You have 50000 and are thinking of investing all of it into

You have $50,000 and are thinking of investing all of it into Acme Holdings for a whole year. Each year there is a 0.5 probability that Acme will generate a return of 20% and a 0.5 probability that you will lose 10% at the end of the year. These probabilities are independent from one year to the next. 1. At the end of the year, in the worst case, how much money will you have? 2. What is the probability of the worst case at the end of the year? 3. What is your expected wealth (total value of investment) at the end of one year? 4. What is the variance of your wealth at the end of year 1? 5. One is often advised to invest for the long term. Suppose you invest the $50,000 for four years (neither adding to nor withdrawing from it). At the end of year 4, in the worst case, how much money will you have? 6. What is the probability of the worst case in part (e). 7. Ignoring net present value, what is your expected wealth (total value of investment) at the end of year 4? 8. What is the variance of your wealth at the end of year 4? 9. Build a simulation model to determine your returns after 10 years (assuming you buy at the start of year 1 and hold until the end of year 10). Use the model to generate 1000 runs. What is the mean value of wealth at the end of year 10 of your 100 runs? What is the variance?

Solution

1.

50,000*120%=60,000

50,000*90%=45000

2.

The probability of generate the return is 0.5

Smilarly for loss is 0.5

3.

At the end of the year, the money will have is

0.5*(50,000*20%)+0.5*(50,000*-10%)

0.5*10,000-0.5*5,000

2500

So, at the end the amount is 50,000+2500=$52,500