Liu on LTCM, Part II

[Les Schaffer <godzilla@xxxxxxxxxxxxxx>]

[part II from Henry Liu]


The main insight provided by Myron Scholes and Fischer Black in 1973
in creating the Black-Scholes model, the classic modern option pricing
model, was that the payoff profile of an option can be created
synthetically by combining a "dynamic" (i.e. continually adjusting)
portfolio consisting first of forward contracts on the underlying
property which is the subject of the option and a portfolio of
"riskless" (i.e. Treasury or other government) securities.

Consider the following. A US investor has US$1 million to invest and
if he were to buy a one year US Treasury security he would earn a rate
of 5.75%. In other words, at maturity he would receive his initial
investment of US$1 million back, together with US$57,500 in
interest. The same investor is, however, attracted by the higher
return he could obtain by buying a 1 year UK government security
instead. This security is, yielding 7% and so if at today's spot
foreign exchange rate of US$1.59/sterling, the US investor were to
sell US$1 million and acquire 628,931 sterling, this amount of
sterling invested for 1 year would yield the investor 44,025
sterling. However, at the maturity of his investment the US investor
will wish to exchange his sterling principal and interest for US
dollars. He is aware, though, of the uncertainty attaching to future
exchange rates and to protect himself against this he enters into an
agreement to sell his total sterling proceeds 1 year forward for US
dollars. The 1 year forward rate is $1.571/sterling which means that
the investor will receive US$1,057,500, a sum exactly equal to the
amount he would have received if he had not ventured into the foreign
arena at all -- in pursuit of higher interest rates -- but had
invested in US Treasury securities.

What the above example demonstrates is that differences in interest
rates for comparable risk-free assets denominated in different
currencies are already reflected in differences between spot and
forward exchange rates.  Put another way, the ratio of the forward
exchange rate to the spot exchange rate is a reflection of interest
rates in the two countries whose currencies are being compared. This
ratio, when expressed mathematically, is referred to as interest rate
parity, but -- to repeat -- the underlying principle can be expressed
quite simply: an investor should not be able to get different risk
free rates of interest in different countries once his investment
proceeds are converted into his domestic currency.

Forward exchange rates are not predictions of the level of current
exchange rates at various future dates. Forward exchange rates are
mathematically derived rates reflecting an arbitrage condition:
interest rate parity.  They are market implications, not predictions.

However, this is not quite the end of the story. If a forward exchange
rate is lower than the current or spot exchange rate, then that
currency is viewed as trading at a premium. Alternatively, if the
forward rate is greater than the spot rate, the currency is trading at
a discount. If the currency is trading at a premium, then the market
expects today, given existing market forces, that the particular
currency in question will be stronger in the future. The converse is
true if the currency is trading at a discount. However, these are
market implications, not predictions, implications that flow from
current information, knowledge and conditions. The forward exchange
rate reflects an arbitrage condition: it is the rate that eliminates
an arbitrage profit.

The one year forward interest rate in any currency must be such that
no arbitrage profit can be derived from investing for one year and
then re-investing for a second year as opposed to investing for two
years initially. The relationship of forward interest rates for
various different future periods is known as the forward yield curve,
a concept and expression that is of fundamental importance in terms of
understanding swaps and in valuing cashflows generally

Forward contracts are not, as contracts, generally traded. If they
have to be reversed or unwound, then the value of a forward contract
prior to maturity is taken to be the difference between the forward
price at which the contract was agreed initially and the forward price
that prevails in the market at the date on which the contract is
unwounded.

A forward foreign exchange contract, by definition, involves a
settlement at maturity which will result in a net cash outflow to one
counterparty and a net cash inflow to the other counterparty. There
is, therefore, credit risk associated with a forward contract. Two
aspects of this risk warrant further consideration.

First, the credit risk implicit in a forward contract can be expressed
as the risk that one party will perform, on the settlement date, the
obligations which the forward contract has imposed, relative to a
change in the value of the forward contract from zero. If during the
life of the forward contract spot prices continually mirror the
forward price on which the contract is based, then there is negligible
credit risk associated with the forward contract.  The greater the
deviation in spot prices from the forward price -- i.e. the greater
the volatility of spot prices -- the greater the credit risk implicit
in the swap because the more probable it becomes that one counterparty
will owe a large settlement amount to the other counterparty at the
maturity date of the contract.

Secondly, the forward contract is a "pure" credit instrument in the
sense that the only payment made under a forward contract is at its
maturity.  There are no payments made at the origination of the
contract and none made during the life of the contract. The risk,
therefore, that one party will not fulfill the settlement obligations
required of him under the contract exists throughout the life of the
contract and that risk increases the longer the maturity of the
contract.

The fact that significant credit risk attaches to forward contracts
has a major impact in determining who uses these instruments. Only
those counterparties -- large corporations, governments, other major
institutions and agencies, both financial and nonfinancial -- who have
access to big credit lines will use forward contracts. Individuals,
partnerships, small business, "start-up" operations and private
companies of limited size will not participate in the forward market
because the cost of obtaining the necessary credit lines -- if these
were obtainable at all, would be disproportionate to the benefits to
be derived from using forward contracts.

Forward contracts can be used potentially in any situation where a
measure of currency risk exists. Classic examples might be a
manufacturing company which is forced to pay for its raw materials in
a foreign currency, even though its finished products are priced in
its domestic currency, or an importer who is importing goods from a
parent company and paying for those goods in the currency of its
parent while pricing those goods in the currency of the country in
which a sales agency is held or in which unrelated agencies are
supplied by the importer.

Something more could usefully be said about the FRA (forward contract
on interest rates). Banks frequently "short fund": that is, their
assets are funded with interest bearing liabilities that have a
shorter maturity than the maturity of the assets being funded. In
periods of falling interest rates this strategy can produce
significant funding profits for banks (as in the 90s in Asia). Their
longer term assets are earning interest rates at a level reflecting a
previous and higher interest rate environment whereas their short term
liabilities are continually being refinanced at a reducing cost as
interest rates fall.

If, however, a bank believes that interest rates will rise, rather
than fall, in the future or if a bank believes that rates have fallen
as far as they are going to in the short term, the bank can protect
itself by using an FRA to fix today the future interest rate or rates
that it will pay on its funded liabilities.

Financial futures contracts are exchange traded contracts which date
from 1972 when foreign currency futures contracts were first
introduced. Futures contracts are now traded on currencies, on various
kinds of interest bearing securities (e.g. US T-notes and bonds, UK
gilts, eurodollar deposits, bonds) and on various equity or stock
indexes (e.g. S&P 500 index, NYSE composite index, FT 100 index,
Nikkei index). Major exchanges are the Chicago Board of Trade (CBOT),
the Chicago Mercantile (CME), the Tokyo Stock Exchange, the London
International Financial Futures Exchange (LIFFE) and the Paris Marche
a Terme d'Instrument Financiers (MATIF).

In terms of their basic structure, futures contracts and forward
contracts are identical: a futures contract is a binding obligation
under which a person either sells or buys a specified asset at a
specified exercise price on the contract maturity date. The specified
asset, the contract, is not literally bought and sold but the market
price of that contract at maturity compared to the contract price will
determine whether the holder of the futures contract has made a profit
or a loss.

Obvious, something went wrong.  But what did was not the Blak/Scholes
models, but the way the unit models were used without a super model
governing the whole picture.

Instead of hedging risks to others, many LTCM trades were actually
hedging to other LTCM trades.  That can happen when you are too big
and the left hand is unaware of what the right hand is doing, at least
in time to make a difference, especially when these trade are computer
executed within seconds before market inefficiencies return to
equalibrium.  It is not a predictive failure. It was a logic flaw
external to the B/S thesis.  The predictability of the future was not
an issue, although it is probably correct that the future is
unpredictable.

The paradigm shift was not that Russia defaulted on its bonds.  The
shift was the herd flight to quality caused by the Russian default and
LTCM's inability to disengage because of the size and extensiveness of
its positions.  The logic of the bailout was to provide enough new
funds to prevent LTCM positions from being forceibly liquidated, to
moderate the loss for a fire sale.  The prospect for the future was in
fact quite stable and it was the present that was in crisis.  The
bailout enable LTCM to fall back in line with the anticipated future.
The key point I wish to point out is that derivatives, while they deal
with the future, function as anchors to fix the future, eliminating
the need to predict it which by definition involves risk.  That is why
the pricing of options is market implications and not market
predictions.  In a way, current prices of shares are basically a
present value discount of aggregate future dividend flows (factoring
in future capital gains which may counteract near term negative cash
flow).

PS: For the official view see: Report of The President's Working Group
on Financial Markets, at:

http://www.cftc.gov/tm/hedgefundreport.htm


LTCM did not lose money by predicting that IBM will be $275.  Its
models said that if IBM rises or falls, AOL will move with it in the
same direction.  When the two stocks move out of sync, then a
convergence or divergence play is identified by the computer model.
ITCM trader then executes and wait for the return of equilibrium,
ususally within a short time span.  The got creamed because the
equilibrium did not return within the time frame of their trades.
LTCM strategies were sophisticated to the extend that when equilibrium
failed to occur, LTCM trade were still hedged by other compensatory
plays.  The trouble was that the compensatory trades were not
executable because they were mimiced within seconds by other traders.
The failures were all concurrent events. The future was not involved.
LTCM models said that no matter which way one slices a sausage, the
cross section come out within a certain range of oval. There problem
was that the sausage casing broke and loose meat came out instead of
slices. And another fatal error was that LTCM traders panicked was
started to override the computers to extend the unwinding periods into
weeks, hoping for a return of normalcy.  If they had stuck to the
models, the losses would have been managable.  LTCM investor began
withdrawing funds, because they sensed panic and did not want to be
supply their good money after bad.

Incidentally, the Merton/Scholes/Black formula is still in use
everyday in trades all the world.  Its validity had not been destroyed
by the LTCM fiasco.

Life is complex and it is composed of many components with different
functions.  Academic economists are engage in a search for truth,
policy economists are engaged in a search for operative rules of the
game, and market participants are engaged in playing the perfect game.
Each needs the others.  Truth is a manifestion of reality, and reality
is governed by a superstructure of rules which market participants
agree to observe in order the have a game.  But each component has a
related but decidedly different view of truth and reality.  A General
Theory is a statement of universal truth, a model is an algorithm to
beat the rules and the performance of the model become the reality.
There is constant feed back and adjustments in this process.  A
General Theory gives meaning, but it is next to useless as an
operational manual.  Policy makers are basically setting handicaps
with the aim of making the perfect rules so that the game always ends
with a draw.  Market participants strive to beat the rule without
violating them.  A general theorist knows that predicting the future
is futile, the policy maker tries to prevent the unthinkable or
unpleasant future and the market participant only hopes to be richer
at the end of each day.  As one character in the TNT series "Bull"
(Tuesdays 10pm) said: "If at the end of the day we have more money
than when we woke up that morning, then we've done opur job."  To the
market particiapant, his future is the next minute.  A piece of bogus
news release caused a compny's market capitalization to drop by $2.5
billion in 15 minutes, before the market caught on.

The future is not an abstact state.  It is an intergation of a
continuos sequential time inmcrement. The Calculus of time-events
makes the future predictable in theory, by considering each instant a
differentiation of continuum. Calculus is a mathematical method of
limiting the value of a function as a variable tends to approach
zero. The basic ideas concern continuity and limits.

Henry C.K. Liu