Tuesday, January 10, 2012

Coin Flips, Samuelson's Problem, and Stock Market Investing

I love this anecdote that Daniel Kahneman wrote about in his book Thinking, Fast and Slow:

The great Paul Samuelson - a giant among the economists of the twentieth century - famously asked a friend whether he would accept a gamble on the toss of a coin in which he could lose $100 or win $200.  His friend responded, "I won't bet because I would feel the $100 loss more than the $200 gain.  But I'll take you on if you promise to let me make 100 bets."

Kahneman goes on to describe why Samuelson's friend was so clever.

The outcome of one coin flip is, of course, a random event.  Over time, however, it will almost certainly be true that heads will come up 50% of the time, which means that:

Matthew Rabin and Richard Thaler pointed out that "the aggregated gamble of one hundred 50-50 lose $100/gain $200 bets has an expected return of $5,000, with only a 1/2,300 chance of losing any money and merely a 1/62,000 chance of losing more than $1,000".

So why am I bringing this up today?

Historically investing in stocks has been a money-winner. According to the brokerage firm Franklin Templeton, looking back over the last 85 years, stock market investors have made money 71% of the time on an annual basis (including 2011, by the way). And for a 10 year period, stock market investors have made money 95% of the time.

The simple solution to investing, then, is to stay invested.

Like Samuelson's friend, you know the longer you play the market, the more likely you are to gain profits.