Tuesday, August 30, 2011

Economics: A love affair

Bill Gross of Pimco uses the metaphor of love, marriage, and divorce to describe disturbing financial events in Europe, United States, and the rest of the world. An entertaining take on a sobering state of affairs.
Oh those feisty Europeans! Always fighting like a dating couple and then finally resolving their differences by saying “I do” sometime in the 1950s with the creation of the Common Market and the European Economic Community (EEC). In doing so, France and Germany said “never again,” and even though they didn’t like each other (read “hate”) they decided to make economic lurv in the hopes that they wouldn’t destroy the continent again. It later turned into a formal union, a European Community (EC), where they invited lots of witnesses to the ceremony and created instant family members, if that’s metaphorically possible. Twenty-seven of them, including Italy, Spain and the U.K. were now relatives despite some liking pasta and others preferring horrid cuisines featuring Shepherd’s Pie or fish and chips. The marriage progressed to the point of a smaller monetary union sometime in 1999, but critically, without a common budget. Husband and Wife – Germany and Greece – decided to have a joint bank account, but with separate allowances and no oversight. Greece could issue bonds at nearly the same yield as could its Northern hard-working neighbors, but were free to spend it any way they chose. This was an economic version of an open marriage where one party gets to have all the fun and the other worked nine-to-five and came home too exhausted for whoopee.

Sunday, August 21, 2011

Bayesian Quote

"a Bayesian is someone who, vaguely expecting a horse, and glimpsing the tail of a donkey, concludes he has probably seen a mule" - John Hussman

Saturday, August 20, 2011

Compound Interest

You may have heard of the famous rule of 72 (about compound interest). If an investment returns X% annually, then the number of years required to double the principal is 72/X. So if you get 7% on something, it will take you approximately 72/7 = 10 years to double your initial investment.

A friend asked me yesterday what the origin of this was, and I figured it wouldn't be hard to discover what someone had already invented.

Consider the standard compound interest formula with compounding rate represented x=X/100 (in decimal rather than %), final amount = initial amount * (1+x)^n, where ^ denotes a power operation. Since we are looking for a double (final amount = 2 * initial amount), we can take the logarithm of both sides of the equation as:

log 2 = n * log (1+x)

For small values of x (compared to 1), log(1+x) is approximately x (from Taylor series expansion). Hence,

n = log(2)/x = 0.693/x = 69.3/X

We probably use 72 instead of 69.3 because it has a large number of factors.