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The material on credit value adjustment (CVA) and debit value adjustment (DVA) has been restructured and improved (see Chapter 20).

      8. A new simpler method for taking volatility changes into account in the historical simulation method is presented (Chapter 13).

      9. There are many new end-of-chapter problems.

      10. A great deal of software on the author's website accompanies the book.

      SLIDES

      Several hundred PowerPoint slides can be downloaded from my website or from the Wiley Higher Education website. Adopting instructors are welcome to adapt the slides to meet their own needs.

      QUESTIONS AND PROBLEMS

      End-of-chapter problems are divided into two groups: “Practice Questions and Problems” and “Further Questions.” Solutions to the former are at the end of the book. Solutions to the latter and accompanying software are available to adopting instructors from the Wiley Higher Education website.

      INSTRUCTOR'S MANUAL

      The instructor’s manual is made available to adopting instructors on the Wiley Higher Education website. It contains solutions to “Further Questions” (with Excel spreadsheets), notes on the teaching of each chapter, and some suggestions on course organization.

      ACKNOWLEDGMENTS

      Many people have played a part in the production of this book. I have benefited from interactions with many academics and practicing risk managers. I would like to thank the students in my MBA and Master of Finance risk management courses at University of Toronto, many of whom have made suggestions as to how the material could be improved.

      Alan White, a colleague at the University of Toronto, deserves a special acknowledgment. Alan and I have been carrying out joint research and consulting in the area of derivatives and risk management for about 30 years. During that time we have spent countless hours discussing key issues. Many of the new ideas in this book, and many of the new ways used to explain old ideas, are as much Alan’s as mine. Alan has done most of the development work on the DerivaGem software.

      Special thanks are due to many people at Wiley, particularly Evan Burton, Vincent Nordhaus, Judy Howarth, and Helen Cho for their enthusiasm, advice, and encouragement.

      I welcome comments on the book from readers. My e-mail address is:

[email protected]

      JOHN HULL

      Joseph L. Rotman School of Management

      University of Toronto

      CHAPTER 1

      Introduction

      Imagine you are the Chief Risk Officer (CRO) of a major corporation. The Chief Executive Officer (CEO) wants your views on a major new venture. You have been inundated with reports showing that the new venture has a positive net present value and will enhance shareholder value. What sort of analysis and ideas is the CEO looking for from you?

      As CRO it is your job to consider how the new venture fits into the company's portfolio. What is the correlation of the performance of the new venture with the rest of the company's business? When the rest of the business is experiencing difficulties, will the new venture also provide poor returns, or will it have the effect of dampening the ups and downs in the rest of the business?

      Companies must take risks if they are to survive and prosper. The risk management function's primary responsibility is to understand the portfolio of risks that the company is currently taking and the risks it plans to take in the future. It must decide whether the risks are acceptable and, if they are not acceptable, what action should be taken.

      Most of this book is concerned with the ways risks are managed by banks and other financial institutions, but many of the ideas and approaches we will discuss are equally applicable to nonfinancial corporations. Risk management has become progressively more important for all corporations in the last few decades. Financial institutions in particular are finding they have to increase the resources they devote to risk management. Large “rogue trader” losses such as those at Barings Bank in 1995, Allied Irish Bank in 2002, Société Générale in 2007, and UBS in 2011 would have been avoided if procedures used by the banks for collecting data on trading positions had been more carefully developed. Huge subprime losses at banks such as Citigroup, UBS, and Merrill Lynch would have been less severe if risk management groups had been able to convince senior management that unacceptable risks were being taken.

      This opening chapter sets the scene. It starts by reviewing the classical arguments concerning the risk-return trade-offs faced by an investor who is choosing a portfolio of stocks and bonds. It then considers whether the same arguments can be used by a company in choosing new projects and managing its risk exposure. The chapter concludes that there are reasons why companies – particularly financial institutions – should be concerned with the total risk they face, not just with the risk from the viewpoint of a well-diversified shareholder.

      1.1 RISK VS. RETURN FOR INVESTORS

      As all fund managers know, there is a trade-off between risk and return when money is invested. The greater the risks taken, the higher the return that can be realized. The trade-off is actually between risk and expected return, not between risk and actual return. The term “expected return” sometimes causes confusion. In everyday language an outcome that is “expected” is considered highly likely to occur. However, statisticians define the expected value of a variable as its average (or mean) value. Expected return is therefore a weighted average of the possible returns, where the weight applied to a particular return equals the probability of that return occurring. The possible returns and their probabilities can be either estimated from historical data or assessed subjectively.

Suppose, for example, that you have $100,000 to invest for one year. Suppose further that Treasury bills yield 5 %.1 One alternative is to buy Treasury bills. There is then no risk and the expected return is 5 %. Another alternative is to invest the $100,000 in a stock. To simplify things, we suppose that the possible outcomes from this investment are as shown in Table 1.1. There is a 0.05 probability that the return will be +50 %; there is a 0.25 probability that the return will be +30 %; and so on. Expressing the returns in decimal form, the expected return per year is:

      This shows that in return for taking some risk you are able to increase your expected return per annum from the 5 % offered by Treasury bills to 10 %. If things work out well, your return per annum could be as high as 50 %. But the worst-case outcome is a −30 % return or a loss of $30,000.

TABLE 1.1 Return in One Year from Investing $100,000 in a Stock

      One of the first attempts to understand the trade-off between risk and expected return was by Markowitz (1952). Later, Sharpe (1964) and others carried the Markowitz analysis a stage further by developing what is known as the capital asset pricing model. This is a relationship between expected return and what is termed “systematic risk.” In 1976, Ross developed the arbitrage pricing theory which can be viewed as an extension of the capital asset pricing model to the situation where there are several sources of systematic risk. The key insights of these researchers have had a profound effect on the way portfolio managers think about and analyze the risk-return trade-offs that they face. In this section we review these insights.

      Quantifying Risk

      How do you quantify the risk you are taking when you choose an investment? A convenient measure that is often used is the standard deviation of the return over one year. This is

      where R is the return per annum. The symbol E denotes expected value so that E(R) is the expected return per annum. In Скачать книгу