Re: LTCM and Low-Probability Events

From: John Conover <>
Subject: Re: LTCM and Low-Probability Events
Date: 20 Jan 1999 03:07:46 -0000 writes:
> Doug Bebb wrote:
> > And I think that the low-probability events Merton
> > ignored came back to haunt him through Long Term
> > Capital Management.
> Does anyone know where Merton and Scholes are now? Do they work for the
> takeover consortium? Have Merton and Scholes published wha hoppen?

I don't know if LTCM used Black-Scholes, or not, (I imagine that they
did, but I'm not privy to their hedging algorithms, so I really don't
know,) but the Black-Scholes algorithm makes a paradigm assumption
that investment values are a random walk fractal, with marginal
increments that have a Gaussian/normal frequency distribution.

I did a lot of measurements on currency, equity values, etc., time
series and my analysis seems to conclude that they is not a random
walk with independent increments-the increments are slightly
persistent, ie., there is about a 60% chance that whatever movement
happened today will happen tomorrow.

The implication is that volatility of concurrent investments would not
add exactly root mean square-it would add t^1.67 = a^1.67 + b^1.67 +
c^1.67 ... instead of t^2 = a^2 + b^2 + c^2 ..., meaning that there
would be more volatility and correlation over time that might be

It also means that there would be more 3 sigma hits in financial
instrument values than would be expected-about an order of magnitude
more, in very rough numbers.

So, if this is the case, it would be that the low-probability events
were not as low as expected.



John Conover,,

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