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You could double up if you win early.
Repeatedly betting a fraction of one's available bankroll with favorable odds is a well-studied probability problem with an optimal solution having been identified by J. L. Kelly in 1956.
The Kelly criterion states that you should bet a fraction of your money
f = p - (1 - p) / b
where p is the probability of winning, and b is odds paid, b=1 for an even money bet.
Now this does not apply perfectly to shorting stock, since you could potentially lose more than you "bet" and you also can get hit with margin calls, but it can at least give us a ballpark answer. Or you could buy put options, in which case Kelly applies more precisely.
Anyway, with your example, each year, for every $100 shorted, you either lose $25 or win $50. We can look at that as betting $25 with 2 to 1 odds, 50% chance of winning. So Kelly says to bet 0.5 - 0.5 / 2 = 25% of your funds each year, which would correspond to shorting 100% each year. In reality, you would want to decrease that number due to margin calls (and margin regulations), but I think it is clear that you should be shorting at least 50% of your funds with such a favorable bet.
Alternatively, consider put options on SPX. June 2010 options with 1050 strike (near the money) are about $112. If SPX goes up 25%, the options expire worthless, but if it goes down 50%, they are worth $525. So p = 0.5, and b = 525/112 = 4.6875, so the Kelly fraction is 0.39. So if you had $100K, you'd buy $39K of put options the first year. If you lost, you'd have $61K left and buy 39% of $61K, or about $24K the second year.
So what ever happened to the idea that the stock market was a place to invest in companies and become a participating owner of the business?
When did we turn it into a casino?
After the recent global financial calamity why is it still okay that it's a casino?
...ken...
It seems to me that there is something wrong with the example. If I had "virtual certainty" that the market would eventually fall to its "fundamental value" of 50 then I would expect the probability that it will fall in any particular year to rise over time until it does fall. It seem to me that the longer the price stays above "fundamental value" the higher the probability that other market participants will realize that the market is over-valued, and thus act in ways that will cause the price to fall.
This is a well studied problem, and I'm glad someone FINALLY mentioned Kelly! Kelly betting is also equivalent to maximizing expected utility where utility = log (money).
You can find an elementary, very good explanation of the Kelly Betting System in section 2.7 of the introductory probability book "Understanding Probability" by Jan Tijms and the whole book is freely downloadable at http://depositfiles.com/en/files/8121640
BTW, I presume that's a LEGAL free book because it's listed at http://freebookshare.com/understanding-probability-chance-rules-in-everyday-life.html
though in truth I don't understand what legal status such downloads have.