I didn’t get any responses on my “climate modeling” post even though I thought it was very good, nor did anyone respond to my brilliant post on “Intelligent Design”. Doesn’t anyone like the hard sciences any more? 😦
I suspect more people are interested in the technical side of the recent fiascoes on Wall Street and in Washington. But to warm you up, I’ll start with a math problem. Warning: having taken undergraduate finance courses will make you more likely to get this wrong.
There are 250 trading days in a year. You have 3 assets with the following return profiles:
Let a=(1.01)^3 = 1.030301. Each trading day the price of Asset A, with equal probability, either increases or decreases by a factor of a.
Asset B is just like asset A but uncorrelated with it.
Asset C either with probability 0.9 goes up by 1% (its price is multiplied by 1.01) or with probability 0.1 goes down by a factor of c = (1.01)^9 = 1.093685272684360901.
What is the annual expected return for A and C?
For each of A, A+B, C, A+C what is the approximate value of X such that this asset or combination of assets has a 95% chance of having lost at most X% of its value at the end of a year?
In Wall Street jargon, this is the “VaR” or “Value at Risk” — a VaR of 25% means that only 1 year in 20, on the average, should your asset have a loss of 25% or more.
This simple example will illustrate some essential mathematical blunders the “rocket scientists” on Wall Street made.
Bonus: I wrote down the exact value of c directly without using a calculator or spreadsheet (which don’t have enough digits anyway). How did I do that?