Investing Under the Threat of a Crash
In the previous chapter, we learned how to allocate money between risky and safe assets in continuous time. The answer was clean: hold a constant fraction in stocks and rebalance. But that result assumed the world follows a smooth lognormal random walk with no sudden jumps. What if you know that a crash could happen at any moment? Not a small dip, but a real crash, like October 1987. Chapter 67 of Wilmott’s book, written with Ralf Korn, tackles exactly this question. The answer is no longer a constant fraction, and the way the optimal allocation changes over time matches our intuition perfectly.