Question

5. A trader is reviewing the following market prices for possible arbitrage opportunity between a US Treasury Bond and US Treasury STRIP where there is an active trading STRIP and Bond market. On 1/2/2018 (.e. 2nd Jan 2018), a US Treasury Bond with a 6%pa coupon maturing on 8/15/2019 (i.e. 15th August 2019) was quoting Bid price (104.6094) and Ask price (104.6719) in clean price on a semiannual basis. (Note. There are 141 days from 1/2/2018 to the PREVIOUS coupon day (8/15/2017) and market trades on dirty price. Day count convention is 30/360) At the same time, the STRIP market has the following quoted prices on the relevant STRIPS: Maturity Ask 2/15/18 99.6563 99.6875 99.1875 8/15/18 98.1719 2/15/19 96.8281 96.8125 95.2656 8/15/19 99.2969 (Hint: Clean = Dirty Price in STRIP market since it is zero coupon) Explain and provide details of the trader's analysis to evaluate if arbitrage exists. (10 marks)

Answer 1

The trader has to spot for arbitrage opportunity between the Treasury Bond and the Strips. Strips are single cash flows more like a zero coupon bond that help you reconsitute a bond to the trader's desire.

Important points to note:

• The bid and ask prices of the Treasury bond are clean prices so the acrrued interest for the period 2nd January 2018 to 15th Febrary 2018 ( the date for the first cash flow of the strip) is accounted for.
• Strips are single cash flows much like zero coupon payments so the dirty price is equal to the clean price.

Step 1: To arrive at the Bid Ask prices for reconstituted bond  in the strip market.

Strip Price %	Strips decimal price (Strip Price % /100)	Bond Cash Flow 6% Coupon (Semiannual)	Price (Decimal Price* Cash flow)
99.6563	0.996563	3	2.989689
98.1719	0.981719	3	2.945157
96.8125	0.968125	3	2.904375
95.2656	0.952656	103	98.123568
		Bid Price	106.962789

Strip Price %	Strips decimal price	Bond Cash Flow 6% Coupon (Semiannual)	Price (Decimal Price* Cash flow)
99.6875	0.996875	3	2.990625
99.1875	0.991875	3	2.975625
96.8281	0.968281	3	2.904843
99.2969	0.992969	103	102.275807
		Ask Price	111.1469

Step 2: Spot for any arbitrage opportunities

	Bid	Ask
US Treasury Bond	104.6094	104.6719
Strips	106.9627	111.1469
Bid: Price at which the trader can buy
Ask: The price at which trader can sell

So clearly, arbitrage opportunity exits. Riskless profit can be made by buying low and selling high without any investment from the trader.

Buy US Treasury bond at 104.67169 ( Ask Price) and

Sell Bond reconsituted with strips at 106.9627 ( Bid Price)

Finally make a profit of 2.2608.