Based on Kelly XXXXXXXXXXYou currently have $100. Each week, you can invest any amount of money you currently have in a risky investment. With probability 0.4, the amount you invest is tripled (e.g.,...

Based on Kelly (1956). You currently have $100. Each week, you can invest any amount of money you currently have in a risky investment. With probability 0.4, the amount you invest is tripled (e.g., if you invest $100, you increase your asset position by $300), and, with probability 0.6, the amount you invest is lost. Consider the following investment strategies:

■ Each week invest 10% of your money.


■ Each week invest 30% of your money.


■ Each week invest 50% of your money.

Use @RISK to simulate 100 weeks of each strategy 1000 times. Which strategy appears to be best? (In general, if you can multiply your investment by M with probability p and lose your investment with probability q, you should invest a fraction [( p(M – 1) – q]/(M – 1) of your money each week. This strategy maximizes the expected growth rate of your fortune and is known as the Kelly criterion.) [Hint: If an initial wealth of I dollars grows to F dollars in 100 weeks, then the weekly growth rate, labeled r, satisfies F = (1+ r)
¹⁰⁰
I, so that r = (F/I)
^1/100
– 1.]