Trading Case
B02A
Case
Objective
To
understand the time value of money; to understand the cash flows from coupon and
zero coupon bonds; to determine the prices of bonds given a yield curve; to
understand arbitrage relationships and cash matching.
Key
Concepts
Time
value of money; discounting; bond prices and interest rates.
Case
description
In
this case, there are 4 bonds. This trading exercise covers three years of
calendar time. However, you will
only trade the first day of each year. That
is, day 1 opens for trading first. At
the end of day 1 time flashes by and year end settlements take place. Shortly after this day 1 for year 2 opens for trading.
Again at the end of day 1, year 2 time flashes by and end of year 2
settlements take place. Finally, day 1 year 3 opens for trading.
At the end of day 1 year 3 time flashes by and end of year 3 settlements
take place which now converts your entire position to cash.
The
first bond is a coupon bond with a coupon interest rate equal to 10% while the
other bonds are zerocoupon bonds. The
zero coupon bonds mature at the end of year 1, year 2, and year 3 respectively.
All four bonds have a face value of 100. The
cash flow from each bond at the end of each year is shown in the table below.
Spot and Expected Rates
The spot interest rate is initially 4% (annual
compound basis). In year 2, the
expected spot rate is 10%, while in year 3, the expected spot rate is 16%.
In year 2 the possible spot rates, equally likely, are 8%, 10%, and 12%.
In year 3 the possible spot rates, equally likely, are 14%, 16%, and 18%.
This means that if you have any cash left at the end of year 1, you will
earn 4% interest on it; cash at the end of year 2 earns 10% if realized, and so
on. You can also borrow at these
rates in each year.
You
can short sell bonds. If you short
sell a bond and don’t cover your position, then you will have to pay
any coupons and/or face value on that bond at the end of the 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 system puts in.
Private
Information
All traders get private information about the year 2 and year 3 spot rates. The private information will be displayed as follows:
Per2: Not low rate, Per2: Not middle rate, Per2: Not high rate, Per3: Not low rate, Per3: Not middle rate and Per3: Not high rate.
This information is never false. Per3:
Not high rate tells the trader that the realized spot rate for year 3
cannot be 18% and so on.
Viewing
Private
Information
in FTS Trader
After the market starts a single click on the name Cp Bnd (under the heading Security Name) reveals your private information in the text box (top middle part of the FTS Trader screen).
Case
Data
The
cash flows from bonds are:

Payout
at end of Year
1 
Payout
at end of Year
2 
Payout
at end of Year
3 
Cp Bond 
10 
10 
110 
Zero C1 
100 
0 
0 
Zero C2 
0 
100 
0 
Zero C3 
0 
0 
100 
Time
Line For The Coupon Bond Contract (Security 1)
Time
Line For The ZeroCoupon Bond Contract (Security 2)
Time
Line For The ZeroCoupon Bond Contract (Security 3)
Time
Line For The ZeroCoupon Bond Contract (Security 4)
Money Market Time Line
In the above money market C0
is your initial endowment of market cash. C1
is your closing balance of market cash after all of the first year's trading
activities are accounted for. C1 can
be positive or negative (if you have borrowed market cash).
C1b is the total cash received
from any bonds you own. At the end
of the first year this will equal the number of coupon bonds that you own times
$10 plus the realized face value from any one year zerocoupon bonds you own.
This amount is negative if you are short coupon bonds at the end of the
first year. The one plus riskfree
rate of interest (4%) is denoted by (1.04).
Years 2 and 3 can be interpreted in an equivalent manner.
In year 2 the one plus riskfree rate is (1.10) and in year 3 this rate
is (1.16). It should also be noted
that C3b includes the total face
value amount that is received (if you own a long bond position) or paid (if you
are short bonds), as well as any coupon payments received (paid).
Your aim is to make as much money as you can which
depends upon how well you trade relative to the prices discovered by the market.
Each trial you earn
grade cash that is cumulated across trials.
Grade case in any trial equals 0.0001 x your closing balance of market
cash. That is, if you end up with
negative wealth then you lose grade cash and if you make money then you gain
grade cash.
Trading is conducted over a number of independent
trials and a record of your cumulative grade cash is maintained.
I
© OS Financial Trading System 2001