Multi-period Investing (Simulation)
An investor has $50,000 Canadian (CDN) they are preparing to invest over the next few years. They are considering shares of Apple (AAPL) and WestJet (WJA). Note that AAPL trades on the Nasdaq in US Dollars (USD), and that WJA trades on the TSX in Canadian Dollars.
At the start of year 1, assume AAPL costs $120 USD per share, while WJA costs $23 CDN per share. The fair exchange rate is $1 USD buys $1.35 CDN.
The expected annual change in the price of AAPL is Normally distributed with a mean of 12%, and a standard deviation of 15%. The expected annual change in the price of WJA is also Normally distributed, with a mean of 8% and a standard deviation of 6%. The annual changes in the prices of AAPL and WSJ are uncorrelated with each other, and also uncorrelated with changes in earlier years.
The annual change in the currency exchange rate is (continuous) uniformly distributed, between -$0.10 CDN and +$0.05 CDN per USD. That is, after the first year, the exchange rate could be anywhere between $1.25 and $1.40 per USD.
There is a special investment available at the beginning of year 3 in a mortgage backed security. The investor must invest exactly $60,000 CDN, and the return after 1 year has a discrete distribution: there is a 95% chance of gaining $9000, a 4% chance of losing $1000, and a 1% chance of losing $10,000. Thus, at the start of year 4, the investor will receive $69,000 CDN with 95% probability, $59,000 CDN with 4% probability, and $50,000 CDN with 1% probability.
The investor devises the following investment plan: he will invest half his money in AAPL (after converting to USD), and half his money in WJA at the start of year 1. At the start of year 3, if he has enough money, he will invest in the mortgage backed security, and leave the rest of his money in AAPL. If he does not have enough money, he will just leave his investments as they are.
Model this investment scenario over 3 years and simulate it 1000 times. Ignore all transaction costs (commissions, exchange rate spreads, etc.) NOTE: If you wish, you may use Excel add-in ASPE, YASAI, or MCSim to automate the task of running 1000 simulations and summarizing the results.
Describe your modelling approach briefly: if you used a simulation table, what does one row represent? How do you handle some of the key logic in the model (be descriptive, don’t just present your formulas)?
What is the probability that the investor has enough money to invest in the mortgage backed security?
At the beginning of year 4, convert all of the investor’s money back into CDN dollars. What is the average amount of money the investor finishes with?
Consider only the years where the investor is able to buy the mortgage backed security. What is the average amount of money he finishes with? Now consider only the years where the investor is not able to buy the mortgage-backed security. What is the average he finished with? Which one is higher? Does this mean the security is a worthwhile investment? Explain.