Trading Case B03A

 

 

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.

 

Spot and Expected Spot Rates

The spot interest rate is initially 4% per annum.  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 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.

 

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 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).   All rates are applied on an annual compound basis to the closing cash balances at the end of a day’s trading.

 

Earning Grade Cash