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 zero-coupon 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 donít 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 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)

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 zero-coupon bonds you own.  This amount is negative if you are short coupon bonds at the end of the first year.  The one plus risk-free 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 risk-free 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).  All rates are applied on an annual compound basis to the closing cash balances at the end of a dayís trading.

Earning Grade Cash

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.

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© OS Financial Trading System 2001