Case analysis: LTCM's leverage arithmetic

Consider a convergence trade with expected excess return 1% a year. (a) What asset volatility makes 25:1 leverage the full Kelly fraction? (b) If volatility then doubles, what Kelly multiple is the fund at, and what is its growth rate at 25:1? (c) What asset-level fall wipes out the equity at 25:1? How many monthly standard deviations is this under the calm volatility and under the doubled volatility? (d) Now suppose the book holds ten such trades, sized as if independent, and in a crisis their correlation goes to one. Using Proposition 3.10, what multiple of the correct Kelly exposure is the book at? (e) Summarise which of the module's assumptions failed in 1998, citing the PWG report.