7.6Market Frictions and Lessons from the Fate of Long-Term

Capital Management

The valuation models discussed in this chapter assume that a portfolio can be formed

that perfectly tracks the cash outflows and inflows of the derivative security being eval-

uated. However, this is not the same as perfectly tracking the valueof a derivative secu-

rity at all points in time in the future. Usually, it is impossible to perfectly track the

valueof a mispricedderivative security at all future dates before the derivative secu-

rity terminates. At least in theory, and perhaps in most cases, this is not a terribly rel-

evant consideration. Amispriced derivative that does not immediately converge to its

no-arbitrage value provides an opportunity to earn additional arbitrage profits, using

the tracking portfolio strategy outlined in this chapter.

An exception occurs when the arbitrageur has limited financial resources, and when

price changes can have cash flow implications.³⁰This is, indeed, the lesson of Long-

Term Capital Management’s (LTCM) demise. (See the opening vignette of this chap-

ter.) To illustrate this point, let’s take a simple example that does not involve deriva-

tives. Suppose that there are two zero-coupon bonds, Bond Aand Bond B, each paying

$1 million one year from now. Thus, these bonds generate a single future cash inflow

of $1 million to anyone who buys them. If Bond Acurrently sells for $900,000 and

Bond B sells for $910,000, Bond Ais underpriced relative to Bond B. It is thus pos-

sible to earn $10,000 in arbitrage profits simply by acquiring Bond Aand short selling

Bond B. This is an oversimplification of the kind of strategy that LTCM might have

engaged in. In a market without frictions, next week’s value would not be very rele-

vant to the effectiveness of the arbitrage. For example, if Bond B’s value appreciated

to $920,000, while Bond A’s value declined to $890,000, there would be a $20,000

paper loss in the portfolio position. However, as long as the positions were held for the

long term, there would be no cash flow ramifications. Indeed, next week, one could

replicate the same arbitrage position, capturing an additional $30,000 in arbitrage prof-

its, the spread between the $920,000 price of shorted Bond B and acquired Bond A.

Suppose, however, that the broker who holds custody of these positions on behalf

of LTCM requires them to mark the positions to market, much as a futures contract is

marked to market (see the last section). In this case, as the spread between the prices

of Bonds B and Awidens from $10,000 to $30,000 over the course of the next week,

the investor has to post an additional $20,000. This is a cash outflow that prevents per-

fect tracking between the future cash flows of Bonds Aand B.

These cash flow implications, which can be a nuisance when an additional $20,000

is needed, can become a major problem if an additional $20 million is needed. This

was part of the predicament faced by LTCM. Their positions were leveraged to mag-

nitudes that required major institutional financing. If they could not come up with the

necessary capital, they would be forced to liquidate the positions, turning the $20 mil-

lion paper loss into a $20 million cash outflow, negating what appeared, just a week

earlier, to be a sure arbitrage.

If the LTCM trades were as simple and transparent as the arbitrage example above,

they probably would have been able to obtain the capital required to maintain their posi-

tions. However, their derivative positions were far more complex. For example, rather

than zero coupon bonds, Bond Awas more like a position in a collateralized mortgage

obligation and Bond B was a complex trading strategy in mortgage passthroughs. Given

30

This issue is discussed in more detail in Shleifer and Vishny (1997).

Grinblatt520Titman: Financial	II. Valuing Financial Assets	7. Pricing Derivatives	© The McGraw520Hill
Markets and Corporate			Companies, 2002
Strategy, Second Edition

252Part IIValuing Financial Assets

the complexity of their positions, it would be difficult to convince a bank that a loan of

$20 million was safe. The safety of the loan would depend on the accuracy of the mod-

els used to evaluate whether Bond Ais undervalued relative to the strategy in Bond B.

While the models of LTCM suggested that the derivatives they acquired were under-

valued and the derivatives they shorted were overvalued relative to their tracking port-

folios, the banks financing LTCM were not privy to these models, and probably also

had less confidence in the models. In the end, even sophisticated investors, such as Stan-

ley Druckenmiller of Soros Fund Management and Warren Buffett, were not convinced

that they should extend credit or capital to Long-Term Capital Management.

Because of the inability to overcome financing constraints (which, indeed, may

have allowed what seemed like arbitrage opportunities to exist in the first place), the

paper losses of LTCM became real losses, turning what seemed like arbitrage oppor-

tunities into massive cash losses for the fund.