How to Calculate Probability of Profit for Leveraged Hedge Fund Investment

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SUMMARY

The discussion centers on calculating the probability of achieving a profit of at least $100,000 from a leveraged hedge fund investment. The investor has $1,000,000 in stock, utilizing $50,000 of personal capital and $950,000 in borrowed funds, resulting in a leverage ratio of 20:1. Given the daily log returns with a mean of 0.05/year and a standard deviation of 0.23/year, the participant seeks to determine the probability P(K > 100,000) and the conditions under which profit is measured, specifically whether it is at the end of the year or with reinvestment.

PREREQUISITES
  • Understanding of leveraged investments and risk management
  • Familiarity with statistical concepts such as mean and standard deviation
  • Knowledge of probability distributions, particularly for financial returns
  • Basic proficiency in financial modeling and calculations
NEXT STEPS
  • Learn about calculating probabilities using normal distribution in finance
  • Study the impact of leverage on investment risk and return
  • Explore financial modeling techniques for predicting stock price movements
  • Investigate methods for calculating profit and loss in leveraged investments
USEFUL FOR

Investors, financial analysts, and anyone involved in hedge fund management or leveraged trading strategies will benefit from this discussion.

Kinetica
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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.
 
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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 the 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?
 

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