During this session we extended the binomial tree methodology to the pricing of European Puts and American Options. Remember that it is never optimal to exercise before expiry an American Call (w/o dividends). However, it may be optimal to exercise an American put (w/o dividends).
We also reviewed Delta (how the premium of the option changes when the price of the underlying asset changes). We saw how to form a Delta Neutral position by hedging with options and what is the role of Delta when calculating the hedging ratio.
Have a look at the presentation here and to an example of Delta Neutral portfolio here.
Tuesday, October 21, 2014
Session 10 - Binomial trees
Remember: there are 3 basic ways to price options: closed formulas (like Black-Scholes), some kind of trees or Montecarlo simulations. During this class, we reviewed how to price a vanilla call with a binomial tree.
We assume a very simple world where the price of the underlying asset can only have two potential scenarios: up or down.
- First we expand the price of the underlying asset in the tree assuming a certain percentage for upward and downward movement.
- Then we price the option at the end of the tree. Given that we are at maturity, we can basically apply the formula for the payoff of the option (the outcome of exercising the option).
- We form a riskless portfolio by buying Delta shares and selling an option (a replicating portfolio). We calculate Delta making the portfolio riskless: it does not matter where the share goes, the value of my portfolio will always be the same.
- If the portfolio is riskless, we can bring it to present value using a risk-free rate. Now we know the value of the portfolio today and the value of the Delta shares today, so we can solve for the price of the option.
One important feature is that it does not matter what the real world probabilities are as we are working in a risk neutral world. In fact, a different way to price the option would be to solve for the expected value of the option using risk-neutral probabilities. The expected price for the share using this risk-neutral probabilities will be the forward.
We extended this methodology by increasing the number of branches in the tree.
Have a look at the presentation here and at the examples we saw in class here.
We assume a very simple world where the price of the underlying asset can only have two potential scenarios: up or down.
- First we expand the price of the underlying asset in the tree assuming a certain percentage for upward and downward movement.
- Then we price the option at the end of the tree. Given that we are at maturity, we can basically apply the formula for the payoff of the option (the outcome of exercising the option).
- We form a riskless portfolio by buying Delta shares and selling an option (a replicating portfolio). We calculate Delta making the portfolio riskless: it does not matter where the share goes, the value of my portfolio will always be the same.
- If the portfolio is riskless, we can bring it to present value using a risk-free rate. Now we know the value of the portfolio today and the value of the Delta shares today, so we can solve for the price of the option.
One important feature is that it does not matter what the real world probabilities are as we are working in a risk neutral world. In fact, a different way to price the option would be to solve for the expected value of the option using risk-neutral probabilities. The expected price for the share using this risk-neutral probabilities will be the forward.
We extended this methodology by increasing the number of branches in the tree.
Have a look at the presentation here and at the examples we saw in class here.
Sunday, October 12, 2014
Session 9 - Strategies with options
Session 8 - Basics on Options
At the very beginning of the session we had a look at Markets and we determined that EURUSD was moving a lot due to the recent activity in short-term interest rates in EUR and USD. This relationship is called the interest rate parity. I have prepared a chart with the following data: x = difference in implied yield for 2 year bond futures (US and EUR); y = EURUSD.
As you can see from R^2, the relationship is quite strong. The chart includes data from Jan-2011 until today.
According to the model, EURUSD should be trading at around 1.2961 given the current level of interest rates in EUR and US.
During this session we reviewed some basics on options. Remember, options provide a right to those who buy them and an obligation to those who sell them. They can be traded both in Exchanges and in OTC Markets.
We saw in class that options can be vanilla or exotic and we also saw that the premium of an option can be decomposed into Intrinsic Value (=payoff of the option) and Time Value (depends on volatility and other parameters).
We also had a look at put-call parity, a way to value option applying no-arbitrage assumptions.
The presentation can be found here.
As you can see from R^2, the relationship is quite strong. The chart includes data from Jan-2011 until today.
According to the model, EURUSD should be trading at around 1.2961 given the current level of interest rates in EUR and US.
During this session we reviewed some basics on options. Remember, options provide a right to those who buy them and an obligation to those who sell them. They can be traded both in Exchanges and in OTC Markets.
We saw in class that options can be vanilla or exotic and we also saw that the premium of an option can be decomposed into Intrinsic Value (=payoff of the option) and Time Value (depends on volatility and other parameters).
We also had a look at put-call parity, a way to value option applying no-arbitrage assumptions.
The presentation can be found here.
Friday, September 26, 2014
Session 7 - Derivatives - FRAs & Eurodollar Futures
During this class we learned what a zero-coupon rate is and how to calculate discount factors (have a look at the Excel file).
We also reviewed how to calculate forward discount factors and forward rates avoiding potential arbitrage opportunities. A forward rate is a rate to be applied to a forward starting loan/deposit. The idea behind this concept is that if I do a 1) 12m deposit or 2) a 6m deposit and I reinvest the proceeds in a new forward starting 6m deposit, the outcome should be the same.
Additionally, we had a look at how FRAs (Forward Rate Agreements) and Eurodollar Futures work.
The presentation can be found here.
We also reviewed how to calculate forward discount factors and forward rates avoiding potential arbitrage opportunities. A forward rate is a rate to be applied to a forward starting loan/deposit. The idea behind this concept is that if I do a 1) 12m deposit or 2) a 6m deposit and I reinvest the proceeds in a new forward starting 6m deposit, the outcome should be the same.
Additionally, we had a look at how FRAs (Forward Rate Agreements) and Eurodollar Futures work.
The presentation can be found here.
Saturday, September 20, 2014
Session 6 - Derivatives - 2014
During this session we reviewed how to price forwards on currencies. Please, have a look at the Excel file. The idea is exactly the same as with other asset classes: if the forward is too expensive (if the forward price should be 1.3062 and it is trading at 1.28 - I can buy less USD for the same amount of EUR), I will sell USD forward; if the forward is too cheap (if the forward price should be 1.3062 and it is trading at 1.32 - I can buy more USD for the same amount of EUR), I will buy USD forward. There is only one no-arbitrage possibility: F = S * e ^ (rd - rf).
Additionally, we had a look at how we should price forwards on consumption assets. In this case, we must take into account any potential convenience yield (for instance, to avoid shortages of the product that could affect our production line) and, also, any storage cost.
Remember the logic behind of the formula:
F = S * e ^ (+ any potential cost - any potential income)
The first day we buy/sell a Forward, the MTM of the position (value) is equal to zero. Remember we do not have to pay anything when we buy/sell a Forward. However, as time goes by and as the underlying asset and interest rates move, the MTM of the Forward will change. Basically, we will compare the price at which we can buy/sell at Maturity with the current Forward price and we will bring the difference to present value.
Finally, in spite of the fact that we will assume both Futures prices and Forward prices to be the same during the course, we reviewed why they are not (correlation between interest rates and price of the underlying asset, different interest rates, credit risk). You can find the presentation here.
Additionally, we had a look at how we should price forwards on consumption assets. In this case, we must take into account any potential convenience yield (for instance, to avoid shortages of the product that could affect our production line) and, also, any storage cost.
Remember the logic behind of the formula:
F = S * e ^ (+ any potential cost - any potential income)
The first day we buy/sell a Forward, the MTM of the position (value) is equal to zero. Remember we do not have to pay anything when we buy/sell a Forward. However, as time goes by and as the underlying asset and interest rates move, the MTM of the Forward will change. Basically, we will compare the price at which we can buy/sell at Maturity with the current Forward price and we will bring the difference to present value.
Finally, in spite of the fact that we will assume both Futures prices and Forward prices to be the same during the course, we reviewed why they are not (correlation between interest rates and price of the underlying asset, different interest rates, credit risk). You can find the presentation here.
Session 5 - Derivatives - 2014
We started this session reviewing how simple interest rates and compounded interest rates work. Remember that for this course we will use continous compounding (discount factor = e ^ (-r*T); future value = e ^ (r*T)). It is interesting to remember also how to work with Natural Logs. Remember that Ln e ^(r*T) = r*T.
When we value Futures, we consider an Eonia curve (Eonia is a riskless interest rate and Futures are riskless due to the margining process). When we value forwards, we consider a Euribor curve. Additionally, we would have to charge an additional spread that depends on the creditworthiness of the counterparty (CVA).
We valued Forward for an asset producing no income assuming a no-arbitrage hypothesis. If the forward is too expensive, we can sell (short) the forward and ask for a loan to buy the underlying asset. At maturity, we give the asset to the person who bought the forward from us and we make a riskless profit. So, if the forward is expensive, many arbitrageurs will enter into this strategy, taking the price of the forward down.
If the forward is too cheap, we buy the forwards and short the underlying asset. We will make a deposit with the amount that we obtain by shorting the asset. At maturity, we buy the asset from the person who sold us the forward and we give it back through the short contract. We would make a riskless profit. So, if the forward is cheap, many arbitrageurs will enter into this strategy, taking the price of the forward up.
The only possible value to avoid any potential arbitrage opportunity would be F = S*e ^ (r*T). Please review the Excel file. Khan Academy explains this potential arbitrage opportunity here and here.
We applied the same logic to assets producing a discrete income and to assets producing a yield. You can find the presentation here.
Tuesday, September 16, 2014
Change in classroom
From Monday 22nd September, we will have a new classroom on Mondays:
- Mondays: 12.30 - 14.30 - Class E301 (I usually join both sessions)
- Tuesdays: 13.00 - 14.30 - Class E306
Monday, September 15, 2014
Visit to MEFF - 20th October 2014 - 13:00
We will make a visit to MEFF on Monday 20th October 2014 at 13:00.
Those of you who would like to attend, please send me an email with your ID number.
Those of you who would like to attend, please send me an email with your ID number.
Friday, September 12, 2014
Session 4 - Derivatives - 2014
During this session we reviewed what type of dealers we can find in the Derivatives Markets (hedger, speculators, arbitrageurs) and we also had a look at how we could hedge with Futures. We gave an example of how a hedger/arbitrageur can become a speculator.
We focused on how to hedge a position. Hedging means buying or selling a financial instrument to offset potential losses/gains that may be incurred by a companion investment.
Usually, if the underlying asset of the Future and the asset that we want to hedge are the same, to determine the amount of contracts that we should buy/sell we should divide the amount (units) of the underlying asset that we want to hedge (in the example, 2,000,000 gallons of jet fuel) by the amount (units) of each contract (in the example, 42,000).
However, if the underlying asset of the Future and the asset that we want to hedge are not the same, we will have to do cross-hedging. When we cross-hedge, two questions arise:
1) What is the hedge ratio that we should apply to determine the number of contracts that we have to buy/sell?
- We use a linear regression where the variable to be explained (y) is the change in price of the asset that we want to hedge and the exogenous variable (x) is the change in price of the Future. With this analysis, we will determine how "y" moves when "x" moves.
- The hedge ratio will be equal to the beta parameter of the regression line (beta = correl. coef * sigma "y" / sigma "x"). Beta means how many units "y" moves when "x" moves by 1 unit.
- In our example, beta = 0.77 (meaning that when "x" moves by 1, "y" moves by 0.77). Then, the number of contracts that we will have to long (I am short the underlying asset, if prices go up, my P&L would be lower) would be 0.77 * 2MM / 42k.
2) How good will the hedge be?
- To determine how good the hedge will be, we must calculate R^2 (R^2 = (Covariance / (Sigma "y" * Sigma "x"))^2.
- Values above 0.75 should indicate that the hedge is quite good.
In the second part of the class, we reviewed how to extrapolate cross-hedging to hedge equity portfolios or single stocks with Futures on an Index.
Why would I want to hedge an equity portfolio?
Typically, if I am long an equity portfolio I would be convinced of the potential positive performance of the portfolio. Then, if I am thinking about hedging, maybe I should sell my portfolio and buy later... There are three reasons to hedge:
- Transaction costs (produced by selling and buying again) may be high.
- Hedging with a Future on an Index would eliminate systematic risk (market risk). I would only be exposed to the relative performance of the portfolio vs. the Index.
- The investment is designed for the long run, while I want to hedge the short run (maybe we are waiting for bad news).
The process of cross-hedging is very similar to the prevous case. First, we must determine the beta of the portfolio. To calculate the beta of the portfolio, we calculate a value-weighted average of the betas of the securities in the portfolio. The betas of the securities that compose the portfolio will be available in Reuters or Bloomberg as beta is a fundamental component of CAPM.
To hedge completely the portfolio, we should long/short a number of contracts equal to beta * Value of Portfolio / Euro Value of Future. Remember that to obtain the Euro Value of the Future we must use the Future multiplier. If I hedge completely my portfolio the beta of my new portfolio (old portfolio + Future) will be equal to zero (it does not matter how the market moves, my new portfolio will not move).
I can also change the beta of the portfolio (reduce/increase it). For instance, if the beta of my portfolio is 1.003 and I want to take it to 2, I will have to long a number of contracts equal to (Objective beta - Current beta) * Value of Portfolio / Euro Value of Future.
You can find the presentation used in class here. You can find the Excel file used in class here. You can find how beta minimizes the variance of the new portfolio here.
We focused on how to hedge a position. Hedging means buying or selling a financial instrument to offset potential losses/gains that may be incurred by a companion investment.
Usually, if the underlying asset of the Future and the asset that we want to hedge are the same, to determine the amount of contracts that we should buy/sell we should divide the amount (units) of the underlying asset that we want to hedge (in the example, 2,000,000 gallons of jet fuel) by the amount (units) of each contract (in the example, 42,000).
However, if the underlying asset of the Future and the asset that we want to hedge are not the same, we will have to do cross-hedging. When we cross-hedge, two questions arise:
1) What is the hedge ratio that we should apply to determine the number of contracts that we have to buy/sell?
- We use a linear regression where the variable to be explained (y) is the change in price of the asset that we want to hedge and the exogenous variable (x) is the change in price of the Future. With this analysis, we will determine how "y" moves when "x" moves.
- The hedge ratio will be equal to the beta parameter of the regression line (beta = correl. coef * sigma "y" / sigma "x"). Beta means how many units "y" moves when "x" moves by 1 unit.
- In our example, beta = 0.77 (meaning that when "x" moves by 1, "y" moves by 0.77). Then, the number of contracts that we will have to long (I am short the underlying asset, if prices go up, my P&L would be lower) would be 0.77 * 2MM / 42k.
2) How good will the hedge be?
- To determine how good the hedge will be, we must calculate R^2 (R^2 = (Covariance / (Sigma "y" * Sigma "x"))^2.
- Values above 0.75 should indicate that the hedge is quite good.
In the second part of the class, we reviewed how to extrapolate cross-hedging to hedge equity portfolios or single stocks with Futures on an Index.
Why would I want to hedge an equity portfolio?
Typically, if I am long an equity portfolio I would be convinced of the potential positive performance of the portfolio. Then, if I am thinking about hedging, maybe I should sell my portfolio and buy later... There are three reasons to hedge:
- Transaction costs (produced by selling and buying again) may be high.
- Hedging with a Future on an Index would eliminate systematic risk (market risk). I would only be exposed to the relative performance of the portfolio vs. the Index.
- The investment is designed for the long run, while I want to hedge the short run (maybe we are waiting for bad news).
The process of cross-hedging is very similar to the prevous case. First, we must determine the beta of the portfolio. To calculate the beta of the portfolio, we calculate a value-weighted average of the betas of the securities in the portfolio. The betas of the securities that compose the portfolio will be available in Reuters or Bloomberg as beta is a fundamental component of CAPM.
To hedge completely the portfolio, we should long/short a number of contracts equal to beta * Value of Portfolio / Euro Value of Future. Remember that to obtain the Euro Value of the Future we must use the Future multiplier. If I hedge completely my portfolio the beta of my new portfolio (old portfolio + Future) will be equal to zero (it does not matter how the market moves, my new portfolio will not move).
I can also change the beta of the portfolio (reduce/increase it). For instance, if the beta of my portfolio is 1.003 and I want to take it to 2, I will have to long a number of contracts equal to (Objective beta - Current beta) * Value of Portfolio / Euro Value of Future.
You can find the presentation used in class here. You can find the Excel file used in class here. You can find how beta minimizes the variance of the new portfolio here.
Wednesday, September 10, 2014
Session 3 - Derivatives - 2014
In today's session, we reviewed how Futures Markets work, how to define a Futures contract and what are its main characteristics, how the price of the Future moves in relation to the price of the underlying asset as expiry approaches and what arbitrage opportunities exist, how the margin process works and what is the intuition behind the margin calculator in MEFF and, finally, what is the main regulation affecting these markets.
Remember that margins are always calculated at a portfolio level.
You can find the presentation here.
You have access to the margin calculator and to a description of EMIR regulation in the links section of the blog.
Remember that margins are always calculated at a portfolio level.
You can find the presentation here.
You have access to the margin calculator and to a description of EMIR regulation in the links section of the blog.
Friday, September 5, 2014
Varia - things that I find interesting
- Traditionally, we've been taught that in Finance risk equals volatility (standard deviation). Have a look at the recent letter to investors from Howard Marks to have a slightly different view.
- Yesterday, the ECB more than satisfied market expectations by announcing a 10bp cut in all official rates (refi rate @ 0.05%, depo rate @ -0.20%, marginal lending rate @ 0.30% - now officially at their lower bound, so no further rate cuts will be delivered) and the introduction of two asset purchase programmes starting in October: the ABSPP (aimed at buying simple ABSs with underlying assets consisting of claims against the Euro area non-financial private sector) and the CBPP3 (designed to purchase euro-denominated covered bonds issued by EUR MFIs). We will comment on the implications of these decisions in the next class.
- Yesterday, the ECB more than satisfied market expectations by announcing a 10bp cut in all official rates (refi rate @ 0.05%, depo rate @ -0.20%, marginal lending rate @ 0.30% - now officially at their lower bound, so no further rate cuts will be delivered) and the introduction of two asset purchase programmes starting in October: the ABSPP (aimed at buying simple ABSs with underlying assets consisting of claims against the Euro area non-financial private sector) and the CBPP3 (designed to purchase euro-denominated covered bonds issued by EUR MFIs). We will comment on the implications of these decisions in the next class.
Wednesday, September 3, 2014
Session 2 - Derivatives - 2014
In this class we reviewed some basic concepts about Derivatives.
- Derivatives are financial instruments whose price depend on the price of an underlying asset. Derivatives can be traded in Exchange-Traded markets (standardized, collateralized) or in OTC markets (customized, usually non-collateralized).
- Futures/Forwards. Agreement to buy or sell an asset in the future at a certain price. Futures are traded in Exchange-Traded markets while Forwards are traded in OTC markets. They represent an obligation. They give you to possibility to bet on underlying asset going up (long - buy the contract) or on the underlying asset going down (short - sell the contract). We saw that they are usually quoted with two prices (high price - low price).
- Options. The offer the right to buy (Call) or sell (Put) the underlying asset at a certain price in the future. We reviewed some of their characteristics and the difference between plain vanilla and exotic option, American and European option...
- Finally, we saw some basic characteristics of IRS, CCS, CDS.
You can find the presentation here.
Maybe, you want to review what is a long position and a short position.
There was a question during the class regarding the difference between delivering the underlying asset on a specified date or on a range of dates. Have a look at the delivery period of this contract. The seller has a whole month to deliver the underlying asset.
Session 1 - Derivatives - 2014
Welcome to Derivatives 2014-2015!!!
Contact.
- The best way to contact me is through email: cueto.josemanuel at gmail.com. Please send me an email with your name saying that you are in my class so I can incorporate your address to the distribution list
- This blog (derivatives101.blogspot.com) will be used as a vehicle to convey any message to the class. I will post presentations, exercises, excel files, articles/papers that I find interesting...
- If you are going to be on exchange during this semester and you need to do the exam, please contact me ASAP.
- If you are going to be on exchange during this semester and you need to do the exam, please contact me ASAP.
Timetable.
- Mondays: 12.30 - 14.30 - Class E303 (I usually join both sessions)
- Tuesdays: 13.00 - 14.30 - Class E306
Evaluation.
- Exam: 60% (the exam will cover only what we review in class). You can have a look at the exams of previous years in the Blog.
- Group Project: 20%. The project will consist on investing 500.000€ in financial derivatives traded in MEFF. You will have to deliver 2 reports:
o In the first one, you will comment on your strategy (why you chose what you chose). You will have to explain what financial intermediaries you have chosen and what are the commissions and margins. You will have to make a presentation in class.
o In the final report, you will comment on the results of your strategy (MTM, greeks, etc.). You will have to make a presentation in class.
- Quizzes: 20%. There will be two quizzes at the end of each of the first two blocks (Futures/Forwards and Options).
Bibliography (the exam will cover only what we review in class).
- Options, Futures and Other Derivatives. John Hull. Pearson, 2011.
- Introducción A Los Mercados De Futuros Y Opciones. John Hull. Pearson, 2011.
- Paul Wilmott on Quantitative Finance. Paul Wilmott. John Wiley & Sons Ltd, 2006.
- An Introduction to the Mathematics of Financial Derivatives (Academic Press Advanced Finance). Salih N. Neftci . Academic Press Inc., 2000.
- Swaps and other derivatives. Richard R. Flavell. John Wiley & Sons Ltd, 2010.
- Counterparty Credit Risk and Credit Value Adjustment. Jon Gregory. John Wiley & Sons Ltd, 2012.
- My Life as a Quant: Reflections on Physics and Finance. Emanuel Derman. John Wiley & Sons Inc., 2004.
Agenda/Schedule.
- Intro to financial derivatives. What are they? What are they used for? What are the main types of derivatives and what are their pay-offs? In what Markets are they traded? What are the main underlying assets?
- Futures/Forwards (September). How can we hedge with a Future? What happens if the characteristics of the Future are not the same as those of the asset to be hedged? How do we value a Future (no-arbitrage)?
- Options (October). How do options work? How to value an options through binomial trees? What are the Greek Letters and what are they used for?
- Swaps (November). Interest Rate Swaps, Cross Currency Swaps and Credit Default Swaps.
Below you can find an extract of the 2002 Berkshire Hathaway's Letter to Investors. Warren Buffet gives his opinion on Financial Derivatives.
_______________________________
Derivatives
Charlie and I are of one mind in how we feel about derivatives and the trading activities that go with them: We view them as time bombs, both for the parties that deal in them and the economic system. Having delivered that thought, which I'll get back to, let me retreat to explaining derivatives, though the explanation must be general because the word covers an extraordinarily wide range of financial contracts.
Essentially, these instruments call for money to change hands at some future date, with the amount to be determined by one or more reference items, such as interest rates, stock prices or currency values. If, for example, you are either long or short an S&P 500 futures contract, you are a party to a very simple derivatives transaction – with your gain or loss derived from movements in the index. Derivatives contracts are of varying duration (running sometimes to 20 or more years) and their value is often tied to several variables.
Unless derivatives contracts are collateralized or guaranteed, their ultimate value also depends on the creditworthiness of the counterparties to them. In the meantime, though, before a contract is settled, the counterparties record profits and losses – often huge in amount – in their current earnings statements without so much as a penny changing hands.
The range of derivatives contracts is limited only by the imagination of man (or sometimes, so it seems, madmen). At Enron, for example, newsprint and broadband derivatives, due to be settled many years in the future, were put on the books. Or say you want to write a contract speculating on the number of twins to be born in Nebraska in 2020. No problem – at a price, you will easily find an obliging counterparty.
When we purchased Gen Re, it came with General Re Securities, a derivatives dealer that Charlie and I didn't want, judging it to be dangerous. We failed in our attempts to sell the operation, however, and are now terminating it. But closing down a derivatives business is easier said than done. It will be a great many years before we are totally out of this operation (though we reduce our exposure daily). In fact, the reinsurance and derivatives businesses are similar: Like Hell, both are easy to enter and almost impossible to exit. In either industry, once you write a contract – which may require a large payment decades later – you are usually stuck with it. True, there are methods by which the risk can be laid off with others. But most strategies of that kind leave you with residual liability.
Another commonality of reinsurance and derivatives is that both generate reported earnings that are often wildly overstated. That's true because today's earnings are in a significant way based on estimates whose inaccuracy may not be exposed for many years. Errors will usually be honest, reflecting only the human tendency to take an optimistic view of one's commitments. But the parties to derivatives also have enormous incentives to cheat in accounting for them. Those who trade derivatives are usually paid (in whole or part) on "earnings" calculated by mark-to-market accounting. But often there is no real market (think about our contract involving twins) and "mark-to-model" is utilized. This substitution can bring on large-scale mischief. As a general rule, contracts involving multiple reference items and distant settlement dates increase the opportunities for counterparties to use fanciful assumptions. In the twins scenario, for example, the two parties to the contract might well use differing models allowing both to show substantial profits for many years. In extreme cases, mark-to-model degenerates into what I would call mark-to-myth.
Of course, both internal and outside auditors review the numbers, but that's no easy job. For example, General Re Securities at yearend (after ten months of winding down its operation) had 14,384 contracts outstanding, involving 672 counterparties around the world. Each contract had a plus or minus value derived from one or more reference items, including some of mind-boggling complexity. Valuing a portfolio like that, expert auditors could easily and honestly have widely varying opinions. The valuation problem is far from academic: In recent years, some huge-scale frauds and near-frauds have been facilitated by derivatives trades. In the energy and electric utility sectors, for example, companies used derivatives and trading activities to report great "earnings" – until the roof fell in when they actually tried to convert the derivatives-related receivables on their balance sheets into cash. "Mark-to-market" then turned out to be truly "mark-to-myth."
I can assure you that the marking errors in the derivatives business have not been symmetrical. Almost invariably, they have favored either the trader who was eyeing a multi-million dollar bonus or the CEO who wanted to report impressive "earnings" (or both). The bonuses were paid, and the CEO profited from his options. Only much later did shareholders learn that the reported earnings were a sham.
Another problem about derivatives is that they can exacerbate trouble that a corporation has run into for completely unrelated reasons. This pile-on effect occurs because many derivatives contracts require that a company suffering a credit downgrade immediately supply collateral to counterparties. Imagine, then, that a company is downgraded because of general adversity and that its derivatives instantly kick in with their requirement, imposing an unexpected and enormous demand for cash collateral on the company. The need to meet this demand can then throw the company into a liquidity crisis that may, in some cases, trigger still more downgrades. It all becomes a spiral that can lead to a corporate meltdown.
Derivatives also create a daisy-chain risk that is akin to the risk run by insurers or reinsurers that lay off much of their business with others. In both cases, huge receivables from many counterparties tend to build up over time. (At Gen Re Securities, we still have $6.5 billion of receivables, though we've been in a liquidation mode for nearly a year.) A participant may see himself as prudent, believing his large credit exposures to be diversified and therefore not dangerous. Under certain circumstances, though, an exogenous event that causes the receivable from Company A to go bad will also affect those from Companies B through Z.
History teaches us that a crisis often causes problems to correlate in a manner undreamed of in more tranquil times. In banking, the recognition of a "linkage" problem was one of the reasons for the formation of the Federal Reserve System. Before the Fed was established, the failure of weak banks would sometimes put sudden and unanticipated liquidity demands on previously-strong banks, causing them to fail in turn. The Fed now insulates the strong from the troubles of the weak. But there is no central bank assigned to the job of preventing the dominoes toppling in insurance or derivatives. In these industries, firms that are fundamentally solid can become troubled simply because of the travails of other firms further down the chain. When a "chain reaction" threat exists within an industry, it pays to minimize links of any kind. That's how we conduct our reinsurance business, and it's one reason we are exiting derivatives.
Many people argue that derivatives reduce systemic problems, in that participants who can't bear certain risks are able to transfer them to stronger hands. These people believe that derivatives act to stabilize the economy, facilitate trade, and eliminate bumps for individual participants. And, on a micro level, what they say is often true. Indeed, at Berkshire, I sometimes engage in large-scale derivatives transactions in order to facilitate certain investment strategies.
Charlie and I believe, however, that the macro picture is dangerous and getting more so. Large amounts of risk, particularly credit risk, have become concentrated in the hands of relatively few derivatives dealers, who in addition trade extensively with one other. The troubles of one could quickly infect the others. On top of that, these dealers are owed huge amounts by non-dealer counterparties. Some of these counterparties, as I've mentioned, are linked in ways that could cause them to contemporaneously run into a problem because of a single event (such as the implosion of the telecom industry or the precipitous decline in the value of merchant power projects). Linkage, when it suddenly surfaces, can trigger serious systemic problems.
Indeed, in 1998, the leveraged and derivatives-heavy activities of a single hedge fund, Long-Term Capital Management, caused the Federal Reserve anxieties so severe that it hastily orchestrated a rescue effort. In later Congressional testimony, Fed officials acknowledged that, had they not intervened, the outstanding trades of LTCM – a firm unknown to the general public and employing only a few hundred people – could well have posed a serious threat to the stability of American markets. In other words, the Fed acted because its leaders were fearful of what might have happened to other financial institutions had the LTCM domino toppled. And this affair, though it paralyzed many parts of the fixed-income market for weeks, was far from a worst-case scenario. One of the derivatives instruments that LTCM used was total-return swaps, contracts that facilitate 100% leverage in various markets, including stocks. For example, Party A to a contract, usually a bank, puts up all of the money for the purchase of a stock while Party B, without putting up any capital, agrees that at a future date it will receive any gain or pay any loss that the bank realizes. Total-return swaps of this type make a joke of margin requirements. Beyond that, other types of derivatives severely curtail the ability of regulators to curb leverage and generally get their arms around the risk profiles of banks, insurers and other financial institutions. Similarly, even experienced investors and analysts encounter major problems in analyzing the financial condition of firms that are heavily involved with derivatives contracts. When Charlie and I finish reading the long footnotes detailing the derivatives activities of major banks, the only thing we understand is that we don't understand how much risk the institution is running.
The derivatives genie is now well out of the bottle, and these instruments will almost certainly multiply in variety and number until some event makes their toxicity clear. Knowledge of how dangerous they are has already permeated the electricity and gas businesses, in which the eruption of major troubles caused the use of derivatives to diminish dramatically. Elsewhere, however, the derivatives business continues to expand unchecked. Central banks and governments have so far found no effective way to control, or even monitor, the risks posed by these contracts.
Charlie and I believe Berkshire should be a fortress of financial strength – for the sake of our owners, creditors, policyholders and employees. We try to be alert to any sort of megacatastrophe risk, and that posture may make us unduly apprehensive about the burgeoning quantities of long-term derivatives contracts and the massive amount of uncollateralized receivables that are growing alongside. In our view, however, derivatives are financial weapons of mass destruction, carrying dangers that, while now latent, are potentially lethal.
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