Decision Tree Example
Exchange rate impacts my living in Melbourne
This is the real situation I faced before I came to Melbourne. I accepted the offer from business
schools with total tuition cost AUD$ 50,000 and estimated living expense is about AUD$40,000
(20 months). The exchange rate at that time (Feb, 2007) between RMB (China Dollar) and
Australia Dollar is around 6.2. So I think total RMB 600,000 is enough to cover the full cost of
my living here. In May, I transferred AUD$2,000 deposit to the school at the exchange rate of 6.23.
But in August, just the last week before I depart, the exchange rate for Australia dollar soared to
6.7. I faced the decision which will potentially impact my living standard here.
I have 3 options at that time before the next tuition payment in December, 2007:
1. Keep the RMB and invested in booming China stock market before December
China stock market has skyrocketed from the beginning of this year. The index soared from under
2000 points to near 4000 in August. Some people think the market will collapse within the year
and others believe it will continue to grow. I consulted my friends, who work in financial institute
and bank system, they told me that it’s about 25% chance to get 50% profit, 25% lost 50% original
amount and 50% get 25% profit before December. I believe what they told is true. Because the
stock marketing is so risky, I even don’t care about exchange rate. So just use 7 as my expectation.
2. Keep the RMB in China bank (almost no interest) and waiting for exchange rate back to
Meanwhile, I paid close attention to the foreign exchange market. According to the report from
Financial Time and WSJ, the Australia dollar has 35% possibility to reach 7 a new high in this
year, also 65% will back to 6.2 before the end of year.
3. Exchange the RMB to AUD and save in Australia bank (interest rate is 6.7% p.a. in
When I checked with my friends in Melbourne, I learned that the interest rate here is pretty high.
So I think I have another choice is changing the money and save in OZ bank to enjoy the higher
interest rate for 4 months.
What should I do to get most from my money?
After learned the decision tree, the best answer maybe lay in investing in China Stock Market. In
real life, I choose the option 3 to bring the money here.
This is a great example of a decision tree where the decision maker has chosen not to take the path
that is indicated by expected values. What is he (implicitly) doing? Why would he choose to take
all the money to Melbourne? How would this be different if he was a company or had a lot of
money or was making 10 of these decisions, independently, in a single year? The other thing that
you’ve had to do with this decision tree is turn what are essentially continuous variables (e.g.
exchange rate and stock market) into discrete variables where you only think about two or three
possible outcomes. That’s OK but it obviously makes the answer a bit less accurate.
We’ll be thinking about some of these questions more in Week 2 when we look at utility. You’ll
also cover this in Data and Decisions in a few weeks’ time.]