Why Can Financial Firms Charge for Diversifiable Risk?
Andrew Smith, Ian Moran and David Walczak
DRAFT Discussion Paper
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Abstract:
It is widely accepted that capital markets do not demand a premium for risk that investors can diversify. On the other hand, insurers’ and banks’ pricing models frequently include an allowance for total risk, diversifiable or not. Why then do competitive product markets not eliminate these pricing margins? We propose an answer to the puzzle, by analysing the frictional costs that financial institutions incur in the course of their risk-bearing function. A series of worked examples demonstrate the implications for pricing, risk management, and financial reporting.
Author Contact Details:
Andrew Smith / B&W Deloitte,Horizon House
28 Upper High Street
Epsom, Surrey
KT18 7LJ
Great Britain. / tel +44 1372 824811
e:
Ian Moran / tel +44 1372 824143
e:
David Walczak /
Deloitte & Touche
400 One Financial Plaza
Minneapolis
MN 55402
USA / tel +1 612 397 4509 ,e:
Introduction
Pricing and accounting have sometimes been uneasy stable-mates in the financial services industry. Firms have been prepared to make an initial accounting loss on a customer, in order to recoup profits later, for example in the sale of life business under UK statutory reporting. In fewer cases, the opposite situation applies and accounting standards permit the recognition of immediate profit when a customer relationship commences, for example when reporting under embedded value techniques.
Fair value accounting will bring financial statements closer than ever before to the assumptions used for product prices. The final form of an insurance accounting standard is some way off, and retail banking is even further from fair value reporting. However, no accounting standard, however well constructed, could comprise a full blueprint for economic pricing. There are good economic reasons for differences between pricing and financial reporting practice. These differences do not imply that one of the components is unsound.
This paper investigates these differences. We focus on the apparent anomaly that diversifiable risk carries a much higher price in retail financial services than in capital markets. We argue that capital market and retail risk pricing are best reconciled using the concept of frictional costs. These are contingent internal costs, which a financial firm faces in managing the risks it retains. Even if capital markets require no premium for diversifiable risk, frictional costs can create the illusion of a non-systematic risk premium for insurance risks.
There are two sets of arguments: demand and supply side. The demand side explains why policyholders may be prepared to pay a premium for diversifiable risk. More subtle arguments are required from the supply side, to explain why competition between insurers does not erode the diversifiable risk margins.
Demand Side Arguments
The first question we must resolve is why policyholders might be prepared to pay for “overpriced” insurance that incorporates margins for risks.
Many financial decision makers do not use a pure expected value approach to the choices they are faced with, such as how much to pay for insurance or whether to purchase one investment vs. another. Instead, individuals seek to balance risk with the possible rewards. For example, utility functions have been proposed for explaining these effects.
The result may very well produce a decision which is not optimal from an expected value or fair value standpoint but allows us to quantify risk averse decision making properly. Investment decisions can be viewed as a utility maximisation problem; investors do not necessarily choose the highest possible mean return but will instead seek to balance risk and return.
The same principle applies to the purchase of insurance. Agents can look at their risk exposures holistically, aggregating traded investment risks and also the specific insurable risks relative to their circumstances. They may well decide to purchase insurance, if
· Doing so materially reduces their total risks
· The cost is acceptable relative to other means of reducing risk such as investing more defensively
· The agent is sufficiently risk averse
Quantifying these effects is helpful because it can indicate an upper bound on how much a policyholder might be prepared to pay for insurance in a monopolistic situation. How much they actually pay, depends on the operation of competition between insurers. As we shall see, this is a much more subtle point to quantify.
Insurance companies themselves also display risk-averse behaviour with regard to using the reinsurance market to mitigate risk. Like insurance policyholders, the company seeking reinsurance is often willing to pay more than the expected value of the reinsurance premium. Views differ as to the best model for explaining this. We could seek to explain corporate behaviour using one of the following:
· An aggregate utility function representing the desires of corporate management
· A shareholder value measure seeking to value risk via its impact on the business
Taking the utility approach, Borch (1969) described the ‘most efficient’ reinsurance contract as that which minimises the insurance company’s variance of net claim distribution for a given reinsurance premium. Risk based decision making has the following consequences:
· A willingness to pay ‘overpriced’ reinsurance premiums
· Setting a ‘retention limit’ (amount of risk a company is willing to hold on a single life)
Underwriters, compensated by net results, may well purchase reinsurance to protect the risk in their own compensation. Insurance companies may take advantage of hedging programs for the same reasons or because regulatory pronouncements often allow companies to take credit for hedging programs on the balance sheet.
There are problems with treating a corporation as driven by the utility of managers, however. The chief difficulty is allowing for the impact of other competing insurers, and of shareholders. It is hard to see why shareholders would appoint managers who subsequently adopt self-interested strategies in defiance of those they are supposed to serve. Why would shareholders pay a manager to reduce risk if the shareholder can achieve the same effect more easily by diversification?
And this brings us to the real puzzle. If shareholders can diversify, then they should not be worried about diversifiable risk inside the companies they buy. This should flow through to product pricing. If insurers generally charged customers for bearing diversifiable risk, we should expect to see new capital entering the market, until the price of diversifiable risk became consistent with returns required by a diversified investor. The remainder of this paper considers these supply side arguments, and how they may be refined to admit the appearance of a positive price for diversifiable risk.
Supply Side Arguments
Our supply-side argument is based on five steps as follows:
Step 1: A frictionless (Modigliani-Miller) insurance market
Step 2: The Myers – Cohn model and frictional costs of investing
Step 3: Accounting equity and franchise value
Step 4: Costs of financial impairment
Step 5: Capital optimisation
Part A of the paper describes these steps in further detail, while part B gives a mathematical formulation in the context of a simplified insurance model. Part C offers some tentative conclusions.
Part A: Verbal Reasoning
Step A1: A frictionless (Modigliani-Miller) insurance market
Even in today’s market conditions most economists accept that the mean required return on stocks exceeds that on bonds. Before 1958, practitioners usually concluded that firms could save money by being financed by debt (ie bond issuance) as far as possible, as the return requirements of bondholders are less demanding than those of shareholders.
Modigliani and Miller (1958, henceforth M&M) considered the implications of a frictionless market on a firm’s capital structure. Their frictionless market assumptions were as follows:
· No transaction costs in capital markets
· Individuals can borrow or lend at the risk free rate
· There are no costs to financial impairment
· Firms issue two kinds of claims: risk-free debt and (risky) equity
· No taxes
· Corporate insiders and outsiders have the same information
· Managers always maximise shareholders’ wealth
They argued that, as a company increased its degree of debt finance, so the residual shareholders were exposed to greater risk as a result of the leverage. The shareholders’ required return is not some historic average stock return, but instead should be sensitive to the risks in the business reflecting current capital structure. This means the required return on equity increases as the leverage increases. Therefore, there is no automatic reduction in required profits for a firm who shifts financing towards bonds.
A key step in the M&M arguments is the notion of shareholders who can also borrow or invest in bonds, on the same terms as the firm itself. The shareholder who wants a risky investment is indifferent between (i) borrowing money to invest in an unlevered stock or (ii) investing his own cash in a company who is partially financed by debt.
There is a parallel set of arguments in the insurance industry. Here the focus has not been primarily on capital structure, but on investment strategy and capital allocation. The M&M arguments also apply in this context. The implications are:
· Investment strategy is irrelevant to value. An insurer who invests his own assets in (other firms’) stocks rather than in bonds, will probably increase risks and returns. The risk premium earned on those stocks in the hands of the insurer is the same as the risk premium in the hands of the insurer’s shareholder. Therefore, there is no overall gain to shareholders when an insurer adopts a risky investment strategy. An insurer can by investing do only what shareholders can do themselves.
· Capital allocation is irrelevant to value. An insurer who allocates more capital to a particular line of business makes that business proportionately less risky. Therefore the percentage return required by shareholders is lower, but this now applies to a larger base. The dollar required profit is slightly higher overall, but we also expect a higher profit because of the return on the extra assets. The two effects cancel out and we are back where we started. Therefore, allocating more capital does not imply a need for a higher policyholder premium.
The remainder of this paper seeks to temper these unintuitive findings with increasing doses of business realism.
Step A2: The Myers – Cohn model and frictional costs of investing
To make the M&M propositions more realistic, we allow for corporate taxation. This is covered in Modigliani and Miller (1963). The corresponding insurance reference is Myers and Cohn (1987).
Myers’ and Cohn’s insight came from an exploration of the different terms under which corporations can invest, relative to direct investments by shareholders. In many cases, the corporate investment is subject to double taxation, as income from investments is a source of taxable profit. As a consequence, in order for shareholders to earn an acceptable return, any insurance premiums must be sufficient not only to pay claims and expenses but also to pay tax bills arising from investment returns.
Therefore, contrary to the pure M&M findings, capital does have a cost, and capital efficiency can create value. Recent advancements in North American capital allocation regulation for insurers allows an entity to hold less capital if a reporting unit uses properly matched assets and liabilities from an interest rate risk standpoint. According to the Myers-Cohn model, this is an instance of higher value of an insurance entity resulting from efficient capital allocation
Under the Myers-Cohn model, pricing of insurance by line of business requires an allocation of investments between classes of business. This requires an allocation not only of liability reserves (usually a simple bookkeeping exercise) but also of the assets constituting shareholder equity. And here we have a bigger puzzle, because the net assets are a single legal pool – any part of the equity can be used to meet deficiencies in any line of business. Paper allocation does not imply any sort of ring-fencing of assets to meet claims in specific lines of business.
The need to allocate equity between lines has spawned a whole industry in capital allocation (also called “economic capital”) for performance measurement. Here we encounter an immediate practical difficulty with the Myers-Cohn framework. The theoretically optimal amount of equity is zero, as this minimises tax. As in practice firms do hold equity, the amount held must be exogenous to the Myers-Cohn model. There is scope for endless argument about how equity should be allocated, with no definitive answer.
Later research has suggested that double taxation is only the tip of the iceberg as regards the cost of holding investments. Usually far greater in magnitude is the risk of poor stewardship of those assets in the hands of corporate managers. For example, managers may be tempted to squander shareholder resources on ambitious acquisitions, which destroy value but enhance the status of the management team concerned. Such effects are called agency costs (see Jensen & Meckling, 1976), arising from conflicts of interest between shareholders and managers. This is a special case of what are more generally called frictional costs. From a shareholder perspective, agency costs act as a form of tax on assets entrusted to third party managers. To justify the existence of an insurance firm, the premiums achievable must not only offset claims, expenses and taxes but also a share of the agency costs associated with the equity in the business.
It may appear circular to expect managers to quantify their own conspiracy against shareholders when setting premiums. We argue that markets allow for such costs when pricing insurance shares; therefore it is natural to use this information also in pricing decisions.
Step A3: Accounting Equity and Franchise Value
Commercial pricing bases usually include an item described as “margin for profit”. This may arise from failure of competition, for example by the operation of cartels or unwarranted entry barriers. The existence of profit margins does not however always point to a market failure. Instead, an insurers’ ability to charge premium margins could be a fair reward on investment in a brand, distribution capability, good customer relationship management or excellent service. The margin for profit is not the same as a loading for risk. The application of economic risk loads to premiums would still not create value for shareholders, as the shareholders also bear the risk taken on. Instead, we are here considering margins for economic profit over and above the cost to shareholders of any risks borne.