Overview

Arbitrage alone goes far to pin down asset prices, but not far enough. In order to obtain definite predictions, it is necessary to embed the arbitrage principle in a framework that imposes additional conditions on the observable pattern of prices.

Factor models, described in section 8.1, provide one such framework. These models postulate that asset prices – or, equivalently, rates of return – are linear functions of a small number of variables, the so-called ‘factors’. As such, factor models can be treated as explanations of asset prices in their own right, without any obligation to appeal to the arbitrage principle. But it will be argued in section 8.1, and also in chapter 9, that factor models are of limited explanatory power on their own. This is where arbitrage becomes useful.

The arbitrage pricing theory, analysed in section 8.2, applies the principles studied in the previous chapter to factor models. Here it is shown how, in an approximate but precise sense, arbitrage portfolios can be constructed when asset returns are assumed to be determined in accordance with a factor model. In the absence of arbitrage opportunities, these portfolios will yield zero payoffs (again, in an approximate but precise sense) in every eventuality. The upshot is a set of restrictions on asset prices (and, hence, rates of return) that are predicted to hold under the stated conditions.

Overview

The aims of this chapter are (a) to extend the analysis of futures markets with illustrations from non-commodity futures contracts; and (b) to study futures contracts for which the underlying asset is not an object that can easily be delivered – or, perhaps, is intangible and, thereby, impossible to deliver – when the contract matures. These contracts are essentially the same as commodity futures. Their specifications may at first sight, however, appear to be peculiar, especially with respect to the nature of the underlying asset, the process of contract settlement and, in some cases, the purposes of the strategies that make use of the contracts.

Much of the chapter focuses on financial futures contracts for which the underlying asset is a financial instrument that could (in principle, if not in fact) be delivered in fulfilment of the contract. The chapter begins, however, with an examination of weather futures contracts (section 16.1), for which ‘delivery’ of the underlying asset appears to be nonsensical.

Section 16.2 turns to financial futures with an outline of the characteristics of typical forms of these contracts. The following sections study three main sorts of financial futures contracts: (i) short-term interest rate futures (section 16.3); (ii) long-term interest rate (or, bond) futures (section 16.4); and (iii) stock index futures (section 16.5). Finally, section 16.6 illustrates the analysis of section 16.5 with a brief discussion of the failure of Barings Bank in late February 1995.

Overview

Bonds share attributes – described in the previous chapter – that make them suitable for treatment as a class separate from, for instance, equities. While they may constitute a separate class, bonds are not homogeneous. Of the dimensions relevant for distinguishing among bonds, the time to maturity is one of the most important. It is on the relationship between each bond's time to maturity and its rate of return that analysis of the term structure of interest rates focuses.

A common way of representing the term structure is as a yield curve that depicts the yields on different bonds as a function of the number of years to maturity. Section 13.1 studies the construction of yield curves for nominal bonds – those with payoffs fixed in units of money – illustrated with a yield curve for British government bonds. The illustration is pursued further in section 13.2, which presents a yield curve for index-linked bonds – those with payoffs adjusted to protect against inflation. Section 13.2 also reviews how estimates of expected future inflation rates can be obtained by comparing the yield curves for nominal and index-linked bonds.

Another way of expressing the term structure of interest rates is via a set of ‘implicit forward rates’ – interest rates that are implicit in, and can be inferred from, the prices of bonds with different maturities. Section 13.3 studies the role and interpretation of implicit forward rates.

Overview

Among all the assets available to investors, bonds are accorded a special status. Their distinctive characteristic is that bonds are low-risk assets. In some circumstances the risks can be ignored altogether. In others the risks can be quantified with a precision that is not available for most other assets, especially stocks and shares.

Consequently, the concept of the ‘yield’ on a bond can be more predictable, less uncertain than for other assets. Also, bonds share characteristics that enable them to be classified according to just a few dimensions, most importantly the time to maturity and the sequence of payments (typically fixed in advance) made in fulfilment of the bond contract.

Section 12.1 describes the main characteristics of bond contracts and outlines some examples of the bonds commonly found in practice. Although zero-coupon bonds are not among the commonest, they are key to an understanding of the links among all bonds. Their properties are studied in section 12.2. The properties of the more familiar coupon-paying bonds are studied in section 12.3, which also introduces an index of the responsiveness of a bond's price to its yield: the Macaulay duration.

Only for those bonds that are openly traded will market prices be readily observable. For others, including bonds that are traded infrequently (illiquid bonds), ways need to be devised for ascribing notional market values. One such method, suggested by the arbitrage principle, is discussed in section 12.4.

Overview

It is universally acknowledged that uncertainty is pervasive in everyday life and, hence, in economic decision making. What is not universally accepted, however, is how to explain decision making under uncertainty, all the candidate models being recognized as unrealistic for some reason or another. By their nature, of course, all models are abstractions and, in some degree, unrealistic. A particular difficulty with uncertainty is that every model proposed, up to the present, has been the target of penetrating criticism. That said, the expected utility hypothesis (EUH), outlined in section 4.2, remains the most popular approach to uncertainty in economics. Two close relatives of the EUH, also studied in this chapter, are: (a) the state-preference model, and (b) the mean-variance model.

The expected utility hypothesis can be interpreted as a special case of the state-preference model (though such an interpretation is not mandatory). Similarly, the mean-variance model (studied in section 4.4) can be interpreted as a special case of the EUH. Thus, the three approaches form a hierarchy, with state-preference being the most general and mean-variance the least. The reason why all three deserve consideration is simple: more general models are applicable to a broader range of phenomena but make fewer definite predictions; more special models apply more narrowly but make more definite (and, hence, testable) predictions.

Section 4.3 digresses from the main theme to review briefly some of the influential but less mainstream approaches to decision making under uncertainty.

Overview

Two of the main determinants of futures prices are speculation (explored in section 15.1) and hedging (section 15.2). Hedging, although associated with risk reduction, rarely succeeds in eliminating price risk entirely. Hence, section 15.3 pursues the analysis further by deriving the degree of hedging needed to minimize risk. Also in section 15.3, it is argued that speculation and hedging may not be so easy to distinguish as first appears. Section 15.4 draws together the motives for trading in futures contracts to offer an overview of the determination of futures prices. Finally, section 15.5 explores how unscrupulous traders can render futures markets vulnerable to manipulation.

Speculation

In chapter 14 the motives for trading in futures contracts were grouped into arbitrage, speculation and hedging. If futures contracts are treated as financial instruments, it may seem odd to analyse the investors' decisions about holding them from the perspective of separate motives (speculation, hedging and arbitrage). Such an approach contrasts with that of portfolio selection, in which the investor's preferences are represented by a single objective function. The investor's objective (usually expressed by an expected utility function or mean-variance trade-off) can, in principle, capture all the relevant motives for asset holding.

Speculation and hedging both involve risk and, hence, could be treated as applications of portfolio selection, or, more generally, of choice under uncertainty. Such an approach, while it yields insights, is sufficiently unconventional to be relegated to appendix 15.1.

Overview

Financial markets encompass a broad, continually evolving and not altogether clearly delimited collection of institutions, formal and informal, that serve to facilitate the exchange of assets. More to the point, the concept of an ‘asset’ is open to a variety of interpretations. Rather than get bogged down in arbitrary classifications – and in ultimately fruitless distinctions – the nature of ‘assets’ and the markets in which they are traded is allowed to emerge from examples. To place the examples in context, the chapter begins by reviewing, in section 1.1, the fundamental properties of financial systems, and identifies various sorts of capital market, several of which receive attention later in the book.

The main objective of this chapter is to outline the ideas that underpin explanations of asset prices and hence rates of return. Sections 1.2, 1.3 and 1.4 describe a framework for modelling asset price determination and comment on alternative approaches.

Central to an understanding of finance is the process of arbitrage. Arbitrage trading policies seek, essentially, to exploit price discrepancies among assets. Of more interest than the policies themselves are their unintended consequences, namely the implications they have for tying asset prices together in predictable patterns. The examples in section 1.5 serve to introduce arbitrage. Its consequences emerge in several places throughout the book.

Observers and analysts of capital markets frequently seek ways to appraise the performance of the markets.

Overview

An option contract provides its owner with the discretion to buy or to sell an underlying asset. A call option confers the discretion to buy the asset, while a put option confers the discretion to sell. Unlike futures contracts, where the owner must either offset the contract or make delivery at maturity, the owner of an option can simply let the contract expire; that is, the option can be thrown away. This is the crucial distinction between futures and options.

Options form a subset of a broader class of ‘contingent claims’ contracts – financial instruments the payoffs on which depend upon the payoffs of some other underlying asset. Thus, for stock options the option to buy or sell a unit of a company's equity depends, among other things, on the market value of the shares. Options are, perhaps, the most commonly encountered sort of contingent claim, but, as shown in chapter 19, the basic ideas can be applied more generally.

This chapter is the first of three that explore option contracts and the markets in which they are traded. Chapter 19 studies option price determination, while chapter 20 applies the principles to a variety of contracts found in financial markets.

Section 18.1 defines call and put options, outlines their main properties and introduces some notation. The most commonly studied option contracts are options to buy or sell the ordinary shares of a publicly traded company – i.e. equity options.

Overview

The extent to which asset prices in the future can be predicted on the basis of currently available information is a matter of great significance to practical investors as well as academic model builders. For academic researchers, the objectives are to obtain an understanding of the determination of prices and to find ways of assessing the efficiency of asset markets. For investors, the objective is to exploit their knowledge to obtain the best rates of return from their portfolios of assets.

The quest for profits implies, in an important though imprecise sense, that market prices should reflect all available information. If investors detect an opportunity to profit on the basis of information, then their actions (collectively, not necessarily in isolation) cause prices to change until the profit opportunity is eliminated. Considerations such as these motivate the famous martingale and random walk models studied in section 3.1.

Section 3.2 discusses much the same material, in the context of informational efficiency as introduced in chapter 1, while section 3.3 studies in more detail the differing patterns of information. Section 3.4 reviews several of the common asset market ‘anomalies’, so named because they are difficult to explain by conventional means and, hence, are often regarded as evidence of inefficiency.

Overview

Empirical work on the CAPM and APT has two main objectives: (i) to test whether or not the theories should be rejected; and (ii) to provide information that can aid financial decisions. The two aims are clearly complementary: only theories that are compatible with the evidence are likely to be helpful in making reliable decisions.

To accomplish objective (i), tests are conducted that could – potentially, at least – reject the model. The model is deemed to pass the test if it is not possible to reject the hypothesis that it is true. Such a methodology imposes a severe standard, for it is invariably possible to find evidence that contradicts the predictions of any testable economic theory. Hence, the methods of statistical inference need to be applied in order to draw sensible conclusions about just how far the data support the model. Definitive judgements are never possible in applied work. This need not be an excuse for despair but should serve as a counsel for cautious scepticism.

Tests are almost never as clear-cut as they at first seem. They are typically tests of joint hypotheses, so that care is necessary to recognize what is, or is not, being tested. Also, the relevant alternative to the hypothesis being tested often remains vague, or, even more commonly, is ignored. For example, if the CAPM is rejected, which theory is it rejected in comparison with? No simple answer may be available.

Overview

Options contracts are used in a multitude of different ways for different purposes. For example, an investor who plans to acquire shares in a company but considers that the current price is too high might choose to write put options on the shares. If the share price remains high during the life of the options, the options are not likely to be exercised and the investor pockets the option premium, without buying the shares. Alternatively, if the share price falls and the options are exercised against the investor, the shares are acquired, as the investor intended, at the exercise price. (In addition, the investor keeps the premium, of course.)

Rather than attempt to catalogue all these policies, this chapter studies several applications that illustrate different aspects of options analysis. Section 20.1 begins with a review of stock index options. Sections 20.2 and 20.3 introduce options on futures contracts, together with a variety of applications. In particular, section 20.3 explains how options on interest rate futures can be used to construct caps and floors on the effective interest rate for borrowing or lending.

Section 20.4 outlines how the inclusion of options in portfolios can mitigate the impact of uncertainty about future asset prices. Hedging, introduced in chapter 15, is re-examined using options (rather than futures) as hedge instruments.

A successful hedge reduces the risks associated with asset price fluctuations. It is not designed to reap the benefits of asset price increases while also protecting the investor against losses when asset prices fall.

Overview

In chapter 18 bounds were obtained on the range of option prices compatible with the absence of arbitrage opportunities. No attempt was made, however, to predict the level of an option price. This is the purpose of the present chapter. While attention concentrates throughout on the arbitrage principle, extra assumptions are required about the determinants of the underlying asset price in order to obtain the option price itself. Armed with these extra assumptions, the objective is to obtain a formula for an option price, where the arguments of the formula comprise a set of explanatory variables including, among other things, the option's exercise price and its time to expiry.

Very often the aim of the analysis is expressed in terms of determining the ‘fair’ option price, or of option ‘valuation’. This approach typically makes most sense for an over-the-counter option that is not exchange traded, where the goal is to calculate the option's price as if the option were openly traded in the absence of arbitrage opportunities – and together with the other assumptions needed to make the calculation. It should be obvious that the ‘fair’ price depends on the assumptions of a model, but in practice it is often overlooked that the computed value may well be sensitive to the model on which it is based.

Section 19.1 outlines the assumptions common to most option price theories and describes the method of analysis.

How can yet another book on finance be justified? The field is already well served with advanced works, many of impressive technical erudition. And, towards the other end of the academic spectrum, an abundance of mammoth texts saturates the MBA market. For the general reader, manuals confidently promising investment success compete with sensational diagnoses of financial upheavals to attract attention from the gullible, avaricious or unwary.

Alas, no one can expect to make a fortune as a consequence of reading this book. It has a more modest objective, namely to explore the economics of financial markets, at an ‘intermediate’ level – roughly that appropriate for advanced undergraduates. It is a work of exposition, not of original research. It unashamedly follows Keynes's immortal characterization of economic theory as ‘an apparatus of the mind, a technique of thinking’. Principles – rather than assertions of doctrine, policy pronouncements or institutional description – are the focus of attention. If the following chapters reveal no get-rich-quick recipes, they should at least demonstrate why all such nostrums merit unequivocal disbelief.

This book evolved, over more years than the author cares to admit, from lecture notes for a course in financial economics taught at the University of Essex. For reasons of space, one topic – corporate finance – has been omitted from the book, though its core insight – the Modigliani–Miller theorem – is slipped in under options (chapter 18, section 6).

Overview

Perhaps the commonest equation in the whole of finance is the one that sets the value of an asset equal to the net present value (or ‘present discounted value’) of a sequence of its payoffs. The equation plays a central role in corporate finance, where NPV criteria constitute the basis for the selection of investment projects. In particular, the NPV rule is applied to value assets (projects) the market prices of which may not be readily observed.

This chapter's objective is somewhat different from, though consistent with, that of corporate finance. Here the NPV relationship appears as a market equilibrium condition that has testable implications for observed asset prices.

In its simplest and most broadly applicable form, studied in section 10.1, the NPV relationship is a consequence of the arbitrage principle. In this sense it is nothing more than the extension of the results of chapter 7 to a multiperiod framework.

While central to financial theory, arbitrage ideas on their own tend to yield few predictions. Stronger assumptions – in particular about investors' expectations – permit predictions about asset price volatility to be derived. Section 10.2 reviews these assumptions and discusses the degree to which empirical evidence casts doubt on the validity of a theory commonly interpreted as expressing rational investor behaviour. By implication, doubt is also cast on asset market efficiency.

Section 10.3 explores other models, also motivated by the NPV, that seek to provide more empirically acceptable explanations of asset price volatility.

Introduction

This chapter serves as an introduction to Bayesian econometrics. Bayesian regression analysis has grown in a spectacular fashion since the publication of books by Zellner (1971) and Leamer (1978). Application to routine data analysis has also expanded enormously, greatly aided by revolutionary advances in computer hardware and software technology. In the light of such major developments, a single chapter can never do adequate justice to the many facets of this subject. This chapter therefore has the very modest goal of providing a rough road map to the major ideas and developments in Bayesian econometrics. Despite this modest objective some parts are still quite technical.

The Bayesian approach, unlike the likelihood or frequentist or classical approach presented in previous chapters, requires the specification of a probabilistic model of prior beliefs about the unknown parameters, given an initial specification of a model. Many researchers are uncomfortable about this step, both philosophically and practically. This has traditionally been the basis of the concern that the Bayesian approach is subjective rather than objective. It will be shown that in large samples the role of the prior may be negligible, that relatively uninformative priors can be specified, and that there are methods available for studying the sensitivity of inferences to priors. Therefore, the charge of subjectivity may not always be as serious as many claim.

Bayesian approaches play a potentially large role in applied microeconometrics, especially when dealing with complex models that lack analytically tractable likelihood functions.