usingR to slove it

Simulation example Suppose a hedge fund owns $1,000,000 of stock and used $50,000 of its own capital and $950,000 in borrowed money for the purchase. Suppose that if the value of the stock falls below $950,000 at the end of any trading day. then the hedge fund will sell all the stock and repay the loan. This will wipe out its $50,000 investment. The hedge fund is said to be leveraged 20:1 since its position is 20 times the amount of its own capital invested. Suppose that the daily log returns on the stock have a mean of 0.05/year and a standard deviation of 0.23/year. These can be converted to rates per trading day by dividing by 253 and 253, respectively. Homework Suppose the hedge fund will sell the stock for a profit of at least 100,000 if the value of the stock rises to at least 1.100.000 at the end of one of the first 45 trading days, sell it for a loss if the value falls below $950,000 at the end of one of the first 45 trading days, or sell after 45 trading days if the closing price has stayed between $950,000 and $1,100,000. Set random seed: 1228: The price of any trading day is "independent" to each other. Problem s What is the probability that the hedge fund will make a profit of at least ut $100,000 Problem 6 What is the probability the hedge fund will suffer a loss! Problem 7 What is the expected profit from this trading strategy Problem s What is the expected return? When anwering this question, member that only $50,000 inated. Also, the units of returnare time, cs, one can care a return a daily return or a weekly return. Therefore, one must keep track of how long the hedge fund holds its position before selling Simulation example Suppose a hedge fund owns $1,000,000 of stock and used $50,000 of its own capital and $950,000 in borrowed money for the purchase. Suppose that if the value of the stock falls below $950,000 at the end of any trading day. then the hedge fund will sell all the stock and repay the loan. This will wipe out its $50,000 investment. The hedge fund is said to be leveraged 20:1 since its position is 20 times the amount of its own capital invested. Suppose that the daily log returns on the stock have a mean of 0.05/year and a standard deviation of 0.23/year. These can be converted to rates per trading day by dividing by 253 and 253, respectively. Homework Suppose the hedge fund will sell the stock for a profit of at least 100,000 if the value of the stock rises to at least 1.100.000 at the end of one of the first 45 trading days, sell it for a loss if the value falls below $950,000 at the end of one of the first 45 trading days, or sell after 45 trading days if the closing price has stayed between $950,000 and $1,100,000. Set random seed: 1228: The price of any trading day is "independent" to each other. Problem s What is the probability that the hedge fund will make a profit of at least ut $100,000 Problem 6 What is the probability the hedge fund will suffer a loss! Problem 7 What is the expected profit from this trading strategy Problem s What is the expected return? When anwering this question, member that only $50,000 inated. Also, the units of returnare time, cs, one can care a return a daily return or a weekly return. Therefore, one must keep track of how long the hedge fund holds its position before selling