HOW THE CASE WORKS
Four fixed-income securities have cash flows extending up to four years. Trading occurs only on Day 1 of Year 1. You begin with a liability in non-tradable Security 1 or 2 and may trade only the 2-year and 3-year zero-coupon bonds.
Prices are set through bids and asks. Borrowing and short selling are allowed. Short positions must make any cash payment due. Year 1 interest is applied to the closing money-market balance before security payments.
REALIZED YIELD CURVE
The Year 1 spot rate is 25%. The initial yield curve is flat at 25%. At the end of Year 1 it remains flat, but can shift by as much as +/-20 percentage points.
After the shift, all remaining cash flows are marked using the new flat curve. A shift to 15% values the 3-year zero at 100/(1.15^2) and the 2-year zero at 100/1.15.
INITIAL POSITIONS - TWO TRADER TYPES
| Position | Type I | Type II |
|---|---|---|
| Security 1 | 0 | -14 |
| Security 2 | -29 | 0 |
| 2-year zero | 0 | 51 |
| 3-year zero | 84 | 0 |
| Cash | 3,200 | 5,000 |
SECURITY CASH FLOWS
| Security | Period 1 | Period 2 | Period 3 | Period 4 |
|---|---|---|---|---|
| Security 1 | 0 | 160 | 200 | 250 |
| Security 2 | 30 | 100 | 47 | 0 |
| 2-year zero | 0 | 100 | 0 | 0 |
| 3-year zero | 0 | 0 | 100 | 0 |
HEDGING LOGIC
A parallel shift changes the present value of every remaining cash flow. The hedge therefore depends on both present value and duration.
Use the 2-year and 3-year zeros to offset the sensitivity of the non-tradable liability. The existing zero holding and cash differ by trader type, so the required trade is type-specific.
At year-end, all remaining positions are marked to the realized curve and converted to market cash.
GRADE CASH
Market cash <= 5,000: 0
Market cash >= 9,999: 10
Intermediate case formula:
5 + [(cash - 5,000)/(9,999 - 5,000)] x 5
Results accumulate across trials.