Say I know the price probability distribution, e.g.,
lognormal(p,s), of a stock
X at a future time
T that is perhaps one or two years into the future.
p is price and
s is a standard deviation.
What should I trade to maximize my expected total return at time
Should I for example roll over short-term stock options, long-term stock options, buy the stock using some amount of leverage, etc?
Is there some way or tool that calculates this automatically?
How do I need to change this problem or my thinking so that the solution is not to simply use infinite amounts of leverage?
I am assuming I have some positive amount of capital C to invest.
Available instruments are:
- Long and short stocks
- Long and short call and put options
- Stock futures and swaps
- T-Bills, notes and bonds
- (If it makes things easier we can ignore warrants and convertibles)