BANKRUPTCY, BANK AS BARRIER OPTIONS, BID-ASK SPREAD, BLACK-SCHOLES


Bankruptcy

A central tenet in economics is that competition drives markets toward a state of long-run equilibrium in which inefficient firms are eliminated and those remaining in existence produce at a minimum average cost. Consumers benefit from this state of affairs because goods and services are produced and sold at the lowest possible prices. A legal mechanism through which most firms exit the market is generally known as insolvency and/or bankruptcy.

Bankruptcy occurs when the assets of a firm are insufficient to meet the fixed obligations to debt holders and it can be defined in an accounting or legal framework. The legal approach relates outstanding financial obligations to “the fair market value” of the firm’s assets while an accounting bankruptcy would simply be a negative net worth in a conventional balance sheet (Weston and Copeland, 1992). Under bankruptcy laws the firm has the option of either being reorganized as a recapitalized going concern (known as Chapter 11 in the USA or administration in the UK) or being liquidated (Chapter 7 in the USA or liquidation in the UK).

Reorganization means the firm continues in existence and the most informal arrangement is simply to postpone the payment required (known as extension) or an agreement for creditors to take some fraction of what is owed as full settlement (composition).

Liquidation, however, occurs as a result of economic distress in the event that liquidation value exceeds the going concern value. Although bankruptcy and liquidation are often confounded in the literature, liquidation (dismantling the assets of the firm and selling them) and bankruptcy (a transfer of ownership from stockholders to bondholders) are really independent events.

The efficient outcome of a good bankruptcy procedure, according to Aghion (1992), should either:

  1. Close the company down and sell the assets for cash or as a going concern, if the present value of expected cash flows is less than outstanding obligations; OR
  2. Reorganize and restructure the company, either through a merger or scaling down or modifying creditors’ claims.

 

Each country has its own insolvency laws, but bankruptcy remedies are very similar in most industrialized nations, incorporating in various ways the economic rationale for:

  1. Fairness among creditors
  2. Preservation of enterprise value
  3. Providing a fresh start to debtors
  4. The minimization of economic costs

 

There is, however, a widespread dissatisfaction with the existing procedures, as laws have been developed haphazardly with little or almost no economic analysis about how regulations work in practice. Governments and legal structures have not kept pace with the globalization of business and internationalization of financial markets and they have particularly not kept pace in the area of resolving the financial problems of insolvent corporations. For both bankruptcy and insolvency procedures, the key economic issue should be to determine the legal and economic screening processes they provide, and to eliminate only those companies that are economically inefficient and whose resources could be better used in another activity.

Company insolvencies have increased very sharply in the last few years, and currently stand at record levels in many countries. Several factors may severely affect corporate default, and although the combination of recession and high interest rates is likely to have been the main cause of this rise in defaults. The more moderate increases in company failures, which have accompanied more severe downturns in the past, suggest that other factors may also have been important. One important common determinant in companies’ failures is the general economic conditions for business, the other is the level of debt.

Both capital leverage (debt as a proportion of assets) and income gearing (interest payments as a proportion of income), together with high levels of indebtedness in the economy, may lead to companies’ insolvencies.

Recent developments in the theory of finance have considerably advanced our understanding of the nature and role of debt. Debt, unlike any other “commodity,” entails a “promise” to pay an amount and the fulfillment of this promise is, by its nature, uncertain. Many of its features, however, can be understood as means of overcoming uncertainty, transaction costs, and incomplete contracts, arising from asymmetric information between the parties concerned.

The risk of bankruptcy and financial distress, however, highlights the fact that conflicts of interest between stockholders and various fixed payment claimants do still exist. These conflicts arise because the firm’s fixed claims bear default risk while stockholders have limited-liability residual claims and influence the managerial decision process. Bankruptcy procedures often do not work well, because incomplete (private) contracts cannot be reconciled so laws have to step in.

Bankruptcy, as such, does not create wealth transfers to shareholders or undermine the provisions of debt finance but it creates, due to asymmetric information, a conflict of interest between creditors and shareholders, which harms companies’ prospects.

The implications of these conflicts of interest have been explored by a number of researchers, including Jensen and Meckling (1976), Myers (1977), and Masulis (1988).

One consistent message in these papers is that these conflicts create incentives for stockholders to take actions that benefit themselves at the expense of creditors and that do not necessarily maximize firm value.

Jensen and Meckling (1976) argue that rational investors are aware of these conflicts and the possible actions firms can take against creditors. Thus when loans are made they are
discounted immediately for the expected losses these anticipated actions would induce.

This discounting means that, on average, stock-holders do not gain from these actions, but firms consistently suffer by making suboptimal decisions. If the firm is confronted with a choice between investment and debt reduction, it will continue to invest past the efficient point. Then creditors will prefer a debt reduction to investment and, since there are no efficiencies, stockholders must prefer investment.

However, if the actions of the owners (managers or shareholders) are unobservable, several complications arise:

  1. There is asset substitution. Since the owner only benefits from returns in non-default states, risky investments of given mean return will be chosen in preference to safer investments (moral hazard). Owners benefit from the upside gains from high risk investments but do not bear the costs of downside losses. Those are inflicted on creditors rather than shareholders. This is the standard consequence that debt can cause firms to take on uneconomic projects simply to increase risk and shift wealth from creditors to stockholders.
  2. There is underinvestment. Owners do not benefit from the effort that they apply to improve returns in insolvency states. Those accrue for creditors not owners. Since some of the returns to investments accrue to bond-holders in bankrupt states, firms may be discouraged from carrying out what would otherwise be profitable investments (Myers, 1977).
  3. There is claim dilution that is an incentive for owners to issue debt that is senior to existing debt. Senior debt has priority over existing debt in the event of bankruptcy, it can therefore be issued on more favorable terms than existing debt, which leaves existing creditor’s claims intact in the event of bankruptcy.

 

The literature suggests, therefore, that bankruptcy impediments to pure market solutions are concerned with the free rider and holdout problems caused by the inconsistent incentives arising in a business contract specifying a fixed value payment between debtor and creditor, particularly given limited liability. Limited liability implies ”moral hazard” and “adverse selection” due to asymmetric information problems. Consequently, the prospect of corporate insolvency may result in increased borrowing costs and, simultaneously, a reduction in the amount of funds available.

 

Resources for Bankruptcy:

Aghion, P. (1992). The economics of bankruptcy reform. Working paper 0 7530 1103 4. London: London School of Economics.

Quarterly Journal of Economics, 84, 488–500. Altman, E. I. (1993). Corporate financial distress and bankruptcy. New York: John Wiley.

Davis, E. P. (1992). Debt, financial fragility, and systemic risk. Oxford: Clarendon Press.

Masulis, R. W. (1988). The debt/equity choice. New York: Ballinger Publishing Company.

Webb, D. (1991). An economic evaluation of insolvency procedures in the United Kingdom: does the 1986 Insolvency Act satisfy the creditors’ bargain?. Oxford Economic Papers, 42, 139–57.

Weston, J. F. & Copeland, T. E. (1992). Managerial finance. Orlando, FL: The Dryden Press.

White, M. J. (1988). The corporate bankruptcy decision. Journal of Economic Perspectives, 3,129–51.

 

Banks As Barrier Options

A barrier option is an option which is initiated or extinguished if the underlying asset price hits a pre specified value. More specifically, a “down and out call” is a call option expiring worthless as soon as the value of the underlying asset hits a lower bound K, which is usually equal to or less than the option’s exercise price, as developed in Merton (1973) and Cox and Rubinstein (1985).

Chesney and Gibson (1993, 1994) applied the down and out call model to the pricing of equity in a levered firm, while Paris (1995, 1996) extended the model to banks and financial intermediaries.

Valuing bank capital as a traditional call option written on the bank assets, with a strike price equal to the total bank deposits, has two main theoretical underpinnings:

  1. As soon as the bank asset value declines to the value of the liabilities, the bank capital is worth zero, while the call value is positive, before the option’s expiration.
  2. In order to maximize the market value of their equity, the bank shareholders systematically choose the most risky projects characterizing the investment opportunity set.

 

The down and out call approach overcomes both of these problems.

This approach to the valuation of bank capital has two fundamental implications: (1) the asset volatility is related to the bank capital structure, meaning that an explicit and positive linkage exists between the two main sources of risk in the bank, and (2) the existence of an optimal asset volatility implies that the bank shareholders may be risk averse instead of risk neutral, as they are traditionally considered in the theoretical literature, eliminating, as a consequence, any behavioral differences among shareholders and bank managers. Distinguishing between a shareholder and a management-controlled bank is thus meaningless, to the extent that the utility function of the bank controller is considered.

Paris (1995) applies the down and out call framework to the valuation of bank capital. This approach has two merits. (1) The market value of the bank capital can be easily computed at any time, once the marking to the market of bank assets and liabilities is assumed to be feasible, and a continuous time model of bank monitoring can be implemented. It is worthwhile to stress that frequent, possibly continuous, monitoring is a necessary, if not sufficient, condition for prompt and effective corrective actions by financial regulators, in case of bank problems. (2) The chosen optimal value of the bank asset volatility, if observed by the market, is an effective signal of the true bank capitalization. The important implication is that observing the bank’s investment strategy allows the market to evaluate the bank’s safety and soundness.

An extension of the down and out call model to any kind of financial intermediary has been applied in Paris (1996) in order to derive relevant properties of alternative regulatory approaches. Once more the optimal intermediary asset volatility is the critical variable determining the intermediary’s response to the regulatory provision, in addition to the regulator’s action in terms of minimum capital requirement. Moreover, under specific conditions, the same volatility measure can be unambiguously inferred by the market, by simply observing the intermediary’s capital ratio.

 
Resources for Bank As Barrier Options:

Chesney, M. & Gibson, R. (1993). The investment policy and the pricing of equity in a levered firm: a re-examination of the contingent claims’ valuation approach. EFA Annual Conference Proceedings. Copenhagen.

Chesney, M. & Gibson, R. (1994). Option pricing theory, security design and shareholder’s risk incentives. AFFI Annual Conference Proceedings. Tunis.

Cox, J. C. & Rubinstein, M. (1985). Options markets. Englewood Cliffs, NJ: Prentice-Hall.

Paris, F. M. (1995). An alternative theoretical approach to the regulation of bank capital. University of Brescia. Working paper 97.

Paris, F. M. (1996). Modelling alternative approaches to financial regulation. University of Brescia. Working paper 103.

 

Bid–Ask Spread

Security dealers maintain a continuous presence in the market and stand ready to buy and sell securities immediately from impatient sellers and buyers. Dealers are willing to buy securities at a price slightly below the perceived equilibrium price (i.e. bid price) and sell securities immediately at a price slightly above the perceived equilibrium price (i.e. ask price). Of course, buyers and sellers of securities could wait to see if they can locate counterparties who are willing to sell or buy at the current equilibrium price. However, there are risks associated with patience. The equilibrium price may change “adversely” in the interim such that it is either higher or lower than the dealer’s current bid or ask quotes. Thus, the willingness of traders to transact at a price that differs from the perceived equilibrium price compensates market makers, in part, for the risks of continuously supplying patience to the market.

Although the dealers’ willingness to post bid and ask quotes springs from their self-interest, their actions generate a positive externality of greater liquidity for the market as a whole.

In general, the bid–ask spread compensates the dealer/market makers for three costs that attend their function of providing liquidity. These costs include order-processing costs, inventory control costs, and adverse selection costs. The order processing costs include maintaining a continuous presence in the market and the administrative costs of exchanging titles (Demsetz, 1968). The inventory control costs are incurred because the dealer holds an undiversified portfolio (see e.g. Amihud and Mendelson, 1986, Ho and Stoll, 1980). The adverse selection costs compensate the dealer for the risk of trading with individuals who possess superior information about the security’s equilibrium price (see e.g. Copeland and Galai, 1983, Glosten and Milgrom, 1985).

A dealer’s quote has two component parts. The first part is the bid and ask prices. The second part is the quotation size which represents the number of shares dealers are willing to buy (sell) at the bid (ask) price. A dealer’s quote can be described as an option position (Copeland and Galai, 1983). To wit, the bid and ask price quotes are a pair of options of indefinite maturity written by the dealer. A put (call) option is written with a striking price equal to the bid (ask) price. The quotation size is the number of shares dealers are willing to buy (sell) at the bid (ask) price. Simply put, the quotation size represents the number of put (call) options written with a striking price equal to the bid (ask) price.

In the parlance of options, the dealer’s position is a short strangle. A strangle consists of a call and a put on the same stock with the same expiration date and different striking prices. The call (put) has a striking price (below) the current stock price. Dealers are short a strangle since they write both options. If one assumes the dealer’s bid and ask prices bracket the market’s estimate of the stock’s current equilibrium price, the analogy is complete.

 
Resources for Bid-Ask Spread:

Amihud, Y. & Mendelson, H. (1986). Asset pricing and the bid–ask spread. Journal of Financial Economics, 17 (2), 223–49.

Copeland, T. & Galai, Dan (1983). Information effects on the bid–ask spread. Journal of Finance, 38 (5), 1457–69.

Demsetz, H. (1968). The cost of transacting. Quarterly Journal of Economics, 82 (1), 33, 53.

Glosten, L. & Milgrom, P. (1985). Bid, ask and transaction prices in a specialist market with heterogeneously informed traders. Journal of Financial Economics, 14 (1), 71–100.

 

Black–Scholes

This is a famous equation for determining the price of an option, first discovered in 1972 by Fischer Black of Goldman Sachs and Myron Scholes of the University of Chicago and published in Black and Scholes (1973). The unique insight of this research was to use arbitrage in solving the option-pricing problem. Black and Scholes reasoned that a position which involved selling a call option and buying some of the underlying asset could be made risk-free. It would be a hedged position and, as such, should pay the risk free rate on the net investment. Using continuous-time mathematics they were able to solve for the call price from the equation for the hedged position. This resulted in an equation for the value of a European option (i.e. one which cannot be exercised before maturity) which did not need to take account of the attitude to risk of either the buyer or seller.

Many academic papers have proposed more complicated models, only to conclude that the simple Black–Scholes model can be modified to give almost equally good results.

Several assumptions are necessary to derive the model, but it is surprisingly robust to small changes in them. The first assumption is that the asset price follows a random walk with drift. This means that the asset price is lognormally distributed and so returns on the asset are normally distributed. This assumption is widely used in financial models. The second assumption is that the distribution of returns on the asset has a constant volatility.

This assumption is clearly wrong and use of the model depends crucially on forecasting volatility for the period to maturity of the option. The third assumption is that there are no transaction costs, so that the proportions of the asset and option in the hedged portfolio may be continuously adjusted without incurring huge costs. This assumption sounds critical, but it is relatively unimportant in liquid markets. The fourth assumption is that interest rates are constant, which is not correct but is of little importance since option prices are not very sensitive to interest rates.

The fifth assumption is that there are no dividends on the asset, which once again is unrealistic, but modification of the model to accommodate them is relatively simple (e.g.
Black, 1975).

While most of the theoretical results in finance have not had any impact on practitioners, the Black–Scholes model is universally known and used. The existence of the equation has facilitated the development of markets in options, both on-exchange (beginning with the Chicago Board Options Exchange in 1973) and over the counter. Without the equation, there could not have been such rapid growth in the use of derivative assets over the last twenty years. Many derivative assets might even not exist.

 

Resources for Black-Scholes:

Black, F. & Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of Political Economy, 81, 637–59.

Black, F. (1975). Fact and fantasy in the use of options. Financial Analysts Journal, 31, 36–41, 61–72.