of University California, San Diego
School of International Relations and Pacific Studies
Professor Bruce N. Lehmann
Risk Management
Office:
Phone:
E-mail:
Class Hours:
Office Hours:
Spring 2011
IRGN 419
1415 Robinson Building
534-0945
[e-mail]
8:00-9:20, Monday and Wednesday
11:30-12:30, Wednesday and by appointment
Recommended Text: Brealey, Richard A., Stewart C. Myers, and Franklin Allen, Principles of
Corporate Finance, 10th Edition (New York, NY:
McGrawHill/Irwin, 2011)
COURSE DESCRIPTION
This course provides an introduction to risk management using derivative assets, with particular
attention given to exchange-traded futures and options on bonds, stocks, and currencies. In order
to do so, I must answer the usual questions: who, what, where, why, when, and how. What is
especially tricky about these questions in this context is that some of the seemingly obvious
answers are not so obvious on deeper examination. In particular, who, why, and when can be
quite dicey while what, where, and how are straightforward given sufficient investment in the
necessary tools. Much of the course will be devoted to tool acquisition that is, to the what,
where, and how of risk management using derivatives but I will always strive to refocus
attention on the deeper questions throughout the course.
Derivative assets are different from other assets because their values devolve, in whole or in part,
from the value of the underlying assets against which they are written. Under some assumptions,
ones that are false but not entirely unreasonable, futures and option contracts can be valued using
only information on the price of the underlying asset, some of its risk characteristics, and other
market statistics such as interest rates. When these assumptions are false, it is still possible to
characterize the likely magnitude of the pricing errors. Put differently, futures and options can
be valued (almost) analytically, a situation that stands in stark contrast to the considerable
uncertainty surrounding bond and stock prices.
The arguments leading to the valuation of options and futures derive from the ability (under
some assumptions) to construct riskless hedges, the values of which are perfectly correlated with
the values of the associated derivative asset. That is, there are plausible assumptions under
which there are identifiable portfolios of riskless bonds and the underlying assets whose values
change one for one with in changes the values of the derivative security. This analytical tool
produces three collateral benefits: (1) a mechanism for determining derivative asset values, (2) a
procedure for hedging derivative securities or, equivalently, for constructing synthetic
derivatives, and (3) a clear description of the risks that can be hedged with them. These benefits
are of enormous importance in the real world, resulting in the explosive growth in an
extraordinary range of financial products that are transforming the way business firms and, for
that matter, individuals measure and manage risk.
This ability to value derivative assets (almost) analytically imposes a cost on students: the
mathematical barriers to entry are much higher for this course than for other finance courses like
introductory finance, corporate finance, and investments. For this reason (among others), I teach
the class very differently. The first two weeks will be devoted to the basics of risk management.
The remainder of the quarter will function (I hope) as in-class workshops that get at the core of
hedging with derivative assets as well as more advanced questions of derivative asset valuation.
The focus in these de facto workshops will be on the spreadsheets I have written that handle
hedging and valuation for a variety of derivatives and canonical risk management problems.
The course is based primarily on my lecture notes and the spreadsheets. Brealey, Myers, and
Allen can serve as a backup; the following outline maps the course to the chapters of that book.
Course Outline
Week 1:
Introduction to Risk Management
Brealey, Myers, and Allen: Chapter 26
Week 2:
The Basics of Derivative Asset Valuation and Hedging
Brealey, Myers, and Allen: Chapters 20 and 26
Week 3:
Hedging Interest Rate Risk
Brealey, Myers, and Allen: Chapters 3, 23, and 26
Week 4:
Hedging Interest Rate Risk for Pension Funds
Brealey, Myers, and Allen: Chapters 3, 23, and 26
Week 5:
Hedging Exchange Rate Risk
Brealey, Myers, and Allen: Chapter 27
Week 6:
Risk Management, Managerial Incentives, and Capital Structure
Brealey, Myers, and Allen: Chapter 24
Week 7:
The Binomial and Black-Scholes Models of Option Valuation
Brealey, Myers, and Allen: Chapter 21
Week 8:
Hedging with Options
Brealey, Myers, and Allen: Chapter 21
Week 9:
Value at Risk
Brealey, Myers, and Allen: Chapters 23 and 26
Week 10:
Modern Risk Management
Brealey, Myers, and Allen: Chapters 23 and 26