You can choose to invest your money in one particular stock or put it in a savin

Question

You can choose to invest your money in one particular stock or put it in a savings account. Your initial capital is 1000 dollars. The initial stock price is 100 dollars. The interest rate rr is 0.5% per month and does not change. Your stochastic model for the stock price is as follows:

next month the price is the same as this month with probability 1/2,

with probability 1/4 it is 5% lower,

and with probability 1/4 it is 5% higher.

The principle applies for every new month. There are no transaction costs when you buy or sell stock.

Your investment strategy for the next 5 years is:

convert all your money to stock when the price drops below 95 dollars,

and sell all stock and put the money in the bank when the stock price exceeds 110 dollars.

Describe how to simulate the results of this strategy for the model given.

Determine number of simulation so the Monte Carlo study would attain the margin of error ±0.01 with probability 0.99.

How does this strategy compared to gains from the savings account for the same period of time? Determine success rate the above strategy related to gains from the savings account.

Calculate 95% confidence interval for estimated strategy success rate.

Assume another investment strategy when you put money in stock when price drops below 100 dollars and sell these stocks when price is above 115 dollars.

Is there a significant difference between two strategies?

Is it true that the difference between strategies is less then 50 dollars?

Formulate and test the hypotheses at a level =0.05=0.05.

You should submit a small report for your project. A well-documented source code of your project should be added to the report appendix section.

Explanation / Answer

Answer:

Stochastic model works on probability

Initial investment =$1000 Stock price =S100 r=0.5% per month

S.no Probability stock price  

1 0.5 100

2 0.25 95

3 0.25 105

The probability of getting below 95 dollars is 25% and probability getting above 110 is zero in any month.

so the strategy would be to buy stock of $1000 dollar which will give 11 share.

2.when price falls below 100 the probability is buying a stock is 25%. so there is no difference in the strategy for buying the stock.

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