a value-increasing
conversion, such a trigger fails to eliminate ambiguity. Further, in the case of a value-decreasing
conversion, a fixed-price trigger introduces multiple equilibria.
To understand these effects intuitively, replace the monitor in the previous subsection
with a mandatory conversion that occurs any time prices fall below ˆ =$5.00. Consider first the
case of a value-increasing conversion, and suppose that the fundamental realization is $3.50, as
shown in Figure 1. Traders, aware that equity is worth $5.50 if transaction prices remain below
the trigger, are faced with the same conflicting incentives observed in the regulatory regime. On
the one hand, if a conversion is triggered, the market value of units exceeds $5.00 and traders
could increase their payoffs by purchasing units for anything up to $5.50. On the other hand,
prices above $5.00 will prevent a conversion, keeping value at $3.50. SW show that, just as for
the regulator regime, when the underlying fundamental is between $3 and $5, no equilibrium
exists.
Now consider a value-decreasing conversion scenario. For specificity, consider a market
fundamental of $5.50. Given that the fundamental value exceeds $5.00, traders, confident that
intervention will occur, should trade at prices close $5.50. In this case, no conversion occurs
12

No prices in the [$3.00, $5.00] range are consistent with an equilibrium. To see this suppose first that traders with
values in the $5.00 to $7.00 range are for some reason pessimistic about possibility of a conversion and incorporate
the value-decreasing conversion into equity prices. This pessimism would generate prices between $3.00 and $5.00.
A subsequent monitor conversion cannot be an equilibrium, since conversion would reduce monitor payoffs. In turn,
a failure of the monitor to convert would make trader beliefs about conversion incorrect ex post. On the other hand,
suppose that traders have fundamentals in the $3.00 to $5.00 range but optimistically assume that no conversion will
occur. If the monitor fails to convert ex post, she could unilaterally increase her payoff by deviating and converting.
But if the monitor does convert, traders bought units on the ex post incorrect belief of no conversion and could
unilaterally increase payoffs by incorporating the value of the conversion into their offers.

6

making traders’ ex ante beliefs correct, establishing an equilibrium. Suppose, however, that
despite knowledge that a conversion is socially undesirable, traders pessimistically suspect that a
conversion will occur. If traders incorporate the value of the intervention into bids and offers, the
price will fall to $3.50, triggering a conversion. Since there is no monitor who could increase her
payoff by changing her conversion decision, trading prices that include the conversion will also
constitute an equilibrium: traders’ ex ante beliefs were correct ex post and no trader can
unilaterally increase his or her payoffs by failing to incorporate the value of the conversion.
Multiple equilibria similarly arise for any market fundamental in the [$5.00, $7.00] range.
2.3 A Prediction-Market Regime. An alternative to a fixed-price trigger rule is to find a
mechanism that provides additional information that allows the monitor to distinguish between
two fundamentals that deliver the same price. BGP prove in their environment that a “prediction
market” that elicits the market’s assessment of the likelihood of a conversion is one such
mechanism. Empirically, the accuracy of prediction markets has been extensively documented.
In over a decade of experience, prices in political stock markets have consistently predicted
ultimate vote counts more accurately than polls (see, e.g., Berg, Forsythe, Nelson, and Rietz,
2008), and prediction markets are now increasingly used in business and policy contexts to
assess event probabilities.13
The potential information-correcting role of a prediction market is easily understood
intuitively. Consider again the parameters in the regulator regime, but suppose that in addition to
equity, traders buy and sell “conversion likelihood tickets”, which take on a value of $1.00 if the
regulator elects to make a conversion following the close of trading and $0.00 otherwise. The
ticket price, which is between $0 and $1.00, reflects traders’ collective expectation of a
conversion. Ticket prices close to $1.00 imply that traders collectively regard conversion to be
very likely. In a value-increasing conversion scenario, for example, a ticket price of $0.95 allows
the monitor to conclude that a price of, say, $6.00 incorporates fully the value of the expected
conversion (implying that the underlying market fundamental is close to $4.00). Similarly, a
ticket price of $0.05, would allow the monitor to conclude that the same $6.00 equity price
reflects the asset’s underlying fundamental value, absent a conversion-induced adjustment.
13

In discussing an internal prediction market conducted by Google, Cowgill, Wolfers, and Zietwitz (2009) observe
that a host of firms have begun using prediction markets to predict events pertinent to the firm. In addition to
Google, examples include Abbott Labs, Arcelor Mittal, Best Buy, Chrysler, Corning, Electronic Arts, Eli Lilly, Frito
Lay, General Electric, Hewlett Packard, Intel, InterContinental Hotels, Masterfoods, Microsoft, Motorola, Nokia,
Pfizer, Qualcomm, Siemens, and TNT.

7

As discussed above, in the case of a value-decreasing conversion, a unique equilibrium
exists for every fundamental realization. Nevertheless, to the extent conversion errors occur in
the experiments with value-decreasing actions, a prediction market may improve informational
efficiency because it provides the monitor with information regarding the appropriate
interpretation of prices in the [$3.00, $5.00] range, where no prices are consistent with an
equilibrium. A monitor, for example, might interpret an equity price of $3.50 as reflecting a
failure of traders to fully incorporate the value of an intervention if ticket prices are close to
$0.00, but as reflecting trader pessimism if ticket prices are close to $1.00.

3. Experimental Design and Procedures
3.1 Background. A relatively large experimental literature examines asset markets. The branch of
this literature most pertinent to the present investigation examines the capacity of traders to
aggregate disparate information regarding a valued asset in a repeated single-period design.14
Plott and Sunder (1988) evaluate 12-trader markets in which traders are uniformly endowed with
a portfolio consisting of cash and a number of homogenous assets, the value of which is
determined at the end of the period by its fundamental. Traders are divided into three groups,
each of which is told one of the three values that the asset will not take. Traders then buy and sell
assets in a standard open book double auction. Plott and Sunder find some evidence that trading
does allow sellers to identify the underlying value. Nevertheless, information aggregation is
often incomplete in the sense that prices often deviate substantially from the underlying
fundamental. Using a similar design, Forsythe and Lundholm (1990) find that experience appears
to improve information aggregation. More recently Hanson et al. (2006) and Opera et al. (2007)
examine variants of the Plott and Sunder design with the modification that a subset of traders
were motivated to bias market prices in a particular direction. Results in both papers indicate that

14

Another branch of the experimental asset market literature, initiated by Smith, Suchanek, and Williams (1988),
considers the capacity of traders to track the underling fundamental value of a relatively long-lived asset that yields
stochastic returns. Results indicate a persistent propensity for speculative pricing bubbles. This result appears
resilient to a variety of conditions, including brokerage fees, short selling or subjects drawn from subpopulations of
corporate managers or professional stock traders (see, e.g., King et al., 1993, Lei, Noussair, and Plott, 2001).
Common experience with the trading institution appears to minimize the propensity toward speculative pricing.
However, recent research by Hussam et al. (2008) indicates that other factors, such as dividend uncertainty and a
capacity to sell short can reignite bubbles even with very experienced traders.

8

even a sizable number of manipulators find altering prices in a desired direction difficult.
Nevertheless, as in the related research, prices often failed to reflect underlying value.
Our research questions require some substantial deviations from these informationaggregation designs. We are interested in examining a market where the fundamental value is
unknown to the monitor and revealed only through trading. Further, to avoid “no trade”
predictions we must induce some heterogeneity in asset values. At the same time, however, we
seek a baseline context where traders aggregate information sufficiently to make market prices
reflect reasonably well the underlying fundamental. Satisfying these design constraints requires
us to deviate somewhat from the theoretical environments used by BGP and SW. Although our
design does not precisely implement either environment, it does provide useful insight into the
interrelationship between various conversion mechanisms and market prices.
3.2. Experiment Design. The experiment consists of a BASE condition and three treatment
regimes: a Regulator regime where a price-informed monitor makes conversion decisions, a
Fixed Trigger regime where the monitor is replaced with a trigger, and a Prediction Market
regime, where the results of a prediction market supplement price information. In each regime
we conduct treatments with value-increasing conversions and value-decreasing conversions. All
treatments are extensions of the BASE condition, which we explain first.
3.2.1 BASE Condition. The base condition consists of 10 traders and 3 monitors. Each
period traders are endowed with two units of an asset, and a cash endowment of E =$16 lab. Six
of the traders realize an underlying fundamental asset value 1 drawn from a uniform distribution
U[$2.00, $8.00]. The remaining four traders are endowed with assets valued 60 cents lower, e.g.,

2 = 1 -60¢. The value distribution, the relation between high and low values, and the aggregate
number of high- and low-value units are provided as common knowledge to traders. Traders,
however, do not know if their fundamental value draw for the period is low or high.
In this market trade accomplishes a very simple information aggregation task: units flow
from the low- to the high-value traders, and in the process reveal 1. Aggregating value
realizations, as shown in Figure 3 reveals a substantial excess demand for high-value units,
providing considerable incentive for prices to rise to the “market” fundamental 1.

9

The market is organized as a standard, open book double auction (similar to the rules
used on the NYSE), and traders may trade their endowments of cash and asset units as they see
fit.15 Trading periods last 110 seconds. At the end of each period, payoffs for each trader of type
k are determined as the sum of residual cash, and the fundamental value of all units owned at the
end of the period, or
nb

ms

i 1

j 1

Payoff k  E   pi   p j   k  (nb  ms  2)

(1)

where nb units are bought at prices pi, i={1,…,nb} and ms units are sold at prices pj, j={1,…,ms}.
Finally, in the BASE condition the three monitors are shown the median transaction price
at the close of each period and then guess 1.16 Monitors make decisions simultaneously, and
once all decisions are complete the actual 1 is revealed. Monitors earn $3 lab if their guess is
within 20¢ of 1, $1 lab if their guess is within 50¢ of 1, and zero otherwise. Absent the
possibility of intervention, markets in BASE periods should aggregate information effectively.
Operationally, this should mean that the deviation between median prices and the market
fundamental 1 should be consistently small. Defining informational efficiency as the extent to
which the median price reflects the underlying market fundamental, and allocative efficiency as
the percentage of total available gains extracted from exchange we form a first conjecture.17
Conjecture 1: In the BASE condition, markets are both informationally and allocationally
efficient.
3.2.2 The Regulator Regime. Conditions for the Regulator treatments duplicate those for
the BASE condition with the following differences. First, in addition to assessing 1 for the
15

Organizing the market as a simultaneous move institution, such as a call market, would be procedurally simpler.
Overall, call markets perform quite favorably relative to double auctions (see, e.g., Cason and Friedman, 2008, and
Kagel, 2004). However, a number of experimental studies indicate that simultaneous move institutions like the call
market are susceptible to information cascades (Anderson and Holt, 1997) and the winner’s curse (Kagel and Levin,
1986), and are thus less desirable as information aggregation mechanisms. See, e.g., Plott (2001), or, for information
aggregation problems in a context that is in some respects related to the one examined here, Duffy and Fisher
(2005).
16
We elected to provide a single price-based measure of market activity both for simplicity and for purposes of
parallelism with relevant natural contexts, where market assessments focus primarily on summary price measures.
Alternative possible price-based measures include the closing price and the average of the final several contracts in a
period. Concerns about traders trying to manipulate prices in order to convince monitors to intervene or not guided
our decision to use the median price, rather than a potentially more manipulable measure of final trading activity,
such as the closing price.
17
We calculate allocative efficiency as the percentage of units held by high-value traders at the end of each trading
period. The maximum gain from efficient portfolio reallocation is $4.80 lab: 60¢ each from the movement of the
eight units held by “low-value” traders (with values of 2) to “high-value” traders (with value of 1).

10

period, monitors must also make a conversion decision under the condition that conversion is
desirable if the market fundamental 1 is less than ˆ  $5.00 . The monitor earns $10 lab for a
correct decision. The relatively large payment for correct conversion decisions was imposed to
reflect incentives for regulators in natural contexts, where the bulk of their returns are
determined by making socially optimal decisions.
After all decisions are complete, 1 is revealed to the monitors, and the action of one of
the three monitors is selected at random and implemented. In the case of a value-increasing
scenario the value of assets increases by $2.00 in the case of a conversion, so for high-value
traders the value is 1+2.00 and for low-value traders it is 1-0.60+2.00. Based on the
nonexistence finding of BGP, we conjecture that the experimental environment will have similar
problems that will be reflected by informational and allocative inefficiencies for the traders and
difficulty for monitors in making conversion decisions.
Conjecture 2. The possibility of a value-increasing conversion by monitors will cause
informational and allocative efficiency to fall relative to the BASE condition. Monitors will make
errant conversion decisions.
Sessions in a value-decreasing scenario are structured in exactly the same way as the
value-increasing scenario except that a conversion transfers value away from rather than to
incumbent equity owners. As discussed above, in the BGP model value-decreasing conversions
do not interrupt the monotonic relationship between fundamentals and price and the markets are
fully efficient. This gives a third conjecture.
Conjecture 3: The possibility of a value-decreasing conversion by monitors will not affect the
informational or allocative efficiency of markets relative to the BASE condition. Monitors should
commit few conversion errors.
3.2.3. Fixed Trigger Regime. To evaluate the performance of markets operating with a
trigger, we replace the monitor, with a mandatory conversion that occurs if the median price in a
period falls below $5. As discussed in section 2, SW find that in a value-increasing scenario no
equilibrium exists in the Fixed-Trigger regime for fundamental realizations between $3.00 and
$5.00. For this reason, our fourth conjecture is that there will be informational and allocative
inefficiencies, as well as a significant numbers of conversion errors.

11

Conjecture 4: In the case of a value-increasing conversion the trigger will cause
informational and allocative efficiency to fall relative to the BASE condition. Monitors will make
errant conversion decisions.
In a value decreasing scenario the use of a trigger creates both high and low price Nash
equilibria for each fundamental realization in the [$5.00, $7.00] range. Based on the findings in
SW, we anticipate that the creation of this second Nash equilibrium would tend to reduce
informational efficiency relative to BASE markets, and as a consequence generate allocative
efficiency losses and conversion errors. This is a fifth conjecture.
Conjecture 5: In the case of a value-decreasing conversion the use of a trigger will cause
informational and allocative efficiency to fall relative to the BASE condition. Monitors will make
errant conversion decisions.
3.2.4 Prediction Market Regime. To examine the corrective capacity of prediction markets,
we conduct a pair of treatments that parallel the initial Regulator treatments, except that at the
beginning of each period traders are endowed with one conversion likelihood ticket. The ticket is
worth $1 (lab) at the end of the period if the monitor intervenes following the close of trade and
$0 otherwise. Prior to the onset of equity trading each period, traders are given the opportunity
to exchange tickets by submitting both maximum bid to purchase a second ticket and a minimum
offer to sell their ticket.18 A call market is used to determine a market ticket price as well as the
number of tickets that change hands: bids are ranked from highest to lowest, offers are ranked
from lowest to highest, and a crossing is found. The market price of a ticket is determined as half
the distance between last “inside” bid and offer.19 All “inside” units exchange, with tickets
passing from sellers to buyers at the market price. Following the ticket exchange, trading
proceeds as in the initial Regulator treatment, except that the market price of a ticket is displayed
to all traders and monitors.
The potential information-correcting role of the prediction market in the BGP model
produces a sixth conjecture.

18

Bids and offers are submitted under the conditions that the maximum offer cannot exceed $1 (since that is the
ticket’s maximum value), and that each trader’s offer must exceed his or her bid (so that the trader does not sell to
himself or herself).
19
That is, the last ranked bid and offer pair where the bid is no greater than the offer. In the case that no offer
exceeds a bid, the price is set as half the distance between the lowest offer and the highest bid.

12

Conjecture 6: Addition of a prediction market to markets in the Regulator regime will yield
informational and allocative efficiency levels comparable to those observed in the BASE
condition. Few conversion errors will occur.
3.3 Experiment Procedures. The experiment was conducted in two temporally distinct
phases. In an initial phase, our primary focus was on examining the consequences of having a
monitor make conversion decisions. In a temporally subsequent second phase we conducted
treatments that (a) added a prediction market to the experiments with a monitor and (b) replaced
the monitor and prediction market with the fixed trigger rule. The initial phase consisted of a
series of 16 twenty-period market sessions. At the outset of each session participants were
randomly seated at visually isolated PCs. An experiment administrator then read aloud a
common set of instructions, which explained incentives for traders and for monitors in the BASE
condition, as well as how to make decisions on the computer interface used in the experiment.20
The experiment was programmed and conducted with the software z-Tree (Fischbacher, 2007).
To facilitate participant understanding, screen shots were projected onto a wall at the front of the
lab. Following the instructions, participants completed a short quiz of understanding, which the
experiment administrator reviewed publicly. Finally, participants completed a practice period for
which they were not paid. At any time during the instructions, quiz, and practice period,
participants were encouraged to ask questions by raising their hands. Questions were answered
privately. Following completion of the practice period, the session commenced.
After five periods in the BASE condition the session was paused and additional instructions
were distributed. In the Regulator treatments, instructions regarding the intervening monitor
were distributed to participants. An experiment administrator read aloud these instructions.
Following a second short quiz of understanding, a second 15-period portion of the session
commenced. After period 20 these initial phase sessions ended.
The second experiment phase consisted of 12 additional 13-participant sessions conducted to
examine the Prediction Market regime, and six 10-participant sessions that examine the Fixed
Trigger regime. Procedures for the Prediction Market treatments were identical to those for the
Regulator treatments, except that following the BASE condition periods, we conducted only five
periods in a value-increasing or value-decreasing Regulator regime. Following these initial 10

20

Instructions are available at http://www.people.vcu.edu/~dddavis.

13

periods, a third set of instructions was passed around that explained to participants the market for
conversion likelihood tickets. Following instructions, a short quiz and practice with the ticket
auction, a third 10-period sequence began in which trading and monitor decisions were informed
by results of the ticket auctions. These sessions also terminated after period 20.
In the Fixed Trigger regime, no monitors were present. Following 5 BASE condition periods,
instructions regarding a trigger in a value-increasing (or value-decreasing) scenario were
distributed to the 10 traders and read aloud by an experiment administrator. Following a short
quiz of understanding, a second 10-period segment of the session commenced. The second
segment was followed by a similarly introduced third 10-period sequence in the value-decreasing
(value-increasing) scenario not conducted in the second segment. The Fixed-Trigger sessions
ended after period 25.21
In total 424 undergraduate student volunteers participated in this experiment. In the initial
phase, 208 volunteers participated in 16 Regulator market sessions (eight in a value-increasing
scenario and eight in a value-decreasing scenario). In the second phase, 216 volunteers
participated in 12 Prediction Market sessions (six in a value-increasing scenario and six in a
value-decreasing scenario), and in six Fixed-Trigger sessions (yielding six 10-period sequences
in a value-increasing scenario and six 10-period sequences in a value-increasing scenario).
Participants were upper-level math, science, engineering, and business students enrolled in
courses at Virginia Commonwealth University in the spring semesters of 2010 and 2011. No one
participated in more than one session. Lab earnings were converted to U.S. currency at $12 lab
=$1 U.S. rate. Participant earnings for the 90-120 minute sessions ranged from $14 to $32.25 and
averaged $23.25 (inclusive of a $6 appearance fee).

4. Experiment Results
We present the results in terms of a series of findings that evaluate Conjectures 1 to 6. In a
second subsection we offer some observations regarding performance across different conversion
rule regimes.
4.1 Evaluation of Conjectures. A first finding pertains to BASE condition results.
21

To facilitate the comparison of outcomes across treatments, a common set of fundamental realizations were used
in all Regulator sessions However, alterations in the number of sequences and the total number of periods forced us
to use a slightly different set of fundamental realizations in the Fixed-Trigger and Prediction Market treatments.
Values for each treatment are displayed in appendix A.

14

Finding 1. BASE condition markets are both informationally and allocationally quite efficient:
median contract prices deviate from the fundamental by an average of 21¢ and trading extracts
95% of the available surplus.
Figure 4 plots median contract prices against underlying market fundamental realizations for
the BASE condition periods. Notice in the figure that for each fundamental realization median
prices (indicated by circles) cluster tightly about the fundamental (noted as a line).
Quantitatively, the absolute deviation of contract prices from underlying fundamentals averages
21¢. Using the 60¢ gap between 1 and 2 as a reference, our BASE markets extract roughly twothirds of the underlying information. While imperfect, performance in our BASE periods is fairly
impressive, relative to other information aggregation experiments (e.g., Plott and Sunder, 1988,
Forsythe and Lundholm, 1990, Hansen et al., 2006, or Oprea et al., 2007).22
Beyond informational efficiency, we observe that our BASE condition markets were also
quite allocatively efficient. As reflected by the horizontal dashes hovering close to the 100% line
at the bottom of Figure 4, units flow from low- to high-value traders quite effectively in the
BASE condition periods. Overall, allocative efficiency averages 95%, a level that parallels results
of many double auction experiments.
4.1.1 The Regulator Treatments
Our second and third findings regard the effects of the Regulator treatments. Consider first the
value increasing scenario.
Finding 2: In a value-increasing scenario, monitor conversion decisions result in significant
informational and allocative efficiency losses relative to the BASE condition. Although the
largest efficiency losses occur in the ambiguous [$3.00, $7.00] range, sizable losses occur even
for fundamentals that do not yield ambiguous price signals. In the ambiguous range conversion,
errors occur in almost 25% of periods.
The upper panel of Figure 5 summarizes results of Regulator markets in the valueincreasing scenario. The active monitor markedly affects informational efficiency, particularly
for market fundamentals below $5.00. In this range, prices “bubble up” very incompletely from
22

It is difficult to draw an explicit standard of comparison across these different experiments. However, the authors
in each case regard information aggregation as “highly incomplete” and price variations are very large.

15

the ex ante fundamental to the ex post level that includes the value of the conversion. Despite this
incomplete adjustment, median prices increasingly exceed $5.00 as the ex ante fundamental
approaches the conversion cutoff, which in turn complicates the monitor’s task of assessing
underlying fundamental values in the neighborhood of $5.00.
Looking at the bottom of the upper panel, observe further that this informational
inefficiency also importantly impacts allocative efficiency. Allocative efficiencies for the
Regulator markets in the value-increasing scenario hover at about 75%, a level both markedly
lower than in the BASE condition, and startlingly low for markets organized under double
auction trading rules.23
The ambiguity of price information also generates numerous conversion errors. This can
be seen by the light gray, dark gray and black fillings for the median price circles, which
indicate, respectively, instances of one, two, and three intervention errors in a trading period.
Although errors occur throughout the ambiguous [$3.00, $7.00] range of fundamental
realizations, the highest concentration of conversion error occur for fundamentals close to the
$5.00 efficient conversion cutoff.
We more formally assess performance in the value-increasing scenario of the Regulator
treatment relative to the BASE condition with a series of simple regressions. For informational
and allocative efficiency we pool BASE and value-increasing Regulator periods, and regress each
efficiency measure against two dummy variables, (i) DActive, which takes on a value of 1 in
periods when the monitor conversion regime is in effect, and 0 otherwise, and (ii) DAmbig , which
takes on a value of 1 in Active periods when the fundamental realization is in the [$3.00, $7.00]
ambiguous range and 0 otherwise. Thus, the coefficient on DActive captures the incremental effect
of the active monitor regime on informational or allocative efficiency, while the coefficient on
DAmbig captures the incremental effect of an ambiguous fundamental realization given an active
monitor. For the conversion error rate regression, observe that conversion errors arise only when
the monitor is active. For this reason, we exclude the BASE periods from the conversion error
rate regression and estimate the incremental effect of ambiguous fundamental realizations in
Active monitor periods. The intercept for this regression reflects the conversion error rate in
23

For example, in a very demanding double auction design with inexperienced traders where each period supply and
demand receive random shocks and where relative cost and value assignments are reshuffled among sellers and
buyers, respectively, Cason and Friedman (1999) observe mean trading efficiencies of 88.4%. In a similar eightseller design, also with inexperienced traders, Kagel (2004) observes average trading efficiencies of 95%.

16

Active monitor periods for fundamentals outside the ambiguous range. In all regressions we
cluster data by markets and use a robust (White “sandwich”) estimator to control for possible
unspecified autocorrelation or heteroskedasticity
Columns (1) to (3) in the left side of Table 1 report results for Regulator markets in the
value-increasing scenario. As can be seen from the coefficients on DActive in row (ii) the
possibility of conversion significantly reduces both informational and allocative efficiency.
Relative to BASE condition periods, absolute median price deviations for Active periods increase
by 29¢, thus reducing information transmission to roughly one-sixth of the spread between 1
and 2. Similarly, allocative efficiency falls by 11 percentage points, as traders with ex post high
values sell units to low value traders. As indicated by the asterisks, both of these effects are
significant at a 5% significance level. Notice further in column (3), however, that despite these
unpredicted efficiency losses, the presence of an active monitor does not importantly undermine
the capacity of monitors to assess when conversion is appropriate, when fundamental realizations
are outside the ambiguous range. Intervention errors occur in only 3% of periods with
“unambiguous” fundamental realizations.
Row (iii) of Table 1 summarizes the incremental effects of ambiguous fundamental
realizations in the Active monitor periods. As seen in columns (1) and (2) of row (iii), ambiguous
fundamental realizations increase absolute median price deviations by 26¢, for a cumulative total
of 76¢ - a difference that exceeds the 60¢ difference between 1 and 2. Similarly, allocative
efficiency falls another 10 percentage points, for a cumulative level of 74%. Perhaps most
prominently, conversion error rates in the ambiguous range increase by a significant 22
percentage points, for a cumulative total of 25%.
Finding 3: In the case of a value-decreasing conversion, the presence of an active monitor
reduces both informational and allocative efficiency relative to BASE condition. Further,
monitors commit a significant number of conversion errors.
Results for the value-decreasing scenario of the Regulator regime, shown in the lower
panel of Figure 5, suggest that, contrary to our expectations, substantial informational efficiency
losses also arise here. For market fundamentals below $5.00, median prices do not always drop
from the ex ante fundamental to the ex post efficient level, as traders incompletely incorporate
into prices the value of what should be an anticipated conversion. On the other hand, for market
17

fundamentals in excess of $5.00, traders in several instances assume (pessimistically) that the
monitor will make a conversion, causing prices to drop. Combining the effects of incomplete
capitalizations of anticipated conversions and trader pessimism regarding the likelihood of
unnecessary conversions, monitors see a large number of prices in the [$3.00, $5.00] range,
where no price is consistent with an equilibrium.
Looking at the bottom of the lower panel, observe further that allocative efficiency in the
Regulator treatment with a value-decreasing scenario suffers relative to the BASE condition. For
most fundamental realizations, traders extract only about 75% of the possible gains from trade.
Finally, as indicated by the light grey, dark grey and black fillings, median prices in the [$3.00,
$5.00] range cause numerous conversion errors, the majority of which occur for fundamentals in
excess of $5.00. Generally speaking, monitors appear to interpret prices in the [$3.00, $5.00]
range as traders incompletely incorporating the value of what should be an anticipated
conversion. As indicated by the high frequency of dots with colored fillings to the right of $5.00,
in those instances where traders do pessimistically adjust for a socially unnecessary conversion,
conversion errors arise frequently.
Regression results in columns (4) to (6) of Table 1, allow a more formal support for
Finding 3. These regressions parallel those for the value-increasing scenario of the Regulator
regime except that we exclude the DAmbig dummy, because no ambiguous range exists in the
value-decreasing scenario. Looking at the entries in row (ii) observe that in a value-decreasing
scenario an active monitor significantly reduces both informational and allocative efficiency.
Median absolute price deviations increase by 42¢ over the BASE condition, and allocative
efficiency falls by 16 percentage points. Both changes are statistically significant. Notice further
from column (6) that conversion errors occur in 8% of instances.
4.1.2 The Fixed Trigger Treatment
The next pair of findings evaluate Conjectures 4 and 5 pertinent to the fixed-trigger regime. We
start with the value-increasing scenario.
Finding 4: In the case of a value-increasing conversion, a fixed trigger results in significant
informational and allocative efficiency losses relative to the BASE treatment, with particularly
large losses in the [$3.00, $5.00] range. In this range, conversion errors occur in 38% of
instances.

18

Figure 6 summarizes results of the fixed trigger regime. In the case of a value-increasing
conversion, shown in the upper panel, dispersion from ex post efficient price illustrates
considerable informational inefficiency relative to the BASE condition. For fundamentals in the
[$3.00, $5,00] range, prices cluster about $5.00, as the trigger prevents traders from
incorporating into prices the value of a socially beneficial conversion. Traders fail to balance
their individual interests in purchasing units at prices below value against the group interest in
keeping the median price below the trigger. This in turn prompts frequent conversion errors.
The regression results summarized in columns (1) to (3) of Table 2 provide more formal
support of Finding 4. These regressions parallel those for the value-increasing Regulator
treatment in Table 1, except that, consistent with SW, we restrict the ambiguous range of
fundamental realizations to the [$3.00, $5.00] range. Starting with the incremental effects of an
active trigger, in row (ii), observe first that the addition of a trigger does not importantly affect
either informational efficiency, as indicated by the small (but significant) 6¢ entry in column (1),
or the incidence of conversion errors, as indicated by the 3% entry in column (3) . However, the
trigger does exert sizable and significant allocative inefficiencies, as reflected in the -11% entry
in column (2). Parallel to the value-increasing Regulator treatment, many traders appear to
encounter some difficulties in efficiently reallocating their portfolios.
Turning to results for the ambiguous [$3.00, $5.00] range, summarized in row (iii), observe
that the consequences of the trigger here increase markedly: absolute price deviations increase by
107¢ (to a cumulative level of 154¢), allocative efficiency falls by another 11 percentage points
(to a cumulative level of 73%), and the incidence of conversion errors increases by 35 percentage
points (to a cumulative level of 38%).
Finding 5: In the case of a value-decreasing conversion, use of a trigger results in sizable
informational and allocative efficiency losses relative to the BASE condition. Substantial
informational efficiency losses occur in the [$5.00, $7.00] range, where the fixed-trigger creates
multiple equilibria. In this range, conversion errors occur in 33% of instances, though most of
these are close to the trigger value.
The bottom panel of Figure 6 illustrates results of a trigger in the case of a value-decreasing
scenario. As indicated by the fairly small differences between median prices and the ex post
efficient price, for fundamentals outside the [$5.00, $7.00] range, prices track underlying
fundamentals quite well (at least relative to the value-decreasing treatment of the Regulator
19

regime). Nevertheless, the multiple equilibria in the [$5.00, $7.00] range, impact negatively on
informational efficiency, as indicated by the median price dots trailing down from the ex post
efficient fundamental. Notice further from the black fillings for those dots, these prices triggered
a large number of socially unnecessary conversions. Also, allocative efficiencies cluster about
the 75% level, which is less than in the BASE condition.
The regression results, listed in columns (4) to (6) of Table 2 summarize these
observations quantitatively. Looking first at row (ii), observe from the small and statistically
insignificant 7¢ coefficient on DActive that for fundamental realizations outside [$5.00, $7.00] a
trigger does not significantly affect informational efficiency relative to the BASE condition.
Further, as seen by the 0 entry in column (6), for fundamentals outside [$5.00, $7.00] traders
commit no conversion errors. Thus, traders appear better able to cause a market adjustment for
the anticipated conversion with the trigger. Nevertheless, the price adjustment process fails to
force the smooth flow of units from low- to high-value traders. As seen in column (5), trading
efficiency with an active trigger falls by 20 percentage points (to a cumulative level of 74%).
Turning to incremental effects for the [$5.00, $7.00] range, summarized in row (iv), observe
that, as predicted by SW, the fixed trigger negatively and importantly affects performance:
Absolute mean price deviations almost double (increasing by 25¢), and conversion errors occur
in one-third of instances, as pessimistic traders coordinate frequently on prices below $5.
Curiously, for fundamentals in the [$5.00, $7.00] range notice that trading efficiency increases
by 10 percentage points. This improvement is likely driven by traders in most instances not
needing to incorporate the value of a conversion into prices.
4.1.2 The Prediction Market Treatments. A sixth finding regards results of the prediction market
regime.
Finding 6: Prediction markets fail to resolve the efficiency losses and conversion errors induced
by the presence of an active monitor.
The scattergrams plotting median prices against fundamentals for the Prediction Market
treatments are shown as Figure 7. Viewing Figure 7 in light of Figure 5 suggests that prediction
markets do exert some ameliorative effects. In particular, for fundamental realizations below $5,
median prices “bubble up” more fully in the value-increasing scenario (shown in the upper
panel) and “sink” more completely in the value-decreasing scenario (shown in the lower panel).
20

Nevertheless, relative to BASE condition prediction markets suffer in all dimensions. Prices do
not cluster about efficient fundamentals with anything close to the precision observed in the
BASE condition, with deviations being particularly pronounced for fundamental realizations
close to the $5.00 cutoff. As indicated by gray and black fillings for many median price dots,
conversion errors also occur with some frequency. Observe finally that allocative efficiencies do
not approach the 95% levels observed in the BASE condition.
Regression results summarized in Table 3, quantify the failure of prediction markets to
restore trading performance observed in the BASE condition. For the value-increasing treatments,
summarized in columns (1) to (3), observe that absolute median price deviations roughly double
(increasing by 19¢). Similarly, allocative efficiency falls by 19 percentage points and conversion
errors occur in 12% of trading periods. Parallel results arise in the value decreasing treatments,
summarized in columns (4) to (6). Relative to the BASE condition, mean absolute price
deviations increase by 26¢, allocative efficiency falls by 12 percentage points, and conversion
errors occur in 12% of all periods.
4.2 Cross-Treatment Comparisons. In evaluating the different trigger mechanisms, we compare
the Fixed-Trigger and Prediction Market treatments with the Regulator treatment, since
empowering a regulator with discretionary authority represents perhaps the default method for
implementing conversions.
For the analysis that follows, we evaluate performance with a finer grid of fundamental
realizations than in our earlier analysis. Specifically, we segment the range of fundamental
realizations into six parts. The first pair of segments consist of the ranges [$4.40, $4.99] and
[$5.00, $5.59]. These segments are of interest because the fundamental is closest to the trigger
point, where presumably the most confusion will occur. The second pair of segments capture the
remainder of what we defined as the ambiguous range in the value-increasing scenario of
Regulator treatment, [$3.00, $4.39] and [$5.60, $6.99]. Efficiency losses and conversion errors
in these segments would capture any failure to accurately reflect underlying fundamentals not
already reflected in the segments closest to the conversion cutoff. The final pair of segments
consists of fundamental values below $3.00 and $7.00 or above. These ranges are furthest from
the trigger, so presumably would have less efficiency losses and conversion errors.

21

The histograms in Figure 8 allow assessment of the incremental effects of the Fixed
Trigger and Prediction Market regimes relative to the Regulator regime. (We exclude
allocational efficiencies from Figure 8 because they do not vary importantly across regimes.) 24
Comparing first the Fixed Trigger and Regulator regimes, shown respectively as black and white
bars, notice first that in a value-increasing scenario, both regimes exhibit very similar patterns of
mean absolute price deviations. As market fundamentals approach the $5.00 cutoff from below,
the spread between median prices and the efficient ex post fundamental increases markedly, with
traders becoming progressively more reluctant to strike contracts that reflect the ex post
fundamental value. Above $5.00, however, concerns about incorporating the value of a
conversion disappear, and absolute price deviations fall to or even below the average level in the
BASE condition (shown as a dashed line) in both regimes.
Continuing down the left column of Figure 8, observe that despite the similarity of price
patterns in the two regimes, the shift from Regulator to Fixed Trigger regimes does affect
conversion error rates. In the Regulator regime, conversion errors are distributed throughout the
[$2.00, $8.00] range of possible fundamental realizations, but with a mode just above the
efficient cutoff, in the [$5.00-$5.59] range, implying that monitors mix errors of omission and
commission, but tend to commit more errors of commission (that is, make more socially
undesirable conversions). In the Fixed Trigger regime, by way of contrast, the incidence of
conversion errors drops significantly relative to the Regulator regime for the [$5.00, $5.59] and
[$5.60-$6.99]. Nearly all errors in the Fixed Trigger regime occur in the segment just below
$5.00, implying that this regime almost exclusively yields acts of omission (e.g., foregoes
socially desirable conversions), and only when the market fundamental is very close to the cutoff
for efficient intervention.
Switching to the value-decreasing scenario, observe that mean absolute price deviations
for the Fixed Trigger regime fall below their Regulator regimes counterpart in every segment,
suggesting that the Fixed Trigger regime improves informational efficiency. Continuing down
the column observe further that in a value-decreasing scenario, the Fixed Trigger regime
24

Notice in the upper panels of Figure 8 that the mean absolute price deviation for the BASE condition is drawn as a
horizontal line, reflecting the overall average for all segments. In fact, as a careful review of Figure 4 suggests, mean
absolute price deviations increased very slightly with increases in the underlying fundamental. The frequencies in
Figure 8 are developed from regressions of Mean Absolute Price Deviations and Conversion Error rates on a series
of indicator variables that separate outcomes by treatment and segment. The BASE condition is the intercept in these
regressions. Regression results appear in Appendix B.

22

concentrates conversion errors entirely in the [$5.00, $5.59] range (where socially undesirable
conversions occur). In that range, the conversion error rate for the Fixed Trigger regime is an
almost pervasive 58%. We summarize these as the following comment.
Comment 1: Substituting a monitor with a trigger improves informational efficiency in the
value-decreasing scenario. Further, in both value-increasing and value-decreasing scenarios,
use of a trigger consolidates the range of fundamental realizations that prompt conversion
errors to the segment either just below the efficient conversion cutoff (in the value-increasing
scenario), or just above the cutoff (in the value-decreasing scenario).
Comparison of the white and gray bars in the panels of Figure 8 allows assessment of the
incremental effects of the Prediction Market regime. Starting with the value-increasing regime,
observe that the Prediction Market regime considerably improves informational efficiency for
fundamental realizations below $5.00. For each of the three segments below $5.00, mean
absolute price deviations in the Prediction Market regime are much lower that their Regulator
regime counterparts. Above $5.00, however, the Prediction Market regime does not importantly
affect informational efficiency.
Continuing down the left side of Figure 8, observe that associated with the informational
efficiency improvements for fundamentals below $5.00 is a sizable reduction in conversion error
rates. In both the [$3.00, $4.39] and [$4.40, $4.99] segments conversion errors for the Prediction
Market regime fall almost to zero. The incidence of conversion errors also falls for fundamentals
in the [$5.00, $5.59] range. Nevertheless, the distribution of conversion errors retains the strong
mode of almost 40% observed in the Regulator regime, implying that while the Prediction
Market regime shifts the type of conversion errors almost exclusively to acts of commission
(e.g., socially undesirable conversions), it does not importantly affect the frequency of such
errors.
The right panels of Figure 8 illustrate incremental effects of the Prediction Market
regime in a value-decreasing scenario. As seen in the upper right panel of Figure 8, the
Prediction Market regime tends to modestly improve informational efficiency. Mean absolute
price deviations are at least marginally smaller than their Regulator regime counterpart for every
segment except [$5.00, $5.59]. These informational efficiency improvements, however, fail to
generate any noticeable changes in conversion error rates. The distribution of conversion error
23

rates for the Prediction Market and Regulator regimes are quite similar. We summarize the
above observations regarding the incremental effects of the Prediction Market regime as a
second and final comment.

Comment 2: The addition of a Prediction Market helps traders and monitors disentangle
underlying fundamental values from the ex post value of conversion, particularly for
fundamental realizations below $5.00. Nevertheless, use of a prediction market does not reduce
the strong tendency for monitors to make many socially undesirable conversions for fundamental
value realizations close to, but above $5.00.
As noted in the introduction, prediction markets have been used to elicit group
perceptions with remarkable accuracy in a variety of contexts ranging from election outcomes to
new product adoption rates. The limited success of prediction markets here merits some
reflection. We cannot dismiss the possibility that limitations in the structure of our simple
prediction markets keep prices from reflecting the underlying market fundamental with more
accuracy. By the standards of field markets, our prediction markets are quite thin (with only 10
participants) and traders’ capacities to affect the market prices is quite limited, since they can
buy or sell only a single unit. Perhaps with a larger ticket endowment, or a capacity to purchase
more than a single ticket, our prediction market prices might reflect more fully the high-value
fundamental. The effectiveness of larger prediction markets in this context certainly merits
investigation.
We observe, however, that we are perhaps asking more of prediction markets in this
context than they can reasonably be expected to deliver. Traders, after all buy and sell tickets on
the basis of their ex ante assessment of the probability of a monitor intervention, that is, they
predict not what is socially efficient, but what actually will happen. In a value-decreasing
condition, for example, for market fundamentals only slightly above $5.00, pessimistic traders
may quite rationally sell tickets at prices close to $0.00 if they assume that a monitor interprets
median prices in the [$3.00, $5.00] range as warranting an intervention. Other traders, uncertain
as to the relative optimism of traders may post ticket prices close to 50¢. Crossing bids and offers
in this case can quite legitimately generate ticket prices that produce little useful information.
Similarly in the case of a value-increasing conversion, when market fundamentals only slightly
24

exceed $5.00 some traders will not know ex ante whether or not a conversion is efficient, and
others (with values only slightly in excess of $5.00) may be uncertain as to whether or not near
$5.00 prices will convince a monitor to not intervene (and in any case, these traders would prefer
that a conversion does occur). Again, these forces combine to provide relatively uninformative
ticket prices. The listing of mean ticket prices by fundamental segment in Table 4 illustrates this
point quite clearly. In both value-increasing and value-decreasing conditions, mean ticket prices
exceed 75¢ for fundamentals below $5.00 and are less than 33¢ for fundamentals $5.60 and
above. However, in the $5.00-$5.59 range, mean ticket prices are essentially uninformative at
52¢ and 62¢ for the value-increasing and value-decreasing conditions respectively.

5. Concluding Comments
This paper reports an experiment conducted to evaluate various price-dependent rules for
triggering contingent capital conversions. We find that if conversion decisions are based on
equity prices, the endogeneity between conversion actions and equity value creates an important
informational problem for a regulatory authority. In the case where a conversion increases value
for incumbent equity holders, our results are consistent with predictions by Bond, Goldstein and
Prescott (2010) and we observe informational inefficiencies that result in allocative inefficiencies
and numerous conversion errors. Not predicted by BGP, we also observe sizable inefficiencies
and conversion errors in the case of a value-decreasing conversion. These results suggest that the
use of regulators to make conversion decisions can create severe informational problems.
We also explore two alternatives to a simple regulatory regime. One alternative replaces the
regulator with a fixed threshold that triggers a conversion. Use of a trigger improves
informational efficiency in the value-decreasing conversion scenario, and narrows considerably
the range of fundamental values that yield conversion errors. Nevertheless, (and consistent with
predictions by Sundaresan and Wang, 2011) we observe sizable informational inefficiencies and
conversion error rates for fundamental realizations just above the conversion trigger (in the
value-increasing scenario), and just below the conversion trigger (in the value-decreasing
scenario). In fact, in these narrow segments, the incidence of conversion errors appears to
actually increase relative to the case of a regulator.
As a second alternative, we supplemented agents’ information sets in a regulatory regime
with results of a prediction market. For fundamental realizations below the efficient conversion
25

cutoff, prediction markets do markedly improve informational efficiency in both valueincreasing and value-decreasing conversion scenarios. Similar to the fixed trigger treatment, use
of a prediction market also tends to concentrate the range of fundamental realizations where
conversion errors occur. Nevertheless, allocative efficiencies remain low, and conversion errors
arise frequently for fundamental realizations just above the efficient conversion cutoff.
In sum, our results suggest that contingent capital creates significant informational
inefficiencies when the regulator bases conversion decisions on market prices. Further,
replacement of a regulator either with a fixed-conversion trigger or supplementing agents’
information sets with results of a prediction market improves market performance, but does not
eliminate the incidence of conversion errors.
We do, however, observe that in all regimes the range of fundamental realizations that results
in frequent conversion errors tends to be more narrowly concentrated about the efficient
conversion cutoff than theoretical models by either BGP or SW would suggest. Further both
fixed-trigger and prediction-market treatments have the effect of narrowing this range almost
entirely to fundamentals just above or just below the efficient conversion cutoff. In fact, in both
the fixed trigger and prediction-market treatments, conversion errors are largely confined to the
range of fundamentals where some traders are uncertain about the underlying market
fundamental prior to trading.
In evaluating contingent-capital proposals, our results imply that if the region in which
conversion errors occur is small enough, then these mechanisms may be reasonable, assuming
that the allocative inefficiencies are not too costly. In the context of the values used in our
laboratory markets, our judgment is that these costs are significant. Whether these costs remain
significant in the pertinent natural contexts is an open question. What is clear from the
experiments, however, is that the feedback between prices and actions reduces the informational
content of prices, which reduces the efficiency of allocations and makes conversion decisions
less effective.

26

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Perspectives 18: 107-126.

29

P 

P
Price Range where
prices are consistent
with multiple values

P 

P $
^

Pi

$

^

P$

i $

^

 $

i$

^

$

^

Value Range where
Price Does not Uniquely
Signal Value

$



Range of Socially Desirable Conversion
Figure 1. Prices and Fundamentals Given the Possibility of a Value-Increasing Conversion.

30

P

Monotonicity with Price Discontunity:
Value draws below ^prompt trades at
^
P( ). Value draws above  prompt
trades at P()

P 
P

^

P $
^

P

$
$3.00

^

P $

^

^

 $ $

Range of Socially Desirable Conversion



Figure 2. Prices and Fundamentals, Given the Possibility of a Value-Decreasing Conversion

31

Figure 3. Market Supply and Demand, Given a Market Fundamental 1.

Figure 4. Median Contract Prices vs. Fundamental Realizations in the BASE Condition.
Key: Circles indicates median contract prices. Horizontal bars at the bottom of the figure indicate
mean allocative efficiencies.
32

Median
Price
$7.00

Regulator Regime
Value-Increasing Conversions

$5.00

$3.00

$1.00
Efficiency
100%
50%
$1.00
Median
Price
$7.00

$3.00

$5.00

$7.00 Fund.

Regulator Regime
Value-Decreasing Conversions

$5.00

$3.00

$1.00
Efficiency
100%
50%

$1.00

$3.00

$5.00

$7.00 Fund.

Figure 5. Median Contract Prices vs. Fundamental Realizations in the Regulator treatments.
Key: Dots indicate median contract prices. Light gray, dark gray and black dots indicate
instances of 1, 2 and 3 intervention errors, respectively. Bars indicate mean allocative efficiency.

33

Median
Price

Fixed-Trigger Regime
Value-Increasing Conversions

$7.00

$5.00

$3.00

$1.00
Efficiency
100%
50%
$1.00

Median
Price
$7.00

$3.00

$5.00

$7.00 Fund.

Fixed-Trigger Regime
Value-Decreasing Conversions

$5.00

$3.00

$1.00
Efficiency
100%
50%

$1.00

$3.00

$5.00

$7.00 Fund.

Figure 6. Median Contract Prices vs. Fundamental Realizations in the Fixed Trigger treatments.
Key: Hollow dots indicate median contract prices. Black fillings indicate instances of
intervention errors. Bars at the bottom of the page reflect mean allocative efficiencies.
34

Median
Price
$7.00

Prediction Market Regime
Value-Increasing Conversions

$5.00

$3.00

$1.00
Efficiency
100%
50%
$1.00
Median
Price
$7.00

$3.00

$5.00

$7.00 Fund.

Predict Market Regime
Value-Decreasing Conversions

$5.00

$3.00

$1.00
Efficiency
100%
50%
$1.00

$3.00

$5.00

$7.00 Fund.

Figure 7. Median Contract Prices vs. Fundamental Realizations in the Prediction Market
treatments. Key: Dots indicates median contract prices, light gray, dark gray and black dots
indicate instances of 1, 2 and 3 intervention errors. Bars indicate mean allocative efficiency.
35

Value-Increasing Conversions

Value-Decreasing Conversions

Mean Absolute Price Deviations
$1.50

$1.50

$1.00

$1.00

$0.50

$0.50

$0.00

<$3.00

$3.00-$4.39 $4.40-$4.99 $5.00-$5.59 $5.60-$6.99

$0.00

>$7.00

<$3.00

$3.00-$4.39 $4.40-$4.99 $5.00-$5.59 $5.60-$6.99

>$7.00

$3.00-$4.39 $4.40-$4.99 $5.00-$5.59 $5.60-$6.99

>$7.00

Conversion Error Rates
60%

60%

40%

40%

20%

20%

0%

0%
<$3.00

$3.00-$4.39 $4.40-$4.99 $5.00-$5.59 $5.60-$6.99

Base Condition

Regulator Regime

>$7.00

<$3.00

Fixed Trigger Regime

Prediction Market Regime

Figure 8: Mean Absolute Price Deviations and Conversion Error Rates by Segments

36

Table 1. Regulator Treatments, Incremental Effects
Value-Increasing Conversions
(1)
(2)
(3)
|Pmed – Pfx|: Allocative Conversion
Efficiency Error Rate
(i) Cons

21¢*

95%*

(ii) Active

29¢*

-11% *

3%†

(iii) Ambig

26¢*

-10%*

22%*

N
Wald 2

320
121.2*

320
162.1*

150
29.18*

Value-Decreasing Conversions
(4)
(5)
(6)
|Pmed – Pfx|: Allocative Conversion
Efficiency Error Rate
21¢*

95%*

42¢*

-16%*

8%*

320
36.4*

320
154.8*

150

†

Key: * and indicate rejection of the null that the coefficient equals zero, p<.05 and p<.10, respectively (2-tailed
tests).

Table 2. Fixed Trigger Treatments, Incremental Effects.
Value Increasing Conversions
(2)
(3)
(1)
|Pmed – Pfx|: Allocative Conversion
Efficiency Error Rate
(i) Cons

21¢*

95%*

(ii) Active

6¢*

-11% *

3%

(iii) Ambigft

107¢*

-11%*

35%*

(iv) MultiEq
N
Wald 2

230
96.77*

230
60.95*

60
8.7*

†

Value-Decreasing Conversions
(4)
(5)
(6)
|Pmed – Pfx| Allocative Conversion
Efficiency Error Rate
21¢*

95%*

7¢

-20%*

0

25¢*

10%*

33%*

230
13.26*

230
81.74*

60

Key: * and indicate rejection of the null that the coefficient equals zero, p<.05 and p<.10, respectively (2-tailed
tests).

37

Table 3. Prediction Market Treatments, Incremental Effects.
Value Increasing Conversions
Value Decreasing Conversions
(2)
(3)
(4)
(5)
(6)
(1)
|Pmed – Pfx|: Allocative Conversion
|Pmed – Pfx|: Allocative Conversion
Efficiency Error Rate
Efficiency Error Rate
(i) Cons

21¢*

95%*

(ii) Active

19¢*

-19% *

N
Wald 2

230
37.05*

230
783.61*

21¢*

95%*

12%*

26¢*

-12%*

12%*

60
--

230
6.41*

230
7.18*

60
-

†

Key: * and indicate rejection of the null that the coefficient equals zero, p<.05 and p<.10, respectively (2-tailed
test)

Table 4. Prediction Markets: Mean Ticket Prices (Standard Deviation)
Fundamental
<$3.00
$3.00-$4.39 $4.40-$4.99 $5.00-$5.59 $5.60-$7.00
93¢ (3¢)
85¢ (16¢)a
77¢ (10¢)
52¢ (18¢)
14¢ (10¢)
VIC
b
94¢ (2¢)
82¢ (19¢)
83¢ (9¢)
62¢ (20¢)
32¢ (19¢)
VDC
a

b

Elimination of 2 low priced outliers changes entry to 92¢ (5¢)
Elimination of 3 low priced outliers changes entry to 93¢ (6¢)

38

>$7.00
10¢ (6¢)
20¢ (21¢)

Appendix A
Sequences of Fundamental Realizations
Table A1. Sequence of Fundamental Value Realizations Initial BASE/Regulator
Sessions
BASE Condition
Period
1
2
3
4
5
Fundamental $2.94 $7.33 $4.76 $2.61 $6.50
Period
6
Fundamental $5.73

7
$3.77

Regulator Periods
8
9
10
$2.61 $7.39 $5.99

11
$3.49

12
$5.74

Period
13
Fundamental $4.54

14
$7.69

15
$2.82

18
$2.53

19
$5.31

16
$4.73

17
$6.33

20
$4.54

Table A2. Sequence of Fundamental Value Realizations — Second Sessions
Period:
1
2
3
4
5
6
7
8
9
Sequence
A5
B5

6.56
6.49

4.80
3.81

2.86
5.45

5.55
2.82

Fundamental
3.73
4.71

A10
B10

6.82
2.94

3.34
4.83
4.52 7.29

6.14
5.27

5.23
3.73

2.92
4.49

5.44
6.27

7.16
3.63

4.70
6.37

10

3.72
5.17

Table A3. Fundamental Realization Sequences for Prediction and Fixed Trigger Markets

BASE
A5
B5
A5
B5

Prediction Market
ValueIncreasing
Regulator Conversion
B5
A10
A5
B10
B5
A5

A5
B5

Fixed-Trigger
A10
B10

39

ValueDecreasing
Conversion

A10
B10

Sessions
3
3
3
3

B10
A10

3
3

Appendix B
Performance by Segment in the Regulator Treatments. Incremental Effects of Fixed Trigger and
Prediction Market Treatments.
Value-Increasing Conversions
Value-Decreasing Conversions
(1)
(2)
(3)
(4)
(5)
(6)
(7)
Range
|Pmed – Pfx| Allocative Conversion
|Pmed – Pfx| Allocative Conversion
Efficiency Error Rate
Efficiency Error Rate
Base
*
*
$2.00 - $8.00
21¢
95%
21¢*
95%*
>$7.00
$5.60-$7.00
$5.00-$5.59
$4.40-$4.99
$3.00-$4.39
<$3.00

25¢
15¢*
21¢
151¢*
112¢*
63¢*

>$7.00
$5.60-$7.00
$5.00-$5.59
$4.40-$4.99
$3.00-$4.39
<$3.00

-6¢
10¢
-5¢
11¢
-8¢
-2¢

>$7.00
$5.60-$7.00
$5.00-$5.59
$4.40-$4.99
$3.00-$4.39
<$3.00
N
Wald 2
†

*

-12¢
1¢
21¢
-74¢*
-71¢*
-30¢*
440
--

*

Regulator
1%
12%*
49%*
34%*
15%*
3%†

43¢*
59¢*
94¢*
64¢*
64¢*
61¢*

85%*
79%*
90%*
77%*
74%*
77%*

0%
8%†
45%*
7%†
1%
0%

Fixed Trigger  Regulator
-3%
-1%
-7¢
*
0%
-13%
-20¢
*
*
11%
-42%
-27¢
†
8%
24%
-39¢*
1%
1%
-36¢†
5%
-4%†
-34¢

-2%
9%*
-8%
-2%
-2%
-4%

0%
-8%†
21%
-7%†
-2%
0%

Prediction Market  Regulator
-6%
-2%
-4¢
*
-1%
-14%
-17¢
-8%
-1%
2¢
5%
-27%*
-21¢
8%
-13%*
-41¢*
1%
-5%†
-37¢*
440
270
440
----

1%
10%*
-3%
0%
6%
-6%
440
--

5%
0%
-6%
4%
-2%
0%
270
--

88%
83%*
71%*
63%*
73%*
81%*

Key: * and indicate rejection of the null that the coefficient equals zero, p<.05 and p<.10, respectively (2-tailed
tests).

40