Someone asks you if you would like to play the following game: A biased coin will be tossed 1778 times. The coin bias is 54.78%, meaning that on the average, heads will come up 54.78% of the time. You win \$85.50 each time the outcome is a head and you pay \$88.47 if it is a tail. No commissions paid and you do not have to worry about consecutive losers that may wipe out your starting bankroll. Does this game sound like something familiar?

Welcome to GLD, the gold ETF.  I have just described the game that has given rise to the chart you see below:

The analogous game in the case of GLD is the following: Each day at the close you purchase 100 shares and exit at the close of the next day. No commissions apply. Each time there is a positive close (heads) you win \$85.50 on the average and each time there is a negative close you lose \$88.47 on the average. The game has of course positive expectation and it is profitable over the period considered. The statistics are as follows:

Total number of days (tosses): 1778
Number of heads (positive close): 974
Number of tails (negative close): 804
Bias (No of heads/No of tosses) = 974/1778 = 0.5478 or 54.78%
Average winner: \$0.8550
Average loser: \$0.8847

The expectation of this GLD game is given by the following formula:

EV = win rate * avg. winner – (1-win rate) * avg. loser
= 0.5478 * \$0.8550 – (1 – 0.5478) * \$0.8847
= \$0.0684

EV x 1778 = \$0.0684 * 1778 = \$121.6

which is equal to the buy and hold profit per GLD share over the period considered.

The lesson is that this spectacular trend in GLD was achieved by a very small bias. Huge profits can be accumulated slowly via a game that offers a very small bias and small positive expectation, even if the average loss is greater than the average winner. Any trader or investor who can spot such games on time can make huge profits over a period of 2 – 4 years. Of course, there are issues of commission cost and risk of ruin due to a streak of consecutive losses that may exceed initial bankroll but these will be topics of another post.

These are the games people play and they give them fancy names like GLD.