Trading Case: GC2
Overview of the Case
In this case you can trade stocks and bonds. Each trading trial covers 5-years of calendar time, but in the FTS markets you will trade day 1 of each of the first four years only. At the end of each year your position is adjusted for any dividends, coupon payments, and interest accrued from your end of day 1 position for the current year. At the end of year 5 your position is marked to market but no trading will be permitted. This is because there is no further interest rate uncertainty by year 5. For year 5 the market will open for approximately one second and then the year will end, so that all cash flows are received/paid including interest accrued or owed by your position. The remaining bond markets that are open will pay their face value and stocks will pay a final liquidating dividend as described below.
Trading years 1-4 will last for approximately 270 seconds of real time.
Key Concepts
Time value of money; discounting; bond prices, stock prices and interest rates.
Case description
There are 5 bonds. The first bond is a coupon bond with a coupon interest rate equal to 5%, a face value of 100 and a life equal to 5-years. The other bonds are zero-coupon bonds. Zero coupon bonds mature at the end of years 2, 3, 4 and 5 respectively. All bonds have a face value of 100. The cash flow from one bond at the end of each year is shown in the table below. For example, suppose you own 10,000 coupon bonds and the coupon payment at year end is 5, then your money market is increased by 10,000*5 = 50,000 units of cash at the end of the year.
There are two stock markets open. Cash produced by each stock each year is sensitive to the current state of the economy, and therefore interest rates, as described below.
Traders will start with a position that has the same present value relative to expected current and future rates prior to receiving any news. Your position will consist of both long and short positions in individual securities and different traders can have different starting positions.
The spot interest rate is initially 2% (compound annually). In years 2-5, in the absence of headline information, the expected spot rate is 3%. In each of the years 2-5 the possible spot rates, which are all equally likely in the absence of any news, can range from 1% to 5%. So in the absence of headline news the expected rates are flat for years 2 to 5. Across these years the realization of rates are correlated but not perfectly. That is, in this trading case a strong economy in year 2 implies that it is more likely to be stronger in years 3-5. This relationship is not perfect and each of the years 3-5 has a correlation of about 0.4 with the previous year.
The year 1 spot rate of interest means that your end of year 1 cash balance in your money market earns 2% interest for the year. Your end of year 2 cash balance will earn the realized rate for year 2, and your cash balance at the end of year 3 earns the realized rate for year 3 and so on. You will see on your trading screen, at the beginning of each year, what the current year’s realized rate is. Future year’s rates will be uncertain but the news headlines provides relevant information that can help you assess what future rates are likely to be.
Stock 1 generates more cash when the short rate of interest is high. In particular, the dividend per share for years 1-4 equals 1000*realized short rate of interest (expressed as a decimal) and the terminal or liquidating value per share is equal to 10000*year 5 realized short rate of interest (expressed as a decimal).
Stock 2 generates more cash when the short rate of interest is low. In particular, the dividend per share for years 1-4 equals 1000*(0.06- realized short rate of interest (expressed as a decimal)) and the terminal or liquidating value per share is equal to 10000*(0.06 - year 5 realized short rate of interest (expressed as a decimal)).
The spot interest rate is initially 2% (compound annually). In years 2-5, in the absence of headline
Trading Restrictions
You can borrow and lend at the realized rate of interest in each year. You can short sell any security. That is, you can sell securities you do not currently own. If you are short a security, at the end of a year, you will have to pay any coupons and/or face value on that security at this time. Payment is made from your money market account after all interest payments are settled resulting from your balance carried forward to year end from the end of the trading year.
Prices in this case are determined by the traders, so all trades will take place at bids and asks that either you or another trader in the trading crowd puts in. For each security you can submit limit orders to buy, or sell, any security at a price you pre-specify. This is referred to as making market. As a market maker you can submit a bid to buy some quantity up to 10,000 units. Alternatively, you can submit an ask to sell some quantity up to 10,000 units.
You can also submit market orders. This is referred to as market taking. A market taker can buy from an existing ask up to the quantity being asked for, or sell to an existing bid up to the quantity being bid for.
News
Throughout a trading year you may receive some news headlines that helps you predict the following year's realized rate. A news headline is noisy in the sense that it is based on the true realized state of the economy (which determines the realized interest rate each year) with some error because it is a forecast. Forecast errors are independent across news headlines and headlines have smaller errors as the year goes on. This means that multiple headlines are more informative than any individual headline and these headlines may repeat the same message. In some years you may not receive multiple headlines.
Interpreting the News
If the economy is expected to improve, there is a tendency for investors to shift from bonds to stocks. As a result, future rates will be higher than average. If the economy is expected to weaken then investors tend to shift from stocks to bonds and so future rates will be lower than average. In addition, if global political conditions deteriorate investors tend to shift from stocks to bonds and vice versa as global political conditions improve. Finally, interest rates will also reflect inflationary expectations. That is, if inflation is expected to pick up then future interest rates will be higher. Headlines can vary or be the same over time. Multiple headlines are more informative because they can point to a trend towards an improving or deteriorating economy.
In year 1 you will receive headlines pertaining to year 2 and in year 2 you will receive headlines pertaining to year 3, and so on.
A full list of the headlines is contained in the appendix to this trading case.
A single click on the name of any security reveals the set of news headlines at any point in time. You will see the headline revealed in the text box on the upper center part of the main trading screen. Headlines are sequenced so that the most recent is on top and the most recent headline is also more reliable (i.e., has a smaller forecast error associated with it) than older headlines.
Case Data
The cash flows from one unit of a fixed income security are as follows:
|
|
Payout at end of Year 1 |
Payout at end of Year 2 |
Payout at end of Year 3 |
Payout at end of Year 4 |
Payout at end of Year 5 |
|
Cp Bond |
5 |
5 |
5 |
5 |
105 |
|
Zero C2 |
0 |
100 |
|
|
|
|
Zero C3 |
0 |
0 |
100 |
|
|
|
Zero C4 |
0 |
0 |
0 |
100 |
|
|
Zero C5 |
0 |
0 |
0 |
0 |
100 |
|
Stock 1 |
1000*0.02 |
1000*spot rate (year 2) |
1000*spot rate year 3 |
1000*spot rate year 4 |
10000*spot rate year 5 |
|
Stock 2 |
1000*0.04 |
1000*(0.06-spot rate year 2) |
1000*(0.06-spot rate year 3) |
1000*(0.06-spot rate year 4) |
10000*(0.06-spot rate year 5) |
In the money market all realized rates of interest are applied on an annual compound basis to the closing cash balances at the end of a trading year. That is, fluctuations in your cash account during the trading year do not accrue any interest. It is only your closing balance that is used for determining the interest you pay or the interest you receive from this account.
Your aim is to make as much money in your final money market balance (i.e., your final total cash) as you can in each market trial. This depends upon how well you trade relative to the prices discovered by the market. Each trial your final money market balance is converted to grade cash and your grade cash is cumulated across trials. Grade case in any trial equals 0.0001 x your closing balance of cash. For example, if you end any trial with a negative balance in your money market, you lose grade cash. Upper bounds will be imposed upon grade cash gains and losses each trial if your market cash becomes extremely large. These upper and lower bounds are large enough so that they are not likely to become binding on any trader's position.
Grade cash is used to rank your trading performance relative to all traders in the market. At the end of each trial your trading screen displays the average, high and low cumulative grade cash for the market plus your personal cumulative grade cash.
Appendix: Description of News Headlines
Suppose the range of possible interest rates is broken up into 10 partitions. That is, the range is 1% to 5% so equal partitions are (5-1)/10 = 0.4. Headlines are generated independently over time from next year's true rate plus noise. The expected error of the noise is zero. That is, headlines are unbiased, but noisy, forecasts of next year's true interest rate. Furthermore, the size of the error reduces during the trading year so by the time of the 5th headline it is generated from the true case plus/minus 1 interval.
Breaking up the range of interest rate forecasts into 10 equal partitions, the following headlines are associated with each partition. Each partition covers an interval of possible rates of size 0.4% and each interval is referred to as a case defined as follows:
Case1 (1-1.4%]
Economic forecasts call for decline in GDP
Recession more likely say economists
No breakthrough at the UN; crisis continues
Consumer confidence is widely tipped at lowest level for over a decade
Case 2 (1.4-1.8%]
Consumer confidence falls, signaling decline in spending
Inventory buildup points to signs of recession
Case 3 (1.8-2.2%]
Early trend in recession, forward indicators raise new questions about the economy
Consumer spending suggests that a declining trend has started.
Case 4 (2.2-2.6%]
Some major corporations have started to trim work force
Geopolitical concerns starting to worry investors
Case 5 (2.6-3.0%]
Leading economic indicators match expectations
Stock funds experiencing mild selling
Case 6 (3.0-3.4%]
Leading indicators suggest positive economic outlook
Fed chairman congressional testimony provides optimism
Case 7 (3.4-3.8%]
Indicators are reinforcing a positive economic outlook
Geopolitical investment concerns are rapidly fading
Case 8 (3.8-4.2%]
Analyst forecast increased earnings for most industries in the economy
Factory orders expected to increase sharply
Case 9 (4.2-4.6%]
Much stronger economic growth is currently being forecast
Sharp jump in strong GDP forecasts
Case 10 (4.6-5.0%]
Inflationary expectations increased sharply
Very strong and unexpected surge in the producer price index
Large jump in both imports and exports plus trade deficit sharply wider
Consumer price index expected to surge
©2003 OS Financial Trading System