Suppose a 7.4% semi-annual coupon 10-year Treasury issue with a par value of $10

Question

Suppose a 7.4% semi-annual coupon 10-year Treasury issue with a par value of $100 issue is priced in the market based on the on-the-run 9-year Treasury yield. Assume further that this yield is 5.86%, so that each cash flow is discounted at 5.86% divided by 2. What is the market price of the Treasury issue based on this assumption? Suppose also that the price of the same Treasury issue would be $110.3324 if it is calculated based on the prevailing Treasury spot rate curve. What action would a dealer take and what would the arbitrage profit be? Can this situation persist in the long run?

Explanation / Answer

Schedule of Cash Flows Discounted at 5.86%

Year

Outflows

Inflows

Net
Cash Flow

Discounted
Cash Flow

0

$100.00

-$100.00

-$100.00

1

$5.86

$5.86

$5.54

2

$5.86

$5.86

$5.23

3

$5.86

$5.86

$4.94

4

$5.86

$5.86

$4.67

5

$5.86

$5.86

$4.41

6

$5.86

$5.86

$4.16

7

$5.86

$5.86

$3.93

8

$5.86

$5.86

$3.72

9

$5.86

$5.86

$3.51

Totals:

$100.00

$52.74

-$47.26

-$59.90

Schedule of Cash Flows Discounted at 5.86%

Year

Outflows

Inflows

Net
Cash Flow

Discounted
Cash Flow

0

$100.00

-$100.00

-$100.00

1

$5.86

$5.86

$5.54

2

$5.86

$5.86

$5.23

3

$5.86

$5.86

$4.94

4

$5.86

$5.86

$4.67

5

$5.86

$5.86

$4.41

6

$5.86

$5.86

$4.16

7

$5.86

$5.86

$3.93

8

$5.86

$5.86

$3.72

9

$5.86

$5.86

$3.51

Totals:

$100.00

$52.74

-$47.26

-$59.90

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