Belligerati

Two obvious problems:

1) This requires an infinite bankroll, as any finite bankroll would be bankrupted by a long enough string of bad luck.

2) This is one reason why casinos have table minimums and maximums. The minimums make doubling prohibitive too quickly for those with small bankrolls, and the maximums (table limits) cut off the few that remain with big ones.

Now consider investing in a bubble. For our purposes a happens when the price of an asset (P) is greater than the discounted value of all future returns from that asset (NPV). Let's say we know there is a bubble, but not the magnitude (P - NPV) bubble nor the duration. If you are bank, required by customer demand to buy and sell this asset as well as its derivatives, you have to invest your money in a bet that is probabilistically going to zero. Similarly, you might be a speculator seeking to make money short term market movements but still believing that the market is in a bubble.

For example, let's say in June of 1998 you buy a mutual fund that tracks the behavior of the NASDAQ stock market index. By June of 2000 you'd have tripled your money. By then the index had already hit its all time peak. Two years after that you'd have returned all (less dividends) the money you'd made between 1998 and 2000.

This is what Dr. Heston calls the the "reverse double or nothing", where you follow a strategy that results in you losing your money every time. By failing to diversify your investments, you were effectively doubling up on on certain assets and scaling down your less successful assets. But, if there is some concern that your assets are in a bubble, then you've got a real problem, you are increasing your bet on something that is going down with certainty some time in the future.

For the personal investor, the solution to these hidden bubbles is to admit your blindness and trust in diversity. On a yearly basis you should be sure to rebalance your portfolio consistent with your financial goals. For example, if you've determined that the optimal investment mix for you is 10% cash, 10% government bonds, 20% US corporate bonds, 10% foreign stocks, and 60% US stocks, but over the course of a year US stocks doubled in value while everything else was flat be sure that at the end of a year your move some (probably 40%) of the gains into your other investments. You won't know if stocks are in a bubble, in fact, one of your other investments might actually be in a bubble. But rebalancing will reduce your exposure to the failure to perform of any of your assets. Of course, there is no free lunch. Under situations such as the trivial example of a run-up in stocks that lasts your whole lifetime, you'd be better off not diversifying. But as long as all your assets aren't highly correlated (go up and down together), you will have much more money under a wider array of less rosy scenarios.