# John Geanakoplos — Financial Theory (ECON 251) — Yale University — Videos

### About the Course

This course attempts to explain the role and the importance of the financial system in the global economy. Rather than separating off the financial world from the rest of the economy, financial equilibrium is studied as an extension of economic equilibrium. The course also gives a picture of the kind of thinking and analysis done by hedge funds.

### Course Structure

This Yale College course, taught on campus twice per week for 75 minutes, was recorded for Open Yale Courses in Fall 2009.

### Course Materials

Download all course pages [zip – 10MB]

Video and audio elements from this course are also available on:

### About Professor John Geanakoplos

John Geanakoplos is James Tobin Professor of Economics at Yale University. He received his Ph.D. in Economics from Harvard University in 1980. He has been Director of the Cowles Foundation for Research in Economics, co-Director of Hellenic Studies Program at Yale, chairman of the science steering committee at the Santa Fe Institute and Managing Director of Fixed Income Research at Kidder, Peabody & Co. Prizes he received include the Samuelson Prize (1999), and the Bodossaki Prize in economics (1994). He is a member of the American Academy of Arts and Sciences (since 1999) and was visiting professor at MSRI in the UC Berkeley, Churchill College, Cambridge, the University of Pennsylvania, Harvard, Stanford, and MIT. He was one of the founding partners of Ellington Capital Management, where he remains a partner. One of his current research topics is the leverage cycle.

## Syllabus

### Professor

John Geanakoplos, James Tobin Professor of Economics

### Description

This course attempts to explain the role and the importance of the financial system in the global economy. Rather than separating off the financial world from the rest of the economy, financial equilibrium is studied as an extension of economic equilibrium. The course also gives a picture of the kind of thinking and analysis done by hedge funds.

### Texts

Bodie, Zvi, and Robert C. Merton. *Finance,* Upper Saddle River, New Jersey: Prentice Hall, 2000.

Chance, Don M.* An Introduction to Derivatives,* 3rd edition, Fort Worth, Texas: The Dryden Press, Harcourt Brace College Publishers, 1995.

DeGroot, Morris H. *Probability and Statistics,* Reading, Massachusetts: Addison-Wesley Publishing Co., 1975.

Elton, Edwin J. and Martin J. Gruber.* Modern Portfolio Theory and Investment Analysis,* 5th edition, New York: John Wiley & Sons, Inc., 1995.

Fabozzi, Frank. *Handbook of Mortgage Backed Securities,* 6th edition, New York: McGraw-Hill, 2001.

Fabozzi, Frank J. *Handbook of Fixed Income Securities,* 6th edition, New York: McGraw-Hill, 2000.

Hull, John C. *Options, Futures, and Other Derivatives,* 5th edition, Upper Saddle River, New Jersey: Prentice Hall, 2002.

Jarrow, Robert and Stuart Turnbull.* Derivative Securities,* 2nd edition, Cincinatti, Ohio: South-Western College Publishing, 2000.

Luenberger, David G.* Investment Science,* New York: Oxford University Press, 1998.

Malkiel, Burton.* A Random Walk Down Wall Street*, New York: W.W. Norton, 1999.

Pliska, Stanley R.* Introduction to Mathematical Finance*. *Discrete Time Models,* Malden, Massachusetts: Blackwell Publishers, 1997.

Ross, Stephen, Randolph Westerfield, and Jeffrey Jaffe.* Corporate Finance*, New York: Irwin, McGraw Hill, 1999.

Sharpe, William F., Gordon J. Alexander, and Jeffery V. Bailey.* Investments,* 6th edition, Upper Saddle River, NJ: Prentice Hall, 1999.

Swensen, David F.* Pioneering Portfolio Management. An Unconventional Approach to Institutional Investment,* New York: The Free Press, 2000.

Taggart, Jr, Robert A.* Quantitative Analysis for Investment Management,* Upper Saddle River, New Jersey: Prentice Hall, 1996.

Tobin, James with Stephen Golub.* Money, Credit, and Capital,* Boston: Irwin-McGraw Hill, 1998.

### Requirements

*Math in the course*

Finance is a quantitative subject that can only be understood by solving concrete problems. But it uses mostly elementary mathematics. You need to be good at arithmetic (the distributive law is the basis for double entry bookkeeping), and be able to solve two or three simultaneous linear equations (x + y =10; x – y = 4. Solve for x and y). You must also be able to differentiate three elementary functions: dxn/dx =nxn-1; d ln x/dx = 1/x; deax/dx= aeax. The functions “log” and its inverse “exponential base e” are so important to finance because of continuous compounding of interest. Though they may be the most important functions in all of mathematics, they were discovered by bankers. You will also be taught how to use Excel.

*Course reading*

The textbook readings are meant to clarify or elaborate material presented in class, or to give you an idea of alternative presentations of the same material. For example, we might discuss bonds, how they pay, and how to value them. The readings might cover the specifics of particular bond markets (local, state, different countries), how they are taxed etc. There is no official textbook. In the past I have used*Corporate Finance*, by former Yale professor Steve Ross and two co-authors, and two others, by Sharpe and Merton, both Nobel Prize winners in economics (for contributions to financial economics). Their books were regarded as insufficiently quantitative, but might be useful to browse in. Another very good book is by Luenberger, but it is a little too advanced for this course. I have listed a dozen or so good alternatives and supplements, to give you an idea of where you could read more if you become interested. None of these is required. You should be able to follow the course simply by attending the lectures, reading the web notes, and doing the problem sets.

### Grading

Problem sets: 20%

Midterm exam 1: 20%

Midterm exam 2: 20%

Final Exam: 40%

# 1. Why Finance?

This lecture gives a brief history of the young field of financial theory, which began in business schools quite separate from economics, and of my growing interest in the field and in Wall Street. A cornerstone of standard financial theory is the efficient markets hypothesis, but that has been discredited by the financial crisis of 2007-09. This lecture describes the kinds of questions standard financial theory nevertheless answers well. It also introduces the leverage cycle as a critique of standard financial theory and as an explanation of the crisis. The lecture ends with a class experiment illustrating a situation in which the efficient markets hypothesis works surprisingly well.

00:00 – Chapter 1. Course Introduction

10:16 – Chapter 2. Collateral in the Standard Theory

17:54 – Chapter 3. Leverage in Housing Prices

33:47 – Chapter 4. Examples of Finance

46:13 – Chapter 5. Why Study Finance?

50:13 – Chapter 6. Logistics

58:22 – Chapter 7. A Experiment of the Financial Market

Complete course materials are available at the Yale Online website: online.yale.edu

# 2. Utilities, Endowments, and Equilibrium

This lecture explains what an economic model is, and why it allows for counterfactual reasoning and often yields paradoxical conclusions. Typically, equilibrium is defined as the solution to a system of simultaneous equations. The most important economic model is that of supply and demand in one market, which was understood to some extent by the Ancient Greeks and even by Shakespeare. That model accurately fits the experiment from the last class, as well as many other markets, such as the Paris Bourse, online trading, the commodities pit, and a host of others. The modern theory of general economic equilibrium described in this lecture extends that model to continuous quantities and multiple commodities. It is the bedrock on which we will build the model of financial equilibrium in subsequent lectures.

00:00 – Chapter 1. Introduction

07:04 – Chapter 2. Why Model?

13:30 – Chapter 3. History of Markets

24:41 – Chapter 4. Supply and Demand and General Equilibrium

37:59 – Chapter 5. Marginal Utility

45:20 – Chapter 6. Endowments and Equilibrium

Complete course materials are available at the Open Yale Courses website: http://open.yale.edu/courses

# 3. Computing Equilibrium

Financial Theory (ECON 251)

Our understanding of the economy will be more tangible and vivid if we can in principle explain all the economic decisions of every agent in the economy. This lecture demonstrates, with two examples, how the theory lets us calculate equilibrium prices and allocations in a simple economy, either by hand or using a computer. In future lectures we shall extend this method so as to compute equilibrium in financial economies with stocks and bonds and other financial assets.

00:00 – Chapter 1. Introduction

02:48 – Chapter 2. Welfare and Utility in Free Markets

16:52 – Chapter 3. Equilibrium amidst Consumption and Endowments

32:43 – Chapter 4. Anticipation of Prices

52:53 – Chapter 5. Log Utilities and Computer Models of Equilibrium

Complete course materials are available at the Open Yale Courses website: http://open.yale.edu/courses

# 4. Efficiency, Assets, and Time

Financial Theory (ECON 251)

Over time, economists’ justifications for why free markets are a good thing have changed. In the first few classes, we saw how under some conditions, the competitive allocation maximizes the sum of agents’ utilities. When it was found that this property didn’t hold generally, the idea of Pareto efficiency was developed. This class reviews two proofs that equilibrium is Pareto efficient, looking at the arguments of economists Edgeworth, and Arrow-Debreu. The lecture suggests that if a broadening of the economic model invalidated the sum of utilities justification of free markets, a further broadening might invalidate the Pareto efficiency justification of unregulated markets. Finally, Professor Geanakoplos discusses how Irving Fisher introduced two crucial ingredients of finance,–time and assets–into the standard economic equilibrium model.

00:00 – Chapter 1. Is the Free Market Good? A Mathematical Perspective

11:20 – Chapter 2. The Pareto Efficiency and Equilibrium

38:42 – Chapter 3. Fundamental Theorem of Economics

46:27 – Chapter 4. Shortcomings of the Fundamental Theorem

52:39 – Chapter 5. History of Mathematical Economics

01:00:21 – Chapter 6. Elements of Financial Models

Complete course materials are available at the Open Yale Courses website: http://open.yale.edu/courses

# 5. Present Value Prices and the Real Rate of Interest

Financial Theory (ECON 251)

Philosophers and theologians have railed against interest for thousands of years. But that is because they didn’t understand what causes interest. Irving Fisher built a model of financial equilibrium on top of general equilibrium (GE) by introducing time and assets into the GE model. He saw that trade between apples today and apples next year is completely analogous to trade between apples and oranges today. Similarly he saw that in a world without uncertainty, assets like stocks and bonds are significant only for the dividends they pay in the future, just like an endowment of multiple goods. With these insights Fisher was able to show that he could solve his model of financial equilibrium for interest rates, present value prices, asset prices, and allocations with precisely the same techniques we used to solve for general equilibrium. He concluded that the real rate of interest is a relative price, and just like any other relative price, is determined by market participants’ preferences and endowments, an insight that runs counter to the intuitions held by philosophers throughout much of human history. His theory did not explain the nominal rate of interest or inflation, but only their ratio.

00:00 – Chapter 1. Implications of General Equilibrium

03:08 – Chapter 2. Interest Rates and Stock Prices

22:06 – Chapter 3. Defining Financial Equilibrium

33:41 – Chapter 4. Inflation and Arbitrage

43:35 – Chapter 5. Present Value Prices

57:44 – Chapter 6. Real and Nominal Interest Rates

# 6. Irving Fisher’s Impatience Theory of Interest

Financial Theory (ECON 251)

Building on the general equilibrium setup solved in the last week, this lecture looks in depth at the relationships between productivity, patience, prices, allocations, and nominal and real interest rates. The solutions to three of Fisher’s famous examples are given: What happens to interest rates when people become more or less patient? What happens when they expect to receive windfall riches sometime in the future? And, what happens when wealth in an economy is redistributed from the poor to the rich?

00:00 – Chapter 1. From Financial to General Equilbrium

06:44 – Chapter 2. Applying the Principle of No Arbitrage

23:50 – Chapter 3. The Fundamental Theorem of Asset Pricing

39:25 – Chapter 4. Effects of Technology in Fisher Economy

51:31 – Chapter 5. The Impatience Theory of Interest

01:06:48 – Chapter 6. Conclusion

# 7. Shakespeare’s Merchant of Venice and Collateral, Present Value and the Vocabulary of Finance

Financial Theory (ECON 251)

While economists didn’t have a good theory of interest until Irving Fisher came along, and didn’t understand the role of collateral until even later, Shakespeare understood many of these things hundreds of years earlier. The first half of this lecture examines Shakespeare’s economic insights in depth, and sees how they sometimes prefigured or even surpassed Irving Fisher’s intuitions. The second half of this lecture uses the concept of present value to define and explain some of the basic financial instruments: coupon bonds, annuities, perpetuities, and mortgages.

00:00 – Chapter 1. Introduction

01:23 – Chapter 2. Contracts in Merchant of Venice

20:23 – Chapter 3. The Doubling Rule

36:07 – Chapter 4. Coupon Bonds, Annuities, and Perpetuities

54:24 – Chapter 5. Mortgage

59:15 – Chapter 6. Applications of Financial Instruments

# 8. How a Long-Lived Institution Figures an Annual Budget. Yield

In the 1990s, Yale discovered that it was faced with a deferred maintenance problem: the university hadn’t properly planned for important renovations in many buildings. A large, one-time expenditure would be needed. How should Yale have covered these expenses? This lecture begins by applying the lessons learned so far to show why Yale’s initial forecast budget cuts were overly pessimistic. In the second half of the class, we turn to the problem of measuring investment performance, and examine the strengths and weaknesses of various measures of yield, including yield-to-maturity and current yield.

00:00 – Chapter 1. Yale’s Budget Set

03:37 – Chapter 2. Analysis of Yale’s Expenditures and Endowment

31:51 – Chapter 3. Yield to Maturity and Internal Rate of Return

51:52 – Chapter 4. Assessing Performance of Coupon Bond

# 9. Yield Curve Arbitrage

Financial Theory (ECON 251)

Where can you find the market rates of interest (or equivalently the zero coupon bond prices) for every maturity? This lecture shows how to infer them from the prices of Treasury bonds of every maturity, first using the method of replication, and again using the principle of duality. Treasury bond prices, or at least Treasury bond yields, are published every day in major newspapers. From the zero coupon bond prices one can immediately infer the forward interest rates. Under certain conditions these forward rates can tell us a lot about how traders think the prices of Treasury bonds will evolve in the future.

00:00 – Chapter 1. Defining Yield

09:07 – Chapter 2. Assessing Market Interest Rate from Treasury Bonds

35:46 – Chapter 3. Zero Coupon Bonds and the Principle of Duality

50:31 – Chapter 4. Forward Interest Rate

01:10:05 – Chapter 5. Calculating Prices in the Future and Conclusion

# 10. Dynamic Present Value

Financial Theory (ECON 251)

In this lecture we move from present values to dynamic present values. If interest rates evolve along the forward curve, then the present value of the remaining cash flows of any instrument will evolve in a predictable trajectory. The fastest way to compute these is by backward induction. Dynamic present values help us understand the returns of various trading strategies, and how marking-to-market can prevent some subtle abuses of the system. They explain how mortgages work, why they’re called amortizing, and what is meant by the remaining balance. In the second half of the lecture we turn to an important application of present value thinking: an analysis of the troubles facing the Social Security system.

00:00 – Chapter 1. Dynamic Present Values

08:49 – Chapter 2. Marking to Market

39:53 – Chapter 3. Mortgages and Backward Induction

50:42 – Chapter 4. Remaining Balances and Amortization

54:52 – Chapter 5. Weaknesses in the U.S. Social Security System

# 11. Social Security

Financial Theory (ECON 251)

This lecture continues the analysis of Social Security started at the end of the last class. We describe the creation of the system in 1938 by Franklin Roosevelt and Frances Perkins and its current financial troubles. For many democrats Social Security is the most successful government program ever devised and for many Republicans Social Security is a bankrupt program that needs to be privatized. Is there any way to reconcile the views of Democrats and Republicans? How did the system get into so much financial trouble? We will see that the mess becomes quite clear when examined with the proper present value approach. Present value analysis reveals the flaws in the three most popular analyses of Social Security, that the financial breakdown is the fault of the baby boomers, that privatization would bring young investors a better return than they anticipate getting from their social security contributions, and that privatization is impossible without compromising today’s retired workers.

00:00 – Chapter 1. Introduction

03:53 – Chapter 2. The Development of the U.S. Social Security System

19:16 – Chapter 3. Economic Imbalances in Social Security

38:48 – Chapter 4. Root Causes of Income Transfer in Social Security

01:05:21 – Chapter 5. Privatization of U.S. Social Security

# 12. Overlapping Generations Models of the Economy

Financial Theory (ECON 251)

In order for Social Security to work, people have to believe there’s some possibility that the world will last forever, so that each old generation will have a young generation to support it. The overlapping generations model, invented by Allais and Samuelson but here augmented with land, represents such a situation. Financial equilibrium can again be reduced to general equilibrium. At first glance it would seem that the model requires a solution of an infinite number of supply equals demand equations, one for each time period. But by assuming stationarity, the whole analysis can be reduced to one equation. In this mathematical framework we reach an even more precise and subtle understanding of Social Security and the real rate of interest. We find that Social Security likely increases the real rate of interest. The presence of land, an infinitely lived asset that pays a perpetual dividend, forces the real rate of interest to be positive, exposing the flaw in Samuelson’s contention that Social Security is a giant, yet beneficial, Ponzi scheme where each generation can win by perpetually deferring a growing cost.

00:00 – Chapter 1. Introduction to the Overlapping Generation Model

12:59 – Chapter 2. Financial and General Equilibrium in Social Security

26:37 – Chapter 3. Present Value Analysis of Social Security

59:24 – Chapter 4. Real Rate of Interest and Social Security

# 13. Demography and Asset Pricing: Will the Stock Market Decline when the Baby Boomers Retire?

Financial Theory (ECON 251)

In this lecture, we use the overlapping generations model from the previous class to see, mathematically, how demographic changes can influence interest rates and asset prices. We evaluate Tobin’s statement that a perpetually growing population could solve the Social Security problem, and resolve, in a surprising way, a classical argument about the link between birth rates and the level of the stock market. Lastly, we finish by laying some of the philosophical and statistical groundwork for dealing with uncertainty.

00:00 – Chapter 1. Stationarity and Equilibrium in the Overlapping Generations Model

16:38 – Chapter 2. Evaluating Tobin’s Thoughts on Social Security

35:07 – Chapter 3. Birth Rates and Stock Market Levels

01:02:30 – Chapter 4. Philosophical and Statistical Framework of Uncertainty

# 14. Quantifying Uncertainty and Risk

Financial Theory (ECON 251)

Until now, the models we’ve used in this course have focused on the case where everyone can perfectly forecast future economic conditions. Clearly, to understand financial markets, we have to incorporate uncertainty into these models. The first half of this lecture continues reviewing the key statistical concepts that we’ll need to be able to think seriously about uncertainty, including expectation, variance, and covariance. We apply these concepts to show how diversification can reduce risk exposure. Next we show how expectations can be iterated through time to rapidly compute conditional expectations: if you think the Yankees have a 60% chance of winning any game against the Dodgers, what are the odds the Yankees will win a seven game series once they are up 2 games to 1? Finally we allow the interest rate, the most important variable in the economy according to Irving Fisher, to be uncertain. We ask whether interest rate uncertainty tends to make a dollar in the distant future more valuable or less valuable.

00:00 – Chapter 1. Expectation, Variance, and Covariance

19:06 – Chapter 2. Diversification and Risk Exposure

33:54 – Chapter 3. Conditional Expectation

53:39 – Chapter 4. Uncertainty in Interest Rates

# 15. Uncertainty and the Rational Expectations Hypothesis

Financial Theory (ECON 251)

According to the rational expectations hypothesis, traders know the probabilities of future events, and value uncertain future payoffs by discounting their expected value at the riskless rate of interest. Under this hypothesis the best predictor of a firm’s valuation in the future is its stock price today. In one famous test of this hypothesis, it was found that detailed weather forecasts could not be used to improve on contemporaneous orange prices as a predictor of future orange prices, but that orange prices could improve contemporaneous weather forecasts. Under the rational expectations hypothesis you can infer more about the odds of corporate or sovereign bonds defaulting by looking at their prices than by reading about the financial condition of their issuers.

00:00 – Chapter 1. The Rational Expectations Hypothesis

12:18 – Chapter 2. Dependence on Prices in a Certain World

24:42 – Chapter 3. Implications of Uncertain Discount Rates and Hyperbolic Discounting

46:53 – Chapter 4. Uncertainties of Default

On the other hand, when discount rates rather than payoffs are uncertain, today’s one year rate grossly overestimates the long run annualized rate. If today’s one year interest rate is 4%, and if the one year interest rate follows a geometric random walk, then the value today of one dollar in T years is described in the long run by the hyperbolic function 1/ √T, which is much larger than the exponential function 1/(1.04)T, no matter what the constant K. Hyperbolic discounting is the term used to describe the tendency of animals and humans to value the distant future much more than would be implied by (exponentially) discounting at a constant rate such as 4%. Hyperbolic discounting can justify expenses taken today to improve the environment in 500 years that could not be justified under exponential discounting.

# 16. Backward Induction and Optimal Stopping Times

Financial Theory (ECON 251)

In the first part of the lecture we wrap up the previous discussion of implied default probabilities, showing how to calculate them quickly by using the same duality trick we used to compute forward interest rates, and showing how to interpret them as spreads in the forward rates. The main part of the lecture focuses on the powerful tool of backward induction, once used in the early 1900s by the mathematician Zermelo to prove the existence of an optimal strategy in chess. We explore its application in a series of optimal stopping problems, starting with examples quite distant from economics such as how to decide when it is time to stop dating and get married. In each case we find that the option to continue is surprisingly valuable.

00:00 – Chapter 1. Calculating Default Probabilities

14:58 – Chapter 2. Relationship Between Defaults and Forward Rates

28:09 – Chapter 3. Zermelo, Chess, and Backward Induction

36:48 – Chapter 4. Optimal Stopping Games and Backward Induction

01:06:47 – Chapter 5. The Optimal Marriage Problem

# 17. Callable Bonds and the Mortgage Prepayment Option

This lecture is about optimal exercise strategies for callable bonds, which are bonds bundled with an option that allows the borrower to pay back the loan early, if she chooses. Using backward induction, we calculate the borrower’s optimal strategy and the value of the option. As with the simple examples in the previous lecture, the option value turns out to be very large. The most important callable bond is the fixed rate amortizing mortgage; calling a mortgage means prepaying your remaining balance. We examine how high bankers must set the mortgage rate in order to compensate for the prepayment option they give homeowners. Looking at data on mortgage rates we see that mortgage borrowers often fail to prepay optimally.

00:00 – Chapter 1. Introduction to Callable Bonds and Mortgage Options

12:14 – Chapter 2. Assessing Option Value via Backward Induction

42:44 – Chapter 3. Fixed Rate Amortizing Mortgage

57:51 – Chapter 4. How Banks Set Mortgage Rates for Prepayers

# 18. Modeling Mortgage Prepayments and Valuing Mortgages

Financial Theory (ECON 251)

A mortgage involves making a promise, backing it with collateral, and defining a way to dissolve the promise at prearranged terms in case you want to end it by prepaying. The option to prepay, the refinancing option, makes the mortgage much more complicated than a coupon bond, and therefore something that a hedge fund could make money trading. In this lecture we discuss how to build and calibrate a model to forecast prepayments in order to value mortgages. Old fashioned economists still make non-contingent forecasts, like the recent predictions that unemployment would peak at 8%. A model makes contingent forecasts. The old prepayment models fit a curve to historical data estimating how sensitive aggregate prepayments have been to changes in the interest rate. The modern agent based approach to modeling rationalizes behavior at the individual level and allows heterogeneity among individual types. From either kind of model we see that mortgages are very risky securities, even in the absence of default. This raises the question of how investors and banks should hedge them.

00:00 – Chapter 1. Review of Mortgages

03:20 – Chapter 2. Complications of Refinancing Mortgages

19:26 – Chapter 3. Non-contingent Forecasts of Mortgage Value

28:40 – Chapter 4. The Modern Behavior Rationalizing Model of Mortgage Value

54:07 – Chapter 5. Risk in Mortgages and Hedging

# 19. History of the Mortgage Market: A Personal Narrative

Professor Geanakoplos explains how, as a mathematical economist, he became interested in the practical world of mortgage securities, and how he became the Head of Fixed Income Securities at Kidder Peabody, and then one of six founding partners of Ellington Capital Management. During that time Kidder Peabody became the biggest issuer of collateralized mortgage obligations, and Ellington became the biggest mortgage hedge fund. He describes securitization and trenching of mortgage pools, the role of investment banks and hedge funds, and the evolution of the prime and subprime mortgage markets. He also discusses agent based models of prepayments in the mortgage market.

00:00 – Chapter 1. Fannie Mae, Freddie Mac, and the Mortgage Securities Market

17:01 – Chapter 2. Collateralized Mortgage Obligations

22:44 – Chapter 3. Modeling Prepayment Tendencies at Kidder Peabody

35:40 – Chapter 4. The Rise of Ellington Capital Management and the Role of Hedge Funds

52:52 – Chapter 5. The Leverage Cycle and the Subprime Mortgage Market

01:13:51 – Chapter 6. The Credit Default Swap

01:18:36 – Chapter 7. Conclusion

# 20. Dynamic Hedging

Suppose you have a perfect model of contingent mortgage prepayments, like the one built in the previous lecture. You are willing to bet on your prepayment forecasts, but not on which way interest rates will move. Hedging lets you mitigate the extra risk, so that you only have to rely on being right about what you know. The trouble with hedging is that there are so many things that can happen over the 30 year life of a mortgage. Even if interest rates can do only two things each year, in 30 years there are over a billion interest rate scenarios. It would seem impossible to hedge against so many contingencies. The principle of dynamic hedging shows that it is enough to hedge yourself against the two things that can happen next year (which is far less onerous), provided that each following year you adjust the hedge to protect against what might occur one year after that. To illustrate the issue we reconsider the World Series problem from a previous lecture. Suppose you know the Yankees have a 60% chance of beating the Dodgers in each game and that you can bet any amount at 60:40 odds on individual games with other bookies. A naive fan is willing to bet on the Dodgers winning the whole Series at even odds. You have a 71% chance of winning a bet against the fan, but bad luck can cause you to lose anyway. What bets on individual games should you make with the bookies to lock in your expected profit from betting against the fan on the whole Series?

00:00 – Chapter 1. Fundamentals of Hedging

15:38 – Chapter 2. The Principle of Dynamic Hedging

24:26 – Chapter 3. How Does Hedging Generate Profit?

43:48 – Chapter 4. Maintaining Profits from Dynamic Hedging

54:08 – Chapter 5. Dynamic Hedging in the Bond Market

01:10:30 – Chapter 6. Conclusion

# 21. Dynamic Hedging and Average Life

Financial Theory (ECON 251)

This lecture reviews the intuition from the previous class, where the idea of dynamic hedging was introduced. We learn why the crucial idea of dynamic hedging is marking to market: even when there are millions of possible scenarios that could come to pass over time, by hedging a little bit each step of the way, the number of possibilities becomes much more manageable. We conclude the discussion of hedging by introducing a measure for the average life of a bond, and show how traders use this to figure out the appropriate hedge against interest rate movements.

00:00 – Chapter 1. Review of Dynamic Hedging

09:15 – Chapter 2. Dynamic Hedging as Marking-to-Market

19:55 – Chapter 3. Dynamic Hedging and Prepayment Models in the Market

30:50 – Chapter 4. Appropriate Hedges against Interest Rate Movements

01:05:15 – Chapter 5. Measuring the Average Life of a Bond

# 22. Risk Aversion and the Capital Asset Pricing Theorem

Financial Theory (ECON 251)

Until now we have ignored risk aversion. The Bernoulli brothers were the first to suggest a tractable way of representing risk aversion. They pointed out that an explanation of the St. Petersburg paradox might be that people care about expected utility instead of expected income, where utility is some concave function, such as the logarithm. One of the most famous and important models in financial economics is the Capital Asset Pricing Model, which can be derived from the hypothesis that every agent has a (different) quadratic utility. Much of the modern mutual fund industry is based on the implications of this model. The model describes what happens to prices and asset holdings in general equilibrium when the underlying risks can’t be hedged in the aggregate. It turns out that the tools we developed in the beginning of this course provide an answer to this question.

00:00 – Chapter 1. Risk Aversion

03:35 – Chapter 2. The Bernoulli Explanation of Risk

12:38 – Chapter 3. Foundations of the Capital Asset Pricing Model

22:15 – Chapter 4. Accounting for Risk in Prices and Asset Holdings in General Equilibrium

54:11 – Chapter 5. Implications of Risk in Hedging

01:09:40 – Chapter 6. Diversification in Equilibrium and Conclusion

# 23. The Mutual Fund Theorem and Covariance Pricing Theorems

Financial Theory (ECON 251)

This lecture continues the analysis of the Capital Asset Pricing Model, building up to two key results. One, the Mutual Fund Theorem proved by Tobin, describes the optimal portfolios for agents in the economy. It turns out that every investor should try to maximize the Sharpe ratio of his portfolio, and this is achieved by a combination of money in the bank and money invested in the “market” basket of all existing assets. The market basket can be thought of as one giant index fund or mutual fund. This theorem precisely defines optimal diversification. It led to the extraordinary growth of mutual funds like Vanguard. The second key result of CAPM is called the covariance pricing theorem because it shows that the price of an asset should be its discounted expected payoff less a multiple of its covariance with the market. The riskiness of an asset is therefore measured by its covariance with the market, rather than by its variance. We conclude with the shocking answer to a puzzle posed during the first class, about the relative valuations of a large industrial firm and a risky pharmaceutical start-up.

00:00 – Chapter 1. The Mutual Fund Theorem

03:47 – Chapter 2. Covariance Pricing Theorem and Diversification

25:19 – Chapter 3. Deriving Elements of the Capital Asset Pricing Model

40:25 – Chapter 4. Mutual Fund Theorem in Math and Its Significance

52:36 – Chapter 5. The Sharpe Ratio and Independent Risks

01:04:19 – Chapter 6. Price Dependence on Covariance, Not Variance

# 24. Risk, Return, and Social Security

Financial Theory (ECON 251)

This lecture addresses some final points about the CAPM. How would one test the theory? Given the theory, what’s the right way to think about evaluating fund managers’ performance? Should the manager of a hedge fund and the manager of a university endowment be judged by the same performance criteria? More generally, how should we think about the return differential between stocks and bonds? Lastly, looking back to the lectures on Social Security earlier in the semester, how should the CAPM inform our thinking about the role of stocks and bonds in Social Security? Can the views of Democrats and Republicans be reconciled? What if Social Security were privatized, but workers were forced to hold their assets in a new kind of asset called PAAWS, which pay the holder more if the wage of young workers is higher?

00:00 – Chapter 1. Testing the Capital Asset Pricing Model

14:08 – Chapter 2. Evaluation of Fund Management Performance Using CAPM

22:30 – Chapter 3. Reassessing Assets within Social Security

53:04 – Chapter 4. Reconciling Democratic and Republican Views on Social Security

59:32 – Chapter 5. Geanakoplos’s Personal Annuitized Average Wage Securities

01:08:48 – Chapter 6. The Black-Scholes Model

# 25. The Leverage Cycle and the Subprime Mortgage Crisis

Standard financial theory left us woefully unprepared for the financial crisis of 2007-09. Something is missing in the theory. In the majority of loans the borrower must agree on an interest rate and also on how much collateral he will put up to guarantee repayment. The standard theory presented in all the textbooks ignores collateral. The next two lectures introduce a theory of the Leverage Cycle, in which default and collateral are endogenously determined. The main implication of the theory is that when collateral requirements get looser and leverage increases, asset prices rise, but then when collateral requirements get tougher and leverage decreases, asset prices fall. This stands in stark contrast to the fundamental value theory of asset pricing we taught so far. We’ll look at a number of facts about the subprime mortgage crisis, and see whether the new theory offers convincing explanations.

00:00 – Chapter 1. Assumptions on Loans in the Subprime Mortgage Market

18:27 – Chapter 2. Market Weaknesses Revealed in the 2007-2009 Financial Crisis

29:00 – Chapter 3. Collateral and Introduction to the Leverage Cycle

38:53 – Chapter 4. Contrasts between the Leverage Cycle and CAPM

43:36 – Chapter 5. Leverage Cycle Theory in Recent Financial History

01:03:55 – Chapter 6. Negative Implications of the Leverage Cycle

01:14:14 – Chapter 7. Conclusion

# 26. The Leverage Cycle and Crashes

Financial Theory (ECON 251)

In order to understand the precise predictions of the Leverage Cycle theory, in this last class we explicitly solve two mathematical examples of leverage cycles. We show how supply and demand determine leverage as well as the interest rate, and how impatience and volatility play crucial roles in setting the interest rate and the leverage. Mathematically, the model helps us identify the three key elements of a crisis. First, scary bad news increases uncertainty. Second, leverage collapses. Lastly, the most optimistic people get crushed, so the new marginal buyers are far less sanguine about the economy. The result is that the drop in asset prices is amplified far beyond what any market participant would expect from the news alone. If we want to mitigate the fallout from a crisis, the place to begin is in controlling those three elements. If we want to prevent leverage cycle crashes, we must monitor leverage and regulate it, the same way we monitor and adjust interest rates.

00:00 – Chapter 1. Introduction

02:15 – Chapter 2. Understanding Leverage

13:45 – Chapter 3. Supply and Demand Effects on Interest Rates and Leverage

21:52 – Chapter 4. Impatience and Volatility on Setting Leverage

34:48 – Chapter 5. Bad News, Pessimism, Price Drops, and Leverage Cycle Crashes

48:01 – Chapter 6. Can Leverage Be Monitored?

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