Trading Case
B03
Case
Objective
To
understand the cash flows from forward contracts on bonds; to determine forward
prices on bonds.
Key
Concepts
Forward
contract; time value of money; discounting; bond prices and interest rates.
Case
description
There
are 4 bonds and two forward contracts. 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 then 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.
Each
bond has a face value of 100. The
cash flow from each bond at the end of each year is shown below. The first
forward contract is on the zero coupon bond that matures in year 2, and the
forward contract matures at the end of year 1.
The second forward contract is on the zero coupon bond that matures at
the end of year 3, and the forward contract itself matures at the end of year 2.
The
interest rate is initially 4% In year
2, it is 10%, while in year 3, it is 16%.
You earn interest on cash at these rates. and so on.
You can also borrow at these rates in each year.
You
can short sell bonds and forward contracts.
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.
If you short sell a forward, you will have to deliver the underlying bond
when the forward matures. Note that
when you trade a forward contract, no money changes hands.
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. The price you bid/ask for a forward contract is the forward
price.
Case
Data
The
cash flows from the 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 Lines
Time line for the coupon
bond contract (security 1)
Time line for the
zero-coupon bond contract (security 2)
Time line for the
zero-coupon bond contract (security 3)
Time line for the
zero-coupon bond contract (security 4)
Time line for the forward
contract on security 3 (security 5)
Time
line for the forward contract on security 4 (security 6)
Money Market Time Line
In the money market c0 is your
initial endowment of market cash, and 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 less (plus) the cost (revenue) from any forward contracts
you purchased (sold) during year 1. The
one plus risk-free rate of interest (4%) is denoted by (1.04).
Years 2 and 3 are interpreted in an equivalent manner.
In year 2 the one plus risk-free rate is (1.10) and in year 3 this rate
is (1.16).
Earning Grade Cash