From: John Conover <john@email.johncon.com>

Subject: Re: LTCM and Low-Probability Events

Date: 20 Jan 1999 03:07:46 -0000

gchand4059@aol.com 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 expected. 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 -- John Conover, john@email.johncon.com, http://www.johncon.com/

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