Safety versus Aﬀordability as Targets of Insurance Regulation in an Opaque Market: A Welfare...

7/29/2019 Safety versus Affordability as Targets of Insurance Regulation in an Opaque Market: A Welfare Approach

1/32

ICIR Working Paper Series No. 10/12

Edited by Helmut Grundl and Manfred Wandt

Safety versus Affordability as Targets of Insurance Regulation

in an Opaque Market: A Welfare Approach

Rayna Stoyanovaand Sebastian Schlutter

Abstract

Insurance regulation is typically aimed at policyholder protection. In particular,

regulators attempt to ensure the financial safety of insurance firms, for example,

by means of capital regulation, and to enhance the affordability of insurance, for

example, by means of price ceilings. However, these goals are in conflict. Therefore,

we identify situations in which regulators should be more concerned with safety

or, alternatively, affordability. Our model incorporates default-risk-sensitive in-

surance demand, capital-related frictional costs, and imperfect risk transparency

for policyholders.

Keywords: Insurance Regulation, Regulatory Targets, Welfare, Opaqueness

Corresponding author. Goethe University Frankfurt, Faculty of Economics and Business Admin-

istration, Department of Finance, International Center for Insurance Regulation, House of Finance,Grueneburgplatz 1, 60323 Frankfurt, phone: +49 69 798 33680, fax: +49 69 798 33691, e-mail:

[email protected]


2/32

2

1 Introduction

In attempting to meet their overall objective of protecting policyholder interests,

insurance regulators employ different techniques aimed at two subordinate objectives. First,

insurance regulators expend significant effort to ensure that insurance companies are

sufficiently solvent to meet policyholder claims. In this context, the future regulatory regime

Solvency II in the European Union, for example, contains risk-based capital requirements,

qualitative requirements regarding insurers risk management practices, and transparency and

disclosure standards for insurer risk profiles.1

Second, regulators frequently employ measures

aimed at making insurance more affordable. For example, in some U.S. states, rate regulation

is in force for workers compensation, automobile, and medical malpractice insurance. Even

though the insurance markets in the European Union were deregulated in 1994, there is also

some degree of price regulation in the EU: in Germany, for example, private health insurers

are required to offer a basic tariff (Basistarif) whose premium is limited in accordance with

the maximum rate in the statutory health insurance.

At first sight, these two regulatory objectivessafety and affordabilityappear to

be in conflict, and there is sparse theoretical work on how insurance regulators should act so

as to effectively protect policyholder interests. Empirically, Klein et al. (2002) demonstrate

that stringent price ceilings induce insurers to attain higher leverage ratios and thus reduce

their safety level. This finding is in line with the (not insurance-specific) theoretical argument

that firms use debt as a strategy to influence the regulator to increase the regulated price.2

In

the context of insurance, there is another, simpler explanation for this observation: since the

regulated premium influences the insurers expected profits per insurance contract, it affects

1

A global overview of the introduction of risk-based capital standards is provided by Eling and Holzmller(2008).2 See Taggart (1981), Spiegel and Spulber (1994), and Dasgupta and Nanda (1993).


3/32

3

their incentive for attracting customers with a strong financial position (Schltter, 2011). A

significant price ceiling therefore is accompanied by relatively high insolvency risk. Vice

versa, there are theoretical arguments that stringent solvency regulation might increase

insurance premiums. First, solvency regulation affects the insurers default put option, which

is reflected by insurance premiums.3

Second, to attain a higher safety level, insurers face

additional risk management costs, such as costs of reinsurance or frictional costs of equity

capital (cf. Froot, 2007), that may be passed on to the consumer in higher insurance

premiums.

This article investigates how regulatory requirements designed to meet the objectives of

safety and affordability influence an insurers optimal capital and pricing strategy, and

how these decisions affect policyholder welfare. Based on these results, we investigate in

which situations regulators should focus either more on safety or, alternatively, on

affordability. Throughout our analysis, we employ a model with an inhomogeneous group

of policyholders whose preferences are represented by an insurance demand function,

depending on the insurance premium and the insurers safety level.4

The insurer decides on its

shareholder-value-maximizing equity-premium combination by anticipating the consequences

for insurance demand. Insurer safety level is not necessarily perfectly transparent to

policyholders and the insurers equity endowment may be subject to frictional costs, such as

corporate taxes.

In a benchmark case, we first derive the insurers optimal strategy in the absence of

regulation. We determine the insurers optimal safety level by balancing its incentives

resulting from demand reaction against the default put option and the frictional costs of

equity. Next, we analyze the influence of risk-based capital requirements. Here, the regulator

3

See, e.g., Doherty and Garven (1986), Grndl and Schmeiser (2002), and Gatzert and Schmeiser (2008).4Our model design is similar to the setups of Cummins and Danzon (1997), Zanjani (2002), Froot (2007), Yow

and Sherris (2008), and Schltter (2011).


4/32

4

can specify the insurers safety level, to which the insurer reacts by adjusting the insurance

premium. We find that the regulator cannot enhance welfare by means of solvency regulation

as long as policyholders are perfectly informed about default risk.5 However, when

policyholders cannot perfectly monitor the insurers safety level, capital regulation can

enhance consumer welfare, even though it causes an increase of insurance premiums. Based

on numerical examples, we demonstrate that the effectiveness of capital regulation increases

with the degree of opaqueness, with the level of capital-related frictional costs and with the

severity of underwriting risks. Finally, we study the consequences of regulatory price ceilings.

We demonstrate that the net effect of enhancing the affordability of insurance, on the one

hand, and reducing the insurers optimal safety level, on the other hand, can be either positive

or negative for policyholder welfare. Our numerical examples indicate that price ceilings will

be effective when the market is transparent and when frictional costs are low. Thus, markets

in which price ceilings are effective have characteristics contrary to markets in which capital

regulation is appropriate.

The remainder of the article is organized as follows. Section 2 presents the model

framework and introduces the objective functions. Section 3 derives the insurers optimal

strategy in the benchmark case without regulation. Section 4 studies the effectiveness of

solvency regulation. Section 5 explores the consequences of price ceilings. Section 6

concludes.

5 This result is in line with the model of Rees et al. (1999).


5/32

5

2 Model Design2.1 Actors and Timing

Our one-period model is based on models proposed by Zanjani (2002) and Schltter

(2011). We consider an opaque insurance market with a homogeneous product and three

stakeholder groups: insurance buyers, an insurer, and a regulator.

Insurance Buyers

The insurance buyers are offered an insurance product at a certain price and default risk.

Their buying decisions are a reaction to these characteristics. Cumulative consumer reaction

is modeled by an aggregate demand function, which depicts the representative preferences of

an inhomogeneous group of insurance buyers and sums to the number of customers for whom

purchase of the offered insurance product is advantageous.

We utilize a two-parametric demand function , where denotes the unit price ofthe insurance product and is the default ratio that the insurer communicates to consumers.We define the default ratio as the ratio of the arbitrage-free value of unpaid claims to the

value of nominal liabilities, that is, liabilities without default risk. The default ration is used in

the model as a measure of risk. To keep the model tractable, we apply a specific form of the

demand function:

AB C D E FA, (1)


6/32

6

where D is a scale parameter and andA are the sensitivity factors with respect to price and

default ratio.6

The demand function has the following properties:AB

C E

AA C A E , that is, policyholders react negatively to increases in price anddefault risk. This exponential form of an insurance demand function was recently derived by

Zimmer et al. (2011) from an experiment in which the participants were confronted with

insurance contracts subject to default risk. The experimental results show participants

willingness to pay for a household insurance contract with a certain default risk level. The

demand function is imperfectly elastic with regard to price and default risk, that is, because of

switching and information costs, small changes in price and default ratio do not reduce the

demand to zero.7

Insurer

The second party in the model, the limited liability insurer, maximizes its shareholder

value () and makes decisions as to its risk management strategy and underwriting activityin the presence of regulatory constraints, that is, it decides on its default ratio andinsurance price .

The insurers objective function is the present arbitrage-free market value of the end-of-

period equity capital ! minus the initial equity endowment ",

C ! " (2)

# is the arbitrage-free valuation function. Equity funds are used as a risk management toolto ensure the realized solvency level. Owing to corporate taxation, agency costs, and

6

The sensitivity parameters andA depict only the aggregate preferences of consumers and do not accountfor any opaqueness effects in the market.7 See DArcy and Doherty (1990), Cummins and Danzon (1997), Zanjani(2002), and Yow and Sherris (2008).


7/32

7

acquisition expenses, equity endowment is assumed to imply up-front frictional costs, which

are modeled by a proportional charge $ % .8 Considering the insurers limited liability, thefinal payoffs to shareholders at time 1 are given by the future value of the available assets&!minus the nominal claims '! plus any unpaid losses above the available assets, that is, theshareholders default put option ()*! C +,-./'! &!0 1. To develop asset and liabilityvalues over time, we assume a geometric Brownian motion process. At time 0, the arbitrage-

free value of the final shareholder payoffs is then 2 C &2 '2 3()*!. The insurersinitial assets are denoted by&2 C E 3 4 $ E ". Furthermore, 5 C '2 6 denotes thearbitrage-free initial value of the nominal liabilities per contract, C ()*2 '26 denotes thedefault ratio, and 7 C &2 '26 denotes the initial asset-liability ratio. Using the option pricingformula, the default ratio can be determined as follows:

9

7 8 C 9: 7 E 9: 8

.............8 C ;8= ?@8

.............: C . 3!= 8

(2)

where 9 is the distribution function of the standard normal distribution, 8< and 8> are thevolatilities of the assets and liabilities, respectively, and @ is the correlation between them.Since

7 8is a continuous and strictly decreasing function in

7 8, there is a unique

inverse function 78.

Appling the above relationships, we represent the shareholder value function as follows:

8

This is a common approach in the literature; see Zanjani (2002), Froot (2007), Yow and Sherris (2008), andIbragimov et al. (2010).9 For explanation, see, e.g. Myers and Read (2001), p. 553.


8/32

8

C.......................C . E 5 E 4 $"

.......................C E G 5 E 4 H!H 5 E 78 I

(3)

(4)

Therefore, the insurers decision problem is to find the optimal and legally allowable

combination of default risk level and insurance price that maximizes its shareholdervalue.

Regulator

The regulator uses two instruments to achieve its safety and affordability targets. It

has the option of introducing solvency regulation, in the sense of capital requirements, as a

way of improving the safety of insurance companies. The second tool is price restriction,

which is used to make insurance products more affordable by setting a maximum allowed

price. The regulators objective function is consumer surplus maximization, which is

calculated as the sum of the differences between the reservation price, that is, the maximum

price a consumer would pay for the insurance product, and the offered price over all

policyholders:

J C K L (5)

To study the effectiveness of the two regulatory tools and be able to compare them, we

bring in an effectiveness variable that measures the percentage change of consumer surplus,

defined as the absolute change in consumer surplus divided by the consumer surplus in an

unregulated market,MNOPMNQRQSOP

MNQRQSOP. Additionally, we look at the percentage change of


9/32

9

shareholder value,NTUOPNTUQRQSOP

NTUQRQSOP , to study the regulatory impact on the insurers

shareholder value.

2.2 Modeling OpaquenessMarket opaqueness is formalized by introducing a deviation parameter V, V W 0 4,

which measures the divergence between promised default ratio and realized default ratio. We

distinguish between the default ratio.A , which the insurer promises and communicates tothe consumers, and the default ratio AXYZ, which it realizes after the contract has beensigned. In a perfectly transparent market, the deviation parameter equals zero: V C .Furthermore, if the insurer can deviate from its promise, that is, V [ , it always does so tothe fullest extent possible and realizes the highest possible default ratio because this raises its

shareholder value.10

Therefore, we introduce the following relations between the realized and

promised default risk:

A C AXYZ4 V\ C AXYZ A C AXYZV

(6)

Consumer Surplus in an Opaque Market

As mentioned, consumer surplus measures the cumulative utility for policyholders of

buying the insurance product. However, in the case of an opaque market, different aspects of

the calculation must be considered.

Calculation of consumer surplus in both a transparent and an opaque market is illustrated

in Figure 1. Assume that the insurer realizes the default ratio AXYZ. The dashed line in Figure

10 For a detailed explanation, see Section 3.


10/32

10

1 shows for how many consumers it is advantageous to buy insurance. Given that the insurer

decides on the premium ]AXYZ, the dark shaded area below the dashed curve gives theconsumer surplus in the transparent market. In an opaque market, the promised default ratio

A deviates from the realized one. The solid curve in Figure 1 represents the number ofconsumers who actually purchase insurance observing the default ratio A. Since the actualdefault ratio is higher than A, consumers overestimate the utility they will derive frominsurance, and there are some consumers whose utility is reduced by purchasing insurance.

The black area in Figure 1 measures the loss of consumer surplus resulting from this effect.

Under the premium ]AXYZ, the consumer surplus in an opaque market is the dark greyarea minus the black area. Formally, consumer surplus is calculated as:

JAXYZ V C K AXYZL] ^YAb.cAY.YAXY

] d E A ] K AXYZ]

d ^eZYfb.YAXY

(7)

Here, d is defined by AXYZ d C A ].

Figure 1: Insurance demand function and welfare loss in a nontransparent market


11/32

11

3 Optimal Solutions in an Unregulated MarketAs a benchmark case and comparison basis for the different regulatory approaches, we

consider an unregulated insurance market in which the insurer can decide on its SHV-

maximizing equity-premium combination without regulatory constraints. Here, the insurers

maximization problem is:

ghiA .AXYZ. C

C AXYZ E 4V E G 5 E 4AXYZ H

!H 5 E 7AXYZ 8 I

(8)

In an opaque market, the insurers realized safety level will deviate from the level

promised: the insurer can increase demand by communicating a lower default risk level than it

actually ensures. The actual default risk level corresponds to a lower equity endowment and

therefore incurs fewer frictional costs.

Based on the first-order condition of Equation (8), we can determine the insurers

optimal premium for a given default ratio AXYZ:

]AXYZ C hjkghi AXYZ..

C 5 E 4AXYZ^Arb. free value oflmnopqr.qplsm

3 $ E 5 E 7AXYZ 8 5 E 4AXYZB^ Transfer of frictional cost of equity

3 !tProfitspounv

. (9)

The optimal price is calculated as the sum of the arbitrage-free value of claim payments,

plus frictional costs transferred to policyholders, plus a profit loading. Note that the

transparency level influences the insurers optimal default risk level, but has no direct effect


12/32

12

on the premium: the optimal premium ]AXYZ depends only on the insurers actual defaultrisk level, not on the promised level.

Let AXYZ] C hjkghiA ] . denote the insurers SHV-maximizing(actual) default ratio. Solving the insurers maximization problem (Equation (8)), the first-

order condition for the optimal choice of AXYZ] ], given that the price is optimallyadjusted, implies that

!w

E

!

!x C y

xz

!x E

{AO|}

{A. (10)

The left-hand side of Equation (10) represents the marginal change of insurers benefits due to

demand reaction when the default ratio is marginally changed. The right hand side measures

the marginal change of default put option and frictional costs of equity. Rewriting Equation

(10) enables us to present the insurers SHV-maximizing asset-liability ratio 7] using aclosed-form solution:

11

7] C ~ H 4 V !HH . (11)

with i C i E ! ! = and ! denoting the quantile function of the standard

normal distribution. One can easily verify that i is a strictly increasing function in x.Therefore, the insurer will optimally avoid default risk by holding a high capital level if, c.p.,

demand reacts strongly to default risk, weakly to price, frictional costs are low and the

insurance market is rather transparent than opaque.

11 The derivation is analogous to Schltter (2011), Proposition 2.


13/32

13

We then have the following equations for the maximal shareholder value and resulting

consumer surplus in the unregulated market:

AXYZ] E 4V ] C AO|}] E!w]B!H . (12)

JAXYZ] E 4V ] C AO|}] E!w]B!AO|}] wB

. (13)

These equations illustrate that shareholders benefit from a greater degree of opaqueness,

whereas consumers suffer: in Equation (13), 4 AAXYZV represents the consumersurplus loss resulting from market opacity. In the numerical examples, we measure the

consequences of opaqueness for safety level, insurance premium, shareholder value, and

consumer surplus in an unregulated market.

Numerical Example

Throughout our analysis, we illustrate our results with a realistically calibrated

numerical example. We set the following risk parameters: 5 C ?, 8< C , 8> C ?,

and @ C ,12.g. 8 C = 3?= #??#. We further assume a frictionalcost ratio of. $ C .13 For. simplicity, we set. C #. The demand-function-related

parameters are as follows:

14

12 These numerical assumptions are consistent with the market-based calibrated model of Yow and Sherris

(2008).13Zanjani (2002) reports that the frictional costs for the reinsurance industry can be approximated with 5%.

14 These parameters are consistent with the regression results estimated by Zimmer et. al (2011).


14/32

14

Demand-function-related parameters

0.015 14

10 000

Table 1: Demand-function-related parameters

In our benchmark scenario, the numerical input variables result in the following optimal

combination of price and default risk, shareholder value, and consumer surplus for the three

transparency levels /0#0#1:

Opaqueness level A

C B

C #C

C #]] 271.81 269.99 268.95]

0.1606%

0.1606%

0.2632%

0.1842%

0.7036%

0.2814%

]] 6 485.90 4 583.44 623.557 165.79 167.21 170.15 11 634.11 11 734.05 11 940.16 11 052.41 11 024.11 10 672.67

Table 2: Numerical results in an unregulated market for three transparency levels

Table 2 compares the perfectly transparent case V C with two levels of opaqueness,V C # and V C #. Interestingly, both the promised and the actual default risk level clearlyincrease with level of opaqueness. Therefore, according to Equation (9), the premium

decreases with opaqueness level. Regarding insurance demand reaction, the premium

reduction overcompensates the higher (promised) default risk in the opaque market and,

therefore, more insurance contracts are sold. While this increases shareholder value, the

higher actual default risk level reduces consumer surplus. The resulting combinations of

consumer surplus and shareholder value are illustrated in Figure 2.


15/32

15

Figure 2: CS and SHV for insurers optimal combination of default risk and price under no regulation for three

transparency levels

4 Effectiveness of Capital RegulationWe next analyze the situation in which the regulator restricts the insurers risk level by

means of risk-based capital requirements, but prices remain unregulated. This situation is

more or less the actual regulatory environment in the European Union ever since insurance

markets were deregulated in 1994.15

In our model, the regulator implements risk-based capital requirements by restricting the

insurers (actual) default ratio at a level AXc, forcing the insurer to hold a sufficient level ofcapital. The restriction is binding when the regulatory default ratio

AXc falls below the

shareholder-value-maximizing level AXYZ] . For the opaque market, we assume that theinsurer can still communicate a better default risk level than AXc.

Facing capital requirements, the insurer adjusts the premium so as to maximize

shareholder value (see Equation (9)):

15

According the Swiss Solvency Test, a confidence level of 99% for the calculation of the risk measure tail-VaRwas stipulated. Solvency II regulations are even more stringent and define a confidence level of 99.5% for the

calculation of the used risk measure VaR.


16/32

16

]AXc C hjkghi AXc.

.C 5 E 4AXc^Arb. free value of

lmnopqr.qplsm

3 $ E 5 E 7AXc 8 5 E 4AXcB^Transfer of frictional cost of equity

3 !tProfitspounv

(14)

Equation (14) demonstrates that the optimal insurance premium is negatively related to

the regulatory default ratio AXc. First, a lower value of AXc means that the insurersdefault put option decreases and thus the first premium component increases. Second, the

insurer needs to hold additional equity capital to achieve a lower default ratio and the related

frictional costs are transferred to policyholders with the second premium component. Thus,

stricter capital requirements will lead to a higher premium. When deciding on the welfare-

optimal policy of capital requirements, the regulator needs to balance their positive influence

on the safety level against their negative influence on affordability. Formally, the consumer

surplus in dependence ofAXc and V is given by:

JAXYZAXc VB CAO|}OP E!w]AO|}OP B!AO|}OP wB

(15)

Taking the first-order derivative of JAXYZAXc VB with respect to AXYZAXc enables us todetermine how strict the capital requirements should be. We have

.A JV C

] 4 AAXYZV4 $ E!w!H 3 5

H!H E

#A

V C (16)

Analogous to Equation (10), we can rewrite Equation 16 as


17/32

17

E 4 V

w!Aw E

!!x C y

xz!x E

{AO|}{A , (17)

and analogous to Equation (11) we arrive at

7AXc] C ~ H 4 V !HH 3

wH!Aw, (18)

Even though Equation (18) is not generally a closed-form representation of 7AXc] (since the

right-hand side depends on ), it can be interpreted by comparing it with Equation (11). IfV C , both equations coincide. In a perfectly transparent market, therefore, the insurer will,based on its own incentives, decide on the consumer-surplus-maximizing safety level.

Consequently, capital regulation is unnecessary in this case. However, if V [ , theconsumer-surplus-maximizing safety level is higher than the SHV-maximizing one, and the

regulator should impose binding capital requirements to enhance policyholders welfare.

Numerical Example and Graphical Representation

We now apply the numerical example from Section 3 to the situation with capital

requirements. Table 3 contains the consumer-surplus-maximizing regulatory default ratios,

the insurers optimal response, and the corresponding welfare levels. The first column of

Table 3 (V C ) illustrates, as discussed above, that the regulator cannot improve policyholderwelfare by capital regulation when the market is perfectly transparent: the consumer-surplus-

maximizing default ratio is equal to the insurers optimal strategy in the absence of regulation

(see Table 1). In the second (V C #) and third columns (V C #), the regulator restricts thedefault ratio below the shareholder-value-maximizing default ratio of 0.1606%. Since the

premium is only affected by the realized default ratio (see Equation (14)), the insurance


18/32

18

premium is optimally adjusted for all three transparency levels. However, the insurer exploits

the opaqueness to promise higher safety levels and therefore insurance demand increases at

higher levels of opaqueness. Compared to our benchmark case with no regulation, optimal

capital requirements are stricter when there is opaqueness and, hence, such requirements can

increase consumer surplus by 0.25% for V C # and by 3.54% for V C #.

Opaqueness level A

C B

C #C

C #]

0.1606%

0.1606%

0.1602%

0.1121%

0.1589%

0.0635%

]]B 271.81 271.814 271.826 165.79 166.91 168.01 11 634.11 11 712.65 11 790.47\ 0.00% -0.19% -1.2% 11 052.41 11 052.15 11 051.40\ 0.00% +0.25% +3.54%

Table 3: Numerical results under capital regulation for three transparency levels

Figure 3 is a graphic illustration of how capital regulation impacts shareholder value and

consumer surplus. Starting at Point A, the straight line illustrates that a binding regulatory

ceiling on the default ratio decreases shareholder value as well as consumer surplus. For an

opaque market with V C #, the thick curve starting at Point B demonstrates that moderatecapital regulation can improve consumer surplus up to Point B, which refers to optimal

capital regulation (see Table 3). The dashed curve starting at Point C shows that capital

regulation in a heavily opaque market V C # has a bigger influence on shareholder andpolicyholder welfare and that the optimal regulatory policy (Point C) greatly enhances

consumer surplus.


19/32

19

Figure 3: Combination of shareholder value and consumer surplus under capital regulation for three transparency

levels: fine line C , thick curve C # , dashed curve C #

5 Effectiveness of Price RegulationNext, we investigate the consequences of regulatory price ceilings imposed with the

intent of meeting the regulators affordability target. The price ceiling will be binding when it

lies below the insurers unregulated premium (see Equation (9)). When only prices are subject

to regulation, and there are no capital requirements, the insurer can react to the mandatory

prices by adjusting its safety level.

Therefore, any regulatory price induces a specific insurers optimal default ratio

AXYZ]

AXc

. The insurers maximization problem can be formalized as:

AXYZ] AXc C hjkghiA AXYZ V AXc, (19)

where AXc denotes the regulated premium. The optimality condition for the choice of adefault ratio level, that is, the first-order derivative of the shareholder value with respect to

default ratio when the price is externally determined implies:


20/32

20

NTUAO|}OP C

AO|}wOPAO|}

AXc 54AXYZ H!H 57#AXc 3 5

...........................5 H!H

#

AO|}C

(20)

The first term is negative and measures demand effects for marginal changes in the default

ratio. The second term is positive and represents the value of the limited liability change. The

third term reflects marginal changes in the frictional costs of equity when the default ratio

varies. The level of opaqueness V has an influence on all three terms because it manipulatesthe demand itself (.

By using price regulation to improve insurance affordability, the regulator aims at

creating maximum consumer surplus. Equation (21) gives the regulators maximization

problem

AXc C hjkghiOP JAXc AXYZ] AXcB.

..........C hjkghiOP K AXYZ]LOP AXc d E A AXc(21)

To study the effect of price restrictions on consumer surplus and to determine the

optimal price ceiling we look at the first-order derivative of the consumer surplus with respect

to price,MN

OP. In the optimum, we obtain

]

AXc 4V4 VB

4V C (22)


21/32

21

The left-hand side of the equation measures the negative effect to which policyholders

are exposed because of the lower safety level resulting from the lower prices. The right-hand

side represents policyholders additional gain through price decrease. Therefore, as soon as

the welfare gain of lower prices outweighs the loss due to the decreased safety level, the

change in consumer surplus is positive and the regulatory intervention leads to an

improvement in policyholder welfare. Maximum consumer surplus is attained when the

equation holds. Further price reduction results in higher losses due to worse default risk.

Numerical Example and Graphical Representation

Once again, we illustrate our analytical findings using the numerical example introduced

in Section 3. The regulator decides on the consumer-surplus-maximizing price ceiling, AXc].The insurer adjusts its realized default risk, AXYZ] AXc] under the objective shareholder-value-maximization. The resulting shareholder value and consumer surplus are set out in

Table 4. The effectiveness of price regulation is measured by the percentage change in

consumer surplus.

When the regulator introduces a price ceiling, we observe an improvement in consumer

surplus in all three cases. For V C , the regulator should optimally reduce the premium from271.81 in the benchmark case (see Table 2) to 222.35 (Table 4). The insurer subsequently

increases the default ratio from 0.16% to 1.18%, meaning that the DPO per contract increases

by 200*(1.18%-0.16%)=2.04. From the policyholder perspective, the premium reduction of

49.46 overcompensates for the DPO increase of 2.04, and therefore the consumer surplus

clearly increases by more than 80%.

In an opaque market (V C #), the insurer adjusts its default ratio to the price ceilingmore strongly, because policyholders have a weaker influence on the insurance safety level.


22/32

22

The regulator should therefore restrict the premium relatively moderately by 269.99-

229.63=40.36. Nevertheless, the DPO increases even more strongly compared to the first case

by 200*(1.37%-0.26%)=2.22. From the policyholder perspective, price restriction still

dominates the unregulated situation, however the effectiveness of price regulation is lower in

opaque markets: for the highly opaque case V C #, the consumer surplus change is only18%.

Opaqueness level A

C B

C #C

C #

] 222.35 229.63 247.60] ]

1.1847%

1.1847%

1.3733%

0.9611%

1.7241%

0.6896%

301.61 279.12 221.73 6906.94 8655.42 11282.85\ -40.6% -26.24% -5.50% 20107.60 17529.27 12641.00\

+81.93% +59.01% +18.44%

Table 4: Numerical results under price regulation for three transparency levels

The resulting combinations of regulatory price and corresponding shareholder-value-

optimal default ratio lead to specific combinations of shareholder value and consumer surplus,

represented by the bent curves in Figure 4. Every curve represents a different transparency

level. The dashed curve is for when

V C #, the thick curve for when

V C #and the fine

curve represents a fully transparent market. Points A, B and C represent the consumer

surplus optimal positions.


23/32

23

Figure 4: Combination of shareholder value and consumer surplus under price regulation for three transparency

levels: fine line C , thick curve C # , dashed curve C #

6 Comparison of capital and price regulationThe previous analysis has shown that capital and price regulation could be beneficial for

policyholders. In this section, we compare the effectiveness of the two regulatory tools and

explore what kind of regulation is most appropriate to improve consumer surplus under

different circumstances.

Impact of frictional costs

In the following subsection, we analyze the effectiveness of capital and price regulation

depending on the level of frictional costs. As before, we consider three levels of opaqueness

V C /0 #0 #1 and plot the maximum achievable percentage change of consumer surpluswhen the regulator chooses the consumer-surplus-maximizing AXYZAXc] and AXc] respectively.

Figure 5 illustrates the case of perfect transparency. The solid line depicts the potential

consumer surplus increase with price regulation and the dashed line the effectiveness of

capital regulation. In the transparent market, policyholders force the insurer to choose a


24/32

24

default risk level that also maximizes consumer surplus. Therefore, irrespective of the level of

frictional costs, capital regulation cannot raise consumer surplus and the dashed curve

remains at 0%. Price regulation, in turn, can significantly enhance consumer surplus, but its

effectiveness decreases with the level of frictional costs. The reason for the decreasing

effectiveness of price regulation is that the insurer will respond with a more drastic reduction

of its safety level when equity capital is subject to high frictional costs.

Figure 5: Effectiveness of price and capital regulation in a perfectly transparent market when the carrying charge of

holding capital changes

In a slightly opaque market V C #, our analysis provides similar results (see Figure 6).Here, the consumer-surplus-maximizing default risk level differs only very slightly from the

shareholder-value-maximizing level, and therefore capital requirements have little influence

on the consumer surplus. Again, price regulation may increase consumer surplus and the

effectiveness of price regulation decreases with the level of frictional costs.

Effectivenessofregu

latory

instruments

Carrying charge of holding equity,

Opaqueness =0

Capital reg.

Price reg.


25/32

25

Figure 6: Effectiveness of price and capital regulation with opaqueness level of 0.3 when the carrying charge of


The case of the high level of opaqueness is illustrated in Figure 7. Here, capital

requirements can clearly raise consumer surplus, particularly when frictional costs are high.

Furthermore, the effectiveness of price regulation is lower and more affected by frictional

costs than in the previous scenarios. If the carrying charge is above 11%, capital regulation is

more effective than price regulation. Therefore, regulators should optimally focus on the

safety goal if insurance markets are rather opaque and frictional costs are extreme. Empirical

studies suggest that the opaqueness problem is severe in insurance markets therefore

providing support for this scenario.16

16

Morgan (2002) and Pottier and Sommer (2006) empirically estimate opaqueness for different industries. Usingthe rating disagreement as a proxy for opaqueness, the studies find that insurance and banking are most severely

affected by the opaqueness problem.

Effectiveness

ofregulatory

instrum

ents


Opaqueness =0.3

Capital reg.

Price reg.


26/32

26

Figure 7: Effectiveness of price and capital regulation with opaqueness level of 0.6 when the carrying charge of


Impact of volatility of liabilities

Next, we examine the effectiveness of capital and price regulation for insurance

portfolios of varying volatility. Again, we look at the three levels of opaqueness, V W

/0#0#1. The results are plotted in Figures 8 to 10.

As before, capital regulation cannot improve policyholder welfare in a fully transparent

market (see Figure 8), which is the case regardless of the portfolio volatility. Price ceilings

strongly increase consumer surplus when the insurance risks are low, and they have a smaller

effect when the insurance portfolio is highly volatile. The reason behind this finding is that

the insurer needs to hold much more equity capital for the high-risk portfolio and the price

ceiling clearly reduces the incentive to hold a large amount of equity. Therefore, the insurer

with high insurance risks responds to a price ceiling with a severe reduction of its safety level,

leading to a smaller increase of the consumer surplus as compared to the low-risk insurer.

A

Effectivenessofregulatory

instrum

ents


Opaqueness =0.6

Capital reg.

Price reg.


27/32

27

Figure 8: Effectiveness of price and capital regulation in a transparent market when the volatility of liabilities changes

Figure 9 illustrates the regulatory effectiveness for different volatility levels in a slightly

opaque market, where we have similar results as for V C . Interestingly, capital regulationstill cannot enhance consumers welfare for all meaningful values of the riskiness of

insurance claims, since the insurers SHV-maximizing safety level is almost identical to the

consumer-surplus-maximizing one.

Figure 9: Effectiveness of price and capital regulation with opaqueness level of 0.3 when the volatility of liabilities

changes

A

B

B

Effectivenesso

fregulatory

instrum

ents

Volatility of liabilities, L

Opaqueness =0

CDEFD

F

A

B

B Effective

nessofregulatory

in

struments


Opaqueness =0.3

CDEFD

F


28/32

28

Figure 10 depicts the considered effects for the highest opaqueness level, V C #. Now,the dashed line has a clearly positive slope, meaning that capital regulation is effective,

especially when insurers have a high-risk portfolio. The solid line has a clearly negative slope,

and the effectiveness of price ceilings thus decreases with the volatility of insurance risks.

When the volatility of the liabilities exceeds 35%, capital regulation becomes more effective

than price regulation.

Figure 10: Effectiveness of price and capital regulation with opaqueness level of 0.6 when the volatility of liabilities

changes

7 ConclusionThis article investigates how regulatory capital requirements and price ceilings influence

an insurers capital level and pricing decisions and what consequences arise for policyholders

welfare. To this end, we employ a model in which insurance demand is sensitive to default

risk and price, policyholders view of the insurers safety level may be opaque and the insurer

faces frictional costs of holding equity capital. The insurers objective is the shareholder

value, which we measure using the present value of shareholders future cash flows minus

their initial equity endowment. Policyholders welfare is measured using the consumer

A

A

A

B

Effectivenessofregulatory

instruments


Opaqueness =0.6

CDEFD

F


29/32

29

surplus, i.e. the integral over the differences between their willingness-to-pay and the actual

insurance premium.

To evaluate the consequences of regulatory intervention, we consider the insurers

strategy in a world with no regulation as a benchmark case. Here, the insurer balances its

incentives for safety (resulting from insurance demand reaction) against the frictional costs of

holding equity capital. The insurer also exploits the policyholders opaqueness problem and

promises a higher safety level than that which it actually ensures. According to the safety

level decision, the insurer also determines the SHV-maximizing insurance premium.

By means of risk-based capital requirements, the regulator can force the insurer to attain

a higher safety level. The insurer will react to this type of regulation by adjusting its premium.

We show that capital requirements cannot enhance policyholders welfare when the insurance

market is transparent, since the insurer finds it optimal to attain the exact safety level that

maximizes consumer surplus. If the regulator requires a higher safety level, premiums become

too high such that policyholders are worse off. In contrast, capital requirements can improve

policyholders welfare in the more realistic case of there being an opaqueness problem.17

Our

numerical examples indicate that capital requirements are especially effective when the

market is highly opaque, when equity capital comes at significant frictional costs, and when

insurers face significant underwriting risks. In these cases, the regulator should concentrate on

the safety goal.

If the regulator imposes a binding price ceiling, the insurer has weaker incentives to

attract consumers with a high safety level, and it will reduce its equity position. Nevertheless,

we point out that price ceilings can be beneficial for policyholders, especially when insurance

buyers reaction drives default risk down and frictional costs of equity capital are rather low.

17 Cf. Morgan (2002) and Pottier and Sommer (2006).


30/32

30

Altogether, our findings suggest that regulators should take both targets, safety and

affordability, into account under the overall objective of policyholder protection. While our

findings on price ceilings do not overrule typical concerns about anti-trust measures, they do

shed light on the insurance-specific interaction between price regulation and safety. Our

sensitivity analyses indicate in which situations insurance regulators should focus their efforts

on solvency regulation in particular, or monitor profit loadings on premiums and create the

basis for antitrust regulation.


31/32

31

References

Cummins, J.D. and Danzon, P.M. (1997) 'Price, Financial Quality, and Capital Flows in

Insurance Markets',Journal of Financial Intermediation,6: 338.

DArcy, S.P. and Doherty, N.A. (1990) 'Adverse Selection, Private Information, and

Lowballing in Insurance Markets',Journal of Business, 63: 145164.

Dasgupta, S. and Nanda, V. (1993). 'Bargaining and Brinkmanship: Capital Structure Choice

by Regulated Firms',International Journal of Industrial Organization, 11: 475497.

Doherty, N. and Garven, J. (1986) 'Price Regulation in Property-Liability Insurance: A

Contingent Claims Approach',Journal of Finance, 41: 10311050.

Eling, M. and Holzmller I. (2008) 'An Overview and Comparison of Risk-Based CapitalStandards',Journal of Insurance Regulation, 26(4): 3160.

Froot, K.A. (2007). 'Risk Management, Capital Budgeting, and Capital Structure Policy for

Insurers and Reinsurers',Journal of Risk and Insurance, 74: 273299.

Gatzert, N. and Schmeiser, H. (2008) 'Combining Fair Pricing and Capital Requirements for

Non-Life Insurance Companies',Journal of Banking Finance, 32: 25892596.

Grndl, H. and Schmeiser, H. (2002) 'Pricing Double-Trigger Reinsurance Contracts:

Financial Versus Actuarial Approach',Journal of Risk and Insurance, 69: 449-468.

Ibragimov, R., Jaffee, D. and Walden, J. (2010) 'Pricing and Capital Allocation for Multiline

Insurance Firms', Journal of Risk and Insurance, 77: 551578.

Klein, R.W., Phillips, R.D. and Shiu, W. (2002) 'The Capital Structure of Firms Subject to

Price Regulation: Evidence from the Insurance Industry', Journal of Financial Services

Research, 21(1/2): 79100.

Morgan, D.P. (2002) 'Rating Banks: Risk and Uncertainty in an Opaque Industry', American

Economic Review, 92: 874888.

Myers, S.C. and Read, J.A. (2001) 'Capital Allocation for Insurance Companies'. Journal of

Risk and Insurance, 68: 545-580.

Pottier, S.W. and Sommer, D.W. (2006) 'Opaqueness in the Insurance Industry: Why Are

Some Insurers Harder to Evaluate than Others?' Risk Management and Insurance Review,

9(2): 149163.

Rees, R., Gravelle, H. and Wambach, A. (1999) 'Regulation of Insurance Markets', Geneva

Papers on Risk and Insurance Theory, 24: 5568.


32/32

Schltter, S. (2011). Capital Requirements or Pricing Constraints?An Economic Analysis

of Measures for Insurance Regulation, working Paper, ICIR Working Paper Series No.

03/2011, Goethe-Universitt Frankfurt, Frankfurt, Germany.

Spiegel, Y. and Spulber, D.F. (1994) 'The Capital Structure of a Regulated Firm', RAND

Journal of Economics, 25: 424440.

Taggart, R.A. Jr. (1981) 'Rate of Return Regulation and Utility Capital Structure Decisions',

Journal of Finance, 36: 383393.

Yow, S. and Sherris, M. (2008) 'Enterprise Risk Management, Insurer Value Maximisation,

and Market Frictions',Astin Bulletin, 38: 293339.

Zanjani, G. (2002) 'Pricing and Capital Allocation in Catastrophe Insurance', Journal of

Financial Economics, 65: 283305.

Zimmer, A., Grndl, H. and Schade, C. (2011) Price-Default Risk-Demand-Curves and the

Optimal Corporate Risk Strategy of Insurers: A Behavioral Approach, working Paper, ICIR

Working Paper Series No. 06/2011, Goethe-Universitt Frankfurt, Frankfurt, Germany.

Safety versus Aﬀordability as Targets of Insurance Regulation in an Opaque Market: A Welfare...

Documents

Transcript of Safety versus Aﬀordability as Targets of Insurance Regulation in an Opaque Market: A Welfare...