2. A Framework for Financial Innovation: Managing Capital Structure
While this volume is not designed to be a technical guide or a textbook, this chapter offers a basic grounding in the foundational theories that have shaped modern finance. It is a good starting place for readers who want a formal introduction to the science behind the numbers. More casual readers, however, may want to skip ahead to subsequent chapters, which focus on real-world applications of financial technologies.
In 1958, Franco Modigliani and Merton Miller published their famous paper on the irrelevance of capital structure for total firm value—and in the process, they ignited a revolution in corporate finance.1 Their great contribution was to provide a clear conceptual framework for thinking about a firm’s choice among debt and equity and other types of securities. In an ideal world, with perfect and complete capital markets and no taxes, they declared, this choice does not matter.
Although this “irrelevance proposition” is the most-often-quoted result from Modigliani and Miller’s paper, the underlying point is a little more subtle. Since we don’t operate in an ideal world, capital market imperfections and taxes become crucial in determining firms’ actual choices of capital structure. The “M&M theorem”—and other important breakthroughs in financial theory—illuminated when, why, and how capital structure matters. Modigliani and Miller’s abstract markets contained no incentive to innovate. Everything could be done with the securities at hand. It is the imperfections in practice—the rough edges of real markets—that lead to financial innovation.
To lay the groundwork for understanding the practical applications of financial innovation described later in this book, we start with an overview of the Modigliani and Miller result. Then we will run down several other basic tools that make innovation possible, including the Capital Asset Pricing Model (CAPM), the Black–Scholes option pricing formula, and Monte Carlo simulation techniques. Together they form a toolkit that has been used in various forms in the innovations described later in the book. These advances in financial theory have found their way into practice, creating new flexibility in the capital structures available to finance firms and projects. At their most powerful, these tools can reinvent, restructure, and relaunch whole economic sectors.
The ability of these models to factor in uncertainty has increased their relevance in a knowledge-based economy.2 Whether dealing with intellectual property in entertainment, biodiversity, or pharmaceuticals, the models outlined in this chapter can account for uncertainty in the cost of completing projects, uncertainty of cash flows, and output impacts of financial innovations on firms and the real economy. Advances in financial technology have intersected with new efficiencies in information processing, resulting in a declining cost of external funds. These lower costs of capital—made possible by financial innovations to overcome frictions, imperfect markets, and sometimes market failures—have fueled growth in the real economy and moderated the business cycle, despite increasing volatility in financial markets.3
All of these models demand an extensive understanding of the relationship between a firm or project and the markets in which it operates. They assume and require data derived from fundamental analyses of financial statements and the cash-flow conditions of a firm or project, of markets, competitive advantages, management, and productivity. The linkages between financial capital and human capital embedded in the corporate leadership, strategy, and structure of a firm are key. As high-profile financial product failures and financial crises continuously remind us, even good models can fail with bad data inputs (as the saying goes in data processing, “Garbage in equals garbage out”). Information asymmetries, agency costs, moral hazard, adverse selection, and other underlying concepts in financial economics help us understand how and why crises can emerge at a firm or in the macroeconomy.
The breakthrough insights described in this chapter garnered Nobel prizes for many of the pioneering thinkers involved in their formulation and application (including Modigliani, Miller, Markowitz, Sharpe, Merton, Scholes, and others). Together they created a body of work that drove financial innovation by an entire generation of practitioners who linked theory to new corporate policy, strategy, and capital structure.4
The Modigliani–Miller Capital Structure Propositions
Historically, corporations have financed their activities with two major types of securities: equity and debt. The owners of the equity (the shareholders) have responsibility for the operation of the firm through the election of the board of directors. The dividends they receive in return for their subscription of capital are not guaranteed and are paid at the discretion of the board of directors. In contrast, the owners of debt (the bondholders) are promised a particular rate of return. They have no rights of control unless payments by the firm do not materialize, in which case they can force the firm into bankruptcy.
The traditional question about firms’ choice of capital structure has been “What is the optimal debt-equity ratio?” This was the focus of Modigliani and Miller’s paper. To understand their basic ideas, let’s consider the case of the hypothetical FI Company, which is reviewing its capital structure.5 It pays no taxes and has access to perfect capital markets. Among other things, this means that the markets are frictionless—there are no transaction costs, and everybody can borrow and lend at the same rate.
FI’s current position is as follows:
The company currently has no debt, and all the operating income is paid out as dividends to the owners of the equity.
The company’s ultimate result depends on the performance of its business. The operating income generated by the firm can take on a whole range of values. For simplicity, we focus on three outcomes: poor, average, and good.
When the operating income is $100, the earnings per share (EPS) are $100 / 100 = $1 (since there are 100 shares). Given that the stock price is $20, the return on equity (ROE) is $1 / $20 = 5%. The EPS and ROE for the other levels of operating income are calculated in the same way.
To keep everything as simple as possible, we assume that the possible scenarios for operating income are expected to be the same every year for the foreseeable future.
By chance, the firm’s president and chief executive officer is Mr. Modigliani. He has considered the situation and come to the conclusion that shareholders would be better off if the company issued some debt. His reasoning goes like this: Suppose the firm issues $1,000 of debt at the risk-free lending and borrowing rate of 10% and uses the proceeds to repurchase 50 shares (leaving 50 shares outstanding). The debt will be rolled over every year, so there is no need to repay it out of earnings. The payoffs to the owners of equity in the three different scenarios are as follows:
The difference from the situation with no debt is that now the firm must pay 10% interest on the $1,000 the firm has borrowed (or $100). This must be subtracted from the operating income when calculating equity earnings. For example, equity earnings in Scenario 2 are $250 - $100 = $150. Since there are now 50 shares outstanding, the earnings per share are $150 / 50 = $3 per share. The return on equity is $3 / $20 = 15%. Because the company pays the interest in full, the return on the debt is 10%. The calculations are similar for the other scenarios.
We can compare the current situation (with all equity and no debt) to Mr. Modigliani’s proposal to have $1,000 of debt.
Figure 2.1. Varying the proportion of debt and equity
Mr. Modigliani argues that the effect of leverage depends on the company’s operating income. If operating income is greater than $200, leverage increases the EPS and the shareholders are better off. If operating income is less than $200, leverage reduces the EPS. The capital structure decision, therefore, depends on the level of operating income. The average operating income is $250. Because this amount is above the critical level of $200, Mr. Modigliani argues that the shareholders will be better off with the capital structure with debt.
The company has just hired a young executive on the fast track. Her name, by chance, is Ms. Miller. She points out that Mr. Modigliani’s analysis ignores the fact that shareholders have the alternative of borrowing on their own account. For example, suppose that a person borrows $20 and then invests a total of $40 in two all-equity FI shares. This person has to put up only $20 of his own money. The payoff on the investment is as follows:
By buying two shares in the all-equity company and borrowing $20, the returns are exactly the same as buying one share of the firm with the $1,000 of debt. Therefore, a share in the company with debt must sell for (2 × 20 - 20) = $20. If the company goes ahead and borrows, it will not enable its investors to do anything that they could not already do; therefore, the action will not increase value.
This is the idea behind Modigliani and Miller Proposition 1.
Modigliani and Miller Proposition 1
With perfect capital markets and no taxes, the total value (meaning the sum of the debt and the equity) of any firm is independent of its capital structure.
Therefore, Modigliani and Miller argue that, with perfect capital markets and no taxes, capital structure is irrelevant. You can’t create value by borrowing or lending. Any combination of securities is as good as another; the value of the firm is unaffected by its choice of capital structure. Why? Because individuals can essentially do or undo anything the firm can do on its own. This is an extremely powerful argument. We illustrated it in the FI Company example, but it works in many others. As Miller once explained, “The firm is like some gigantic pizza, represented by its underlying earning power. You can’t increase the value of that pizza by cutting it up into different slices—in this case, of debt and equity securities.”6
The assumptions of no taxes and perfect capital markets are crucial for the result. If individuals are taxed differently than firms (say, if interest is deductible for corporations but not for individuals), then the result will not hold. The assumption of perfect capital markets ensures that individuals can borrow at the same 10% rate as the firm. If this rate were different, the result would not hold.
For a firm with any proportion of risk-free debt in its capital structure, investors can create the equivalent payoffs from any other proportion by borrowing or lending on their own account. Investors will always hold the level of debt that is optimal for them. If the firm changes its capital structure, investors will simply take offsetting positions to undo what the firm has done so they can go back to their optimal level. Therefore, a firm cannot create value by changing its capital structure—provided there are perfect capital markets and no taxes.
Before considering what happens with taxes and capital market imperfections, and how these introduce possibilities for financial innovation, let’s continue a little further with our example of the FI Company.
The Relationship between Return and Debt
Consider the expected returns on FI stock in the two cases we examined:
Intuitively, what is happening here? Why is the expected return on the firm with debt higher? The firm can borrow at 10% and the return on its assets is 12.5%. It therefore makes 12.5% - 10% = 2.5% from borrowing against its assets. If it borrows half its value, it makes 2.5% on the half it borrows plus 12.5% on the half it still owns. This gives a total return of 2.5% + 12.5% = 15%.
This example illustrates that borrowing leads to a higher return on equity because the firm can borrow at a rate that is lower than the return on its assets. The more the firm borrows, the higher the return on the equity; the spread between the return on assets and debt is earned on a larger amount of debt. This idea underlies Modigliani and Miller’s second result.
Modigliani and Miller Proposition 2
The expected rate of return on the equity of a firm increases in proportion to the firm’s debt-to-equity ratio, expressed in market values. The rate of increase depends on the spread between the return on assets and the return on debt.
Modigliani and Miller’s second proposition has the important implication that it is possible to raise the expected return on equity by borrowing. However, their first proposition shows that this does not create value for shareholders. How can the expected return go up while value stays the same?
The Relationship between Risk and Debt
Total value remains the same, even though expected return is going up as debt is increased, because the risk of the equity is also increasing—which exactly offsets the increase in expected return. To see this intuitively, consider our example. Look at what happens to the risk of FI’s equity if it moves from all equity to 50% debt and 50% equity.
The difference in operating income between Scenarios 1 and 3 is $300 - $100 = $200, regardless of whether the firm is all equity or has $1,000 debt. With all-equity financing, this $200 change is spread over 100 shares, so the variation in EPS is $2 per share. With 50% debt and 50% equity, the same change in operating income is spread over 50 shares, so the variation in earnings is $4 per share. The spread of percentage returns is also amplified: The percentage spread with debt is 20%, as opposed to 10% with all equity. Therefore, the risk is doubled.
The Modigliani and Miller propositions revolutionized corporate finance because they provided a clear framework for thinking about the effects of debt. It is possible to obtain a higher expected return by borrowing. But this does not create value because risk is going up in a manner that exactly offsets the increase in expected return. This leads to one of the most basic insights in finance: When comparing expected returns in different investments, be sure to adjust for risk. In many parts of the financial services industry, such as private equity, returns are not adjusted for the amount of debt used in the financing. This makes them seem more attractive than they are in reality.
The Modigliani–Miller Propositions and Optimal Capital Structure
The Modigliani–Miller propositions were initially used as a starting point in analyzing how firms should choose their optimal capital structure. They indicate what we should look for to answer this question. Earnings per share and return on equity are not important in determining optimal capital structure—firms can always increase these ratios by borrowing more. Shareholders are not any better off, however, and risk has gone up, offsetting any increase in expected return. The factors that are important in determining optimal capital structure are taxes and market imperfections.
In the United States and many other countries, interest on debt is deductible from taxable corporate income, but dividends on equity are not. This creates a clear bias in favor of debt.7 If a payment to owners of securities is labeled as interest, the firm pays less in taxes to the government. On the other hand, if it is labeled dividends, no reduction in taxes occurs. If the tax deductibility of interest is the only factor in play, then firms will have an incentive to use large amounts of debt to shield their income from corporate taxes. But in practice, firms do not use such large amounts of debt, and most of them do in fact pay corporate income taxes. Why?
If a corporation has a large amount of debt, its chances of going bankrupt are high. An important implication of the perfect capital markets assumption in the Modigliani–Miller framework is that bankruptcy is not costly. The firm can quickly be refinanced without interfering with its operations. However, this is not the case in practice. Bankruptcy is an expensive process. A number of authors have suggested that firms trade off the benefits of reduced taxes with the increased expected costs of bankruptcy when debt is increased.8 This became the textbook theory of capital structure. Many other models have been suggested, but none has fully replaced the “trade-off” theory.
Our interest in the Modigliani–Miller propositions is somewhat different. In their ideal world, with no taxes and perfect capital markets, there would be no benefit from financial innovation. There are no problems preventing the smooth allocation of resources, and thus no problems for financial innovation to solve. In the next section, we turn to the world of capital market imperfections and taxes to understand the role that financial innovation has to play.
Innovations in an Imperfect World
Modigliani and Miller posed the question, how should a firm choose the optimal amount of debt and equity as well as other securities? With financial innovation, the relevant question is, how can we change securities, markets, or processes to improve the situation? In this section, we consider imperfections in the context of the Modigliani–Miller framework that provide a role for financial innovation.9
Incomplete Markets
In the simple example of the FI Company, the debt the company issued was risk free and shareholders borrowing on their own account was also risk free. If FI were to borrow more than $1,000, it would not be able to pay the interest in Scenario 1 and would go bankrupt. Even when bankruptcy is cost free, the Modigliani–Miller results would not hold unless the individual shareholders could borrow on exactly the same terms as the company. This is the case in which markets are complete, meaning it is possible to trade a security where the payoff is contingent on any conceivable event. (In this case, the event would be the bankruptcy of FI.)10 In a complete market, the individual shareholder could borrow on exactly the same terms as the firm, and the logic of the proof for Modigliani and Miller’s Proposition 1 would be valid. However, if markets are incomplete such that individual shareholders cannot borrow on the same terms as the FI Company, then the firm’s capital structure matters.
Suppose the firm can borrow on better terms than individual stockholders (since banks incur large costs when making and servicing small loans to consumers). In this case, a firm might be able to increase its value by borrowing and issuing debt that allows the individual shareholders to reduce their more costly personal borrowing. The problem a financial innovator would face in this circumstance how to design debt contracts so they are attractive to small investors. Small denominations and ease of trading such debt would certainly be important factors. By designing and issuing such debt, a firm might be able to obtain a premium and increase its value.
This simple example provides one illustration of how an incomplete market might enable a financial innovator to profit. However, the principle is much more general. Whenever markets are incomplete and do not provide full opportunities to trade state-contingent securities, potential exists for financial innovation to improve the allocation of resources.
One of the most important roles of the financial markets is to allow risks to be fully shared, and many innovations are designed to improve risk sharing. Investors are prepared to pay a premium for securities with risk characteristics they prefer. One simple example is a situation in which the equity of a company is split into two components: prime and score. The prime component receives the dividends and capital gains up to a prespecified price, while the score component receives the capital appreciation above this price. A careful study by Robert A. Jarrow and Maureen O’Hara found that the sum of the values of the prime and score components exceeded the value of the equity.11 In other words, splitting the equity into two parts created value for shareholders.
In the 1970s, many new specialized financial markets were introduced to make the overall markets more complete and improve risk sharing. These included markets for financial futures, which allowed investors to buy a security on a future date at a price that is fixed today. Futures on government securities that enable financial institutions to hedge the risks on their substantial holdings of these instruments were particularly successful. The greater the improvement in risk sharing that a contract created, the more likely it was to be viable.12
Another significant market introduced during this period traded options on stocks. The Chicago Board Options Exchange (CBOE) was introduced in 1973 to enable trading of standardized options (which give investors the option to buy or sell stocks at a prespecified price on or before the maturity date of the instrument). The CBOE was instantly successful, and by 1984, it had become the second-largest securities market in the world (trailing only the New York Stock Exchange). Theoretical work suggests that introducing an option on a stock can enable better sharing of the risk associated with the stock. As a result, demand for the stock increases, raising its price.13 Empirical studies support this finding. During the 1970s and early 1980s, when an option was introduced, the price of the stock that the option was written on increased by approximately 2%–3%, and the volatility of the stock was reduced. When an option was delisted, the opposite effects occurred (that is, the stock price fell and the volatility increased).14
James Van Horne has argued that the incompleteness of markets provides a large part of the rationale for financial innovation, accounting in particular for the rapid growth in futures and options and other derivative markets that occurred around the world in the 1970s.15 It can also explain the introduction new securities, such as prime and scores, by corporations. Market incompleteness has been the basic driver of financial innovation in many other situations.16
Agency Concerns, Information Asymmetries, and Transaction Costs
In a seminal paper, Michael Jensen and William Meckling pointed to the importance of agency problems (or misaligned incentives for different parties) in the determination of capital structure. Agency problems occur when conflicts of interests arise between creditors, shareholders, and management because of differing goals.17 Jensen and Meckling argued that a firm could be thought of as a set of contracts between different parties with different interests. According to this view, the form of securities issued is crucial in regulating the relationships between different groups. If a firm has a large amount of debt outstanding, the equity holders earn a return only if there is a high payoff. They (or the managers acting on their behalf) have an incentive to undertake risky projects even if the projects are not profitable.
Consider the following simple example. The interest rate is 10%. Suppose there is a safe project in which, for every unit of funds invested, there is a return of 1.25 one period later. A risky project also arises in which, for every unit invested, the probability is 0.5 of a 0 payoff and the same for a 1.8 payoff. The next table summarizes these payoffs.
Clearly, the risky project should not be undertaken, since it cannot recover its investment on average. However, a firm with sufficient debt outstanding would choose the risky project instead of the safe one.
Suppose the firm starts with 0.7 in debt. Because the interest rate is 10%, the firm would owe 1.1 × 0.7 = 0.77 at the end of the period. The payoff from the safe asset for the equity holders is less than the expected payoff from the risky asset.
Payoff to safe asset = 1.25 - 0.77 = 0.48
Expected payoff to risky asset = 0.5 × 0 + 0.5 × (1.8 - 0.77) = 0.52
The debt holders would want to prevent the firm from undertaking the risky project because they would obtain 0.77 if the firm undertakes the safe project and 0.5 × 0.77 = 0.39 on average if it chooses the risky one. This is where asymmetric information plays an important role. If possible, the debt holders would write covenants that would prevent the firm from doing the risky project. If there is asymmetric information, this would not be possible and the firm would choose the risky project. It would do this for any level of debt greater than 0.64. Below that level, the firm would choose the safe project.
Financial innovation can solve this problem by developing securities other than debt and equity.18 If the debt is convertible, so that the bondholders would receive 49% of the equity if the equity price was more than 1, this would ensure it is not worth it to the equity holders to choose the risky project. If the equity holders did undertake the risky project and it was successful, the bondholders would convert their bonds into 49% of the equity of the firm. In this case, they would receive 0.49 × 1.8 = 0.88. If they did not convert, they would receive 0.77. The initial equity holders would receive 0.51 × 1.8 = 0.92. They would no longer have an incentive to choose the risky project in the first place, since their expected payoff would be 0.5 × 0.92 = 0.46, which is less than the 0.48 they would receive from undertaking the safe project.
In another seminal contribution, Stewart Myers pointed out a second agency problem (conflict of interest between various parties with competing claims on the firm’s cash flow).19 In the previous example, the firm was willing to undertake a bad, risky project. Here the firm will not undertake a good, safe project. Consider the same safe project as the previous example, in which the investment is 1 and the payoff is 1.25. Because the interest rate is 10% and this project earns 25%, it is clearly a desirable undertaking. However, if there is existing debt of 0.3 and the project needs to be financed, it might not be possible for the firm to raise the necessary funds.
The problem is that the equity holders would receive 1.25 - 0.3 = 0.95 when the project pays off, so they would not be willing to put in 1 unit at the initial date to fund the project. The bondholders who are owed the 0.3 in debt would be willing to put up the funds if they could be sure the project really was the safe one, since this would allow them to recover part of their initial debt as well as the subsequent debt. However, if there is asymmetric information that prevents the bondholders from observing the project quality and it could be the risky one, they will not provide the finance. Therefore, the project would not be undertaken.
Again, financial innovation can solve the problem. If the debt converts to 10% of the equity when the stock price falls below 0.2, the equity holders will be willing to put up the funds. They would receive 0.9 × 1.25 = 1.125. This allows them to obtain a 12.5% return on their initial investment. This is preferable to the 10% interest rate (abstracting the effects of risk).
Stephen Ross has suggested that the interaction of agency issues and marketing costs is an important driver of financial innovation.20 Agency considerations lead borrowers to contract with commercial banks. A shock, such as a change in regulation or taxes, can change the amount of lending they wish to do. As a result, they sell some of these low-grade assets by approaching investment banks to market these assets using financial innovations to reduce the costs of selling them.
Robert Merton has also stressed agency costs.21 In addition, he points to the role of transaction costs savings and improvements in liquidity as important benefits of financial innovations such as commercial paper, financial futures, options, and swaps.
Subsequent chapters offer specific examples of innovations to solve agency problems.
Taxes and Regulation
Miller has argued that much of the innovation that occurred in the 1970s and early 1980s came in response to government regulation and features of the tax code.22 However, these types of restrictions had caused innovation even before that. In the middle of the nineteenth century, the popularity of preferred stock in England arose from the fact that corporations were prohibited from borrowing more than one-third of their total share capital. More recently, in the 1960s, the U.S. Interest Equalization Tax, which excluded most foreign issuers from the U.S. market, significantly spurred the development of Euromarkets (markets for dollar securities and deposits outside the United States).
Another classic example of innovation in response to the tax code is zero-coupon bonds, which offer a single payment at the end of the bond’s life that includes both principal and interest.23 Before the Tax Equity and Fiscal Responsibility Act of 1982 (TEFRA), the tax liability on zero-coupon bonds was allocated on a straight-line basis—the annual interest deduction was the amount to be repaid at the due date minus the issue price, divided by the number of years until repayment. This rule ignored the effect of interest compounding and created an opportunity for corporations to avoid taxes by issuing long-term zero-coupon bonds to tax-exempt investors. When interest rates were high in the early 1980s, the potential tax benefits from this type of security became significant, and corporations raced to issue these bonds. Although TEFRA closed this loophole, the market for zero-coupon bonds continued. Investment banks first satisfied the demand for these securities, and then the Treasury provided strips of government securities (in which bonds were broken into principal and interest components).
Edward Kane has stressed that the “regulatory dialectic” is an important source of innovation.24 In this process, regulation leads to innovations, which lead in turn to new regulations, and so on. One example is bank capital requirements, which prompted banks to introduce capital notes and preferred stocks that would count toward their capital. Similarly, the first swaps occurred in the 1960s; they were currency swaps, motivated by a desire to avoid British exchange controls.
Tools for Financial Innovation
Now that we’ve considered how the Modigliani–Miller propositions and agency theory laid a theoretical framework for financial innovation, we outline a number of other models that propelled the field forward. We begin with the Capital Asset Pricing Model (CAPM), the first model that made it possible to properly quantify a security’s risk, and the Black–Scholes option pricing model, which opened a whole new way of thinking about finance and allowed new financial products to be engineered in a way that had not been possible before. Finally, we look at Monte Carlo simulation techniques, which can evaluate the properties of options and complex new financial instruments when the assumptions of the Black–Scholes model are not satisfied.
The CAPM
In 1952, Harry Markowitz introduced the idea of thinking about the risk of portfolios of securities in terms of the mean and standard deviation of returns.25 An efficient portfolio is one in which the standard deviation is minimized for a given expected return. The portfolio efficiency locus gives the possible trade-off between risk and return.
What does this really mean? Markowitz’s innovation enabled people to formally consider diversification and the important role it could play in reducing the risk of a portfolio. He showed that a portfolio’s risk, as measured by its standard deviation, depended on the standard deviations and covariances (or the correlations) of the returns of the stocks in a portfolio. In other words, if a portfolio contains many independent stocks, so that the covariances of their returns are zero, the portfolio’s risk is eliminated. However, in practice, stock returns are not independent, because the business cycle affects most companies to some extent. Not all risk can be eliminated.
It would be another 12 years before the next step was taken, enabling William Sharpe and John Lintner to independently derive the CAPM.26 The crucial innovation was to not only consider risky stocks, but to also introduce a risk-free government bond. They showed that, in this case, all investors will hold a combination of the risk-free asset and the market portfolio, consisting of all the risky securities that exist, so that they can achieve the maximum possible degree of diversification. Risk-averse people will hold a high proportion of their wealth in the risk-free government bond, while less-risk-averse people will hold more in the market portfolio. Sharpe and Lintner were also able to derive a simple relationship between the expected return on a stock and its risk as measured by its beta (β), which depends on its correlation with the market portfolio. The formula follows:
r = rF + β(rM – rF),
Here, r is the expected return on the stock, rF is the return on the risk-free government security, rM is the expected return on the market portfolio, and
β = Covariance (Stock, Market)
(Standard deviation of M)2
β is important for determining the stock’s expected return because it measures the contribution of the stock to the risk of the market portfolio. If the amount of the stock in the market portfolio increases slightly, it indicates how much the risk of the market portfolio would change. The other way to think about β is that it measures the slope of the regression line of the stock’s return against the market returns. It shows how much the return of the stock increases on average for every 1% increase in the return on the market portfolio.
The CAPM revolutionized the way people thought about risk. They no longer focused on the standard deviation of a stock’s returns, but rather on its contribution to the risk of a portfolio as measured by its β. The risk that is unique to the firm is not included in the measure because this risk is diversified away. Instead, β focuses on the risk of the firm that covaries with the market.
The Black–Scholes Model
The year 1973 saw two seminal events: the opening of the Chicago Board Options Exchange and the publication of two groundbreaking papers (one by Fischer Black and Myron Scholes, and the other by Robert Merton) on valuing options.27 In 1997, Scholes and Merton were awarded Nobel prizes for their work (unfortunately, Black had died in 1995, so he was not eligible).
Why was their work so pivotal? Options might be significant, but it was really the broader ideas introduced by these economists that proved to be game changing. These concepts are applicable in many different contexts and have revolutionized the practice of finance. The two crucial components of their theory are arbitrage and dynamic trading. These allow financial engineering, which involves the manufacture of securities and portfolios with any desired payoffs.
We consider these ideas in the context of options, the field in which they were first introduced. Options are used in many settings and are useful because they allow insurance. For example, options on foreign exchange enable firms to eliminate the undesirable effects from fluctuations in exchange rates. In addition to options on foreign exchange, options can be used on stocks. Using options together with stocks and bonds allows investors to design a desirable set of portfolio payoffs. For example, if you are worried about the possibility of a fall in stock prices, you can buy options to insure against the downside risk. Markets for options on stocks are among the most active in the world. Although we focus on options on stocks, the methodologies can be applied to other types of options, such as those on foreign exchange.
First off, what exactly is an option? Purchasers of a call option have the right, if they want, to buy a share of the stock from the seller of the option at a prespecified exercise price on or before the maturity date. Purchasers of a put option have the right to sell a share of the stock to the seller of the option at a prespecified exercise price on or before the maturity date.28
The Black–Scholes formula and its many extensions have been found to work well in practice.29 Despite what appear to be strong assumptions and the abstract nature of the model, the empirical evidence strongly supports the Black–Scholes model and its extensions.
The basic idea behind the Black–Scholes model is to create a dynamic trading strategy using stock and risk-free bonds to create the equivalent to a call. Calls are not the only items that can be dynamically synthesized—in fact, almost any kind of asset can be dynamically created. This is why the model has revolutionized finance. You can always create any arbitrary pattern of payoffs using an appropriate dynamic trading strategy. The methodology enables investors to evaluate and price new financial products, which is why its discovery represented a quantum leap forward for financial innovation. It is difficult to believe that the Chicago Board Options Exchange would have been so successful without the discovery of the Black–Scholes formula.
Monte Carlo Methods
The assumptions of the Black–Scholes model are very strong. Phelim Boyle later pointed out that Monte Carlo techniques could be used to value options in many situations in which the Black–Scholes assumptions were not satisfied.30 The method involves considering a particular random path of the stock price and evaluating the value of the option of interest at each point. This is done many thousands or hundreds of thousands times. The initial price of the option is found by averaging across all these different possible paths and then discounting this value back at the risk-free rate. The methods are very powerful because they enable analysts to incorporate a wide range of deviations from the Black–Scholes model. For example, they allow option prices to be evaluated when there are jump processes.
Just as the analytical approach of the Black–Scholes model can be applied to securities other than options, Monte Carlo simulations can be applied in many situations. The methods are particularly useful when there are multiple sources of risk.
Conclusions
This chapter set forth a framework for thinking about financial innovation. The concepts and theoretical models that comprise this toolkit have been empirically applied across a range of financial products and in real markets. In the ideal world of Modigliani and Miller, in which capital markets are perfect and there are no taxes, financial innovation has no role to play. But the act of translating this abstract model into the empirical rough-and-tumble world of real markets has produced important insights and applications. Only in a world with frictions can financial innovation improve the situation. Whenever markets are incomplete, agency problems arise between parties, or regulations and taxes present hurdles, there will be an incentive to innovate and create value by reducing the frictions.
In the following chapters, we show how this plays out in the real world and how creative practitioners have put these concepts to work in financing new businesses, increasing homeownership, funding medical solutions, solving environmental problems, and spurring economic development in emerging markets.
The recent crisis notwithstanding, a clear and well-documented link between finance and growth has held true over time. By moving these formulas and theories into practice, financial innovators have transformed industrial organization and corporate strategy over the centuries. Today they are still striving to open new frontiers in the twenty-first-century economy.
Endnotes
1 Franco Modigliani and Merton H. Miller, “The Cost of Capital, Corporation Finance and the Theory of Investment,” American Economic Review 48, no. 3(1958): 261–297.
2 Jacques Bughin, “Black–Scholes Meets Seinfeld,” McKinsey Quarterly (May 2000); Eduardo S. Schwartz, “Patents and R&D As Real Options,” Economic Notes 33, no. 1 (February 2004): 23–54.
3 J. Christina Wang, “Financial Innovations, Idiosyncratic Risk, and the Joint Evolution of Real and Financial Volatilities,” Proceedings, Federal Reserve Bank of San Francisco (November 2006).
4 Thomas E. Copeland, John F. Weston, and Kuldeep Shastri, Financial Theory and Corporate Policy, 4th ed. (New York: Addison-Wesley, 2005).
5 For a full analysis of firms’ choice of capital structure, see Chapters 17 and 18 of Richard A. Brealey, Stewart C. Myers, and Franklin Allen, Principles of Corporate Finance, 10th ed. (New York: McGraw-Hill, 2010).
6 Merton Miller, as quoted by Matt Siegal in “How Corporate Finance Got Smart: The Modigliani–Miller Theorem Turns 40,” Fortune (25 May 1998).
7 Franco Modigliani and Merton H. Miller, “Corporate Income Taxes and the Cost of Capital: A Correction,” American Economic Review 53 (1963): 261–297.
8 For example, see Alan Kraus and Robert Litzenberger, “A State-Preference Model of Optimal Financial Leverage,” Journal of Finance 28 (1973): 911–922; James Scott, “A Theory of Optimal Capital Structure,” Bell Journal of Economics and Management Science 7 (1976): 33–54; and E. Han Kim, “A Mean-Variance Theory of Optimal Capital Structure,” Journal of Finance 33 (1978): 45–63.
9 This section draws on Franklin Allen and Douglas Gale, Financial Innovation and Risk Sharing (Cambridge, MA: MIT Press, 1994); and Peter Tufano, “Financial Innovation,” in George M. Constantinides, Milton Harris, and René Stulz, eds., Handbook of the Economics of Finance, Volume 1a, Corporate Finance (New York: Elsevier-North Holland, 2003).
10 In effect, such a contingent security would be a credit default swap in which there is a payoff when a company defaults. See Chapter 3, “Innovations in Business Finance,” for a full discussion of these instruments.
11 Robert A. Jarrow and Maureen O’Hara, “Primes and Scores: An Essay on Market Imperfections,” Journal of Finance 44 (1989): 1263–1287.
12 See Deborah G. Black, “Success and Failure of Futures Contracts: Theory and Empirical Evidence,” Salomon Brothers Center for the Study of Financial Institutions Monograph Series in Finance and Economics, Graduate School of Business Administration, New York University (1986); and Darrell Duffie and Matthew Jackson, “Optimal Innovation of Futures Contracts,” Review of Financial Studies 2, no. 3 (1989): 275–296.
13 Jerome Detemple and Lawrence Selden, “A General Equilibrium Analysis of Option and Stock Market Interactions,” International Economic Review 32 (1991): 279–303.
14 See Jennifer Conrad, “The Price of Option Introduction,” Journal of Finance 44 (1989): 487–498; and Jerome Detemple and Philippe Jorion, “Option Listing and Stock Returns: An Empirical Analysis,” Journal of Banking and Finance 14 (1990): 781–801.
15 James C. Van Horne, “Of Financial Innovation and Excesses,” Journal of Finance 40 (1985): 621–631.
16 See Franklin Allen and Douglas Gale, Financial Innovation and Risk Sharing (Cambridge, MA: MIT Press, 1994); and Darrell Duffie and Rohit Rahi, “Financial Market Innovation and Security Design: An Introduction,” Journal of Economic Theory 65 (1995): 1–42.
17 Michael C. Jensen and William H. Meckling, “Theory of the Firm: Managerial Behavior, Agency Costs, and Ownership Structure,” Journal of Financial Economics 3 (1976): 305–360.
18 See Richard Green, “Investment, Incentives, Debt, and Warrants,” Journal of Financial Economics 13 (1984): 115–136; and Amir Barnea, Robert Haugen, and Lemma Senbet, Agency Problems and Financial Contracting (Englewood Cliffs, NJ: Prentice Hall, 1985).
19 Stewart C. Myers, “Determinants of Corporate Borrowing,” Journal of Financial Economics 5 (1977): 147–175.
20 Stephen Ross, “Institutional Markets, Financial Marketing, and Financial Innovation,” Journal of Finance 44 1989): 541–556.
21 Robert C. Merton, “The Financial System and Economic Performance,” Journal of Financial Services Research 4 (1990): 263–300.
22 Merton H. Miller, “Financial Innovations: The Last Twenty Years and the Next,” Journal of Financial and Quantitative Analysis 21 (1986): 459–471.
23 Zero-coupon bonds are discussed further in Chapter 3.
24 Edward J. Kane, “Technology and the Regulation of Financial Markets,” in Anthony Saunders and Lawrence J. White (eds.), Technology and the Regulation of Financial Markets: Securities, Futures, and Banking (Lexington, MA: Lexington Books, 1986): 187–193.
25 Harry M. Markowitz, “Portfolio Selection,” Journal of Finance 7 (1952): 77–91.
26 William F. Sharpe, “Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk,” Journal of Finance 19 (1964): 425–442; and John Lintner, “The Valuation of Risk Assets and the Selection of Risky Investments in Stock Portfolios and Capital Budgets,” Review of Economics and Statistics 47 (1965): 13–37.
27 Fischer Black and Myron Scholes, “The Pricing of Options and Corporate Liabilities,” Journal of Political Economy 81 (1973): 637–654; and Robert C. Merton, “Theory of Rational Option Pricing,” Bell Journal of Economics and Management Science 4 (1973): 637–654.
28 Strictly speaking, these are American options. European options allow exercise only on the date of maturity. The Black–Scholes model applies to European options.
29 See the Appendix for the formula and the assumptions underlying it.
30 Phelim P. Boyle, “A Monte Carlo Approach to Options,” Journal of Financial Economics 4 (1977): 323–338.