How to Calculate Probability of Profit for Leveraged Hedge Fund Investment

[Kinetica]

Homework Statement

What is the probability that the hedge fund will make a profit of at least $100,000?

I own 1,000,000 dollars of stock and use 50,000 dollars of my own capital and 950,000 dollars of borrowed money. If the value of the stock falls below 950,000 dollars, then I must sell stock and repay the loan, which wipes out my $50,000 investment. It is leveraged 20:1 since borrowed money is 20 times the amount of my own capital. The daily log returns have mean of 0.05/year and stdev 0.23/year. Rates per trading day: divide by 253 and sqrt(253) respectively.


I don't know if all this information is needed. It is a probability question.

Any possible help will be greatly appreciated.

 

[lanedance]

So say K is you're profit, you want to find P(K>100,000), when is profit measured? Is it at the end of a year or is teh money re-invested each year

based on what you know about the mean and SD of return, can you find a pdf for stock price X at a given time? then how do you calculate profit K from X?