Capital Markets

Homework Answers - Session 3

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Topic: Bond Arbitrage and T-Bills

1.       Use the attached page from the Nov. 16th 1999 WSJ (quotations as of Nov. 15th). There is a Treasury bill that matures on Jan. 6^th, 2000.  Assume settlement (payment) on Nov 16th.

a)      What is the bill’s quoted bank discount asked yield?

b)      What would you have to pay (cash) to buy this bill at the quoted price on Nov. 16th?

c)      Adjust this yield to compare it with the quoted yield on a 5 3/8% U.S. Treasury note, which matures Jan 15, 2000? (i.e. adjust it to a bond-equivalent yield)

  Answer: 

a)      4.92%. Straight out of the paper (the 3^rd column from right, “Asked”)

b)      From the T-bill formula on the Pink Sheet, we can see that if knowing the Bank Discount Yield (d) and the Days to Maturity (t), we will be able to solve for the price of a T-bill (Price_TB).

In this case d=4.92%, t=51.

So for a $100 par value, Price_TB = 100 * (1-dt/360) = 100 * (1-0.0492*51/360) = 99.303

c)      5.02%.  It is also out of the paper, the far right-hand column, “Asked Yld”. It is the Bond Equivalent Yield of the T-Bill. 

To verify, use the T-Bill Bond Equivalent Yield (y_BEQ) formula on the Pink Sheet. Note that when annualizing the holding period return, you should use 365 days, instead of 360 days, to get the Bond Equivalent Yield. The quoted yield on a bank discount basis is not a meaningful measure of the return from holding a Treasury bill.  This is mainly because it is not an apples-to-apples comparison with other yields, hence we make the conversion to bond equivalent yield for comparability.

2.       Use the attached issue of the WSJ to answer the following questions.  Assume all trades settle (money exchanges hands) on November 15^th at the prices quoted.

a)      If you wanted to buy a $1,000,000 face value position in the 7 1/2 % Treasury Bond which matures on November 15, 2001, what is the total price you would have to pay?  i.e. the WSJ quote plus accrued interest?

There is no accrued interest since the settlement date = coupon date.  Therefore, the

total price is simply the price of the bond x par value = $1,031,562.50

b)      What is the yield to maturity on this security?

What do you know? Since there are no partial periods, one can do a simple RATE calculation: N = 10, PMT = 3.75, PV = -$103.156, FV = $100.00, ACT/ACT; YTM = 5.805%

c)      What would the quoted price of this bond have to be in order for its yield to maturity to equal 6%?

Using a calculation similar to the one above (solving for PV instead of RATE), the price would have to be 102.788.

d)      Construct a schedule of cash flows resulting from the purchase of $1,000,000 face value of this note assuming it is held to maturity.

e)      Now assume that settlement is on November 16^th, rather than 15^th.  What is the total price the buyer would pay if the WSJ quoted price remained the same? 

Now there is one day of accrued interest since the settlement date is one day after the coupon date.  The accrued interest is 37,500 (1/182) = $206.04.  The total price is $1,031,562.50 + $206.04 = $1,031,768.54.

3.       (Easier with a spreadsheet)  Refer to the bond in Question 2 to answer the following questions. Settlement date remains November 15, 1999.

a)      Consider the schedule of cash flows constructed in Question 2, part (d) for the 7½ % Treasury Note which matures November 15, 2001.  Can a portfolio of strips be purchased which would replicate the Treasury Note?  (Hint:  The answer is YES!)  If so, how?  Use "ci" Strips for coupon interest payments and "np" Strips for the ending principal payment. (Hint: use the T. Strips that are marked with dots on the attached WSJ Government Bond Page.)

Yes, it is no coincidence that there are strips that make up the exact T-note that we are looking at above.  In fact, the strips that are underlined in the paper make and came from the exact T-note (they were stripped apart by investors who took the T-note to the Fed window and asked for separate pieces.  The Fed does this for a small fee.)

b)      What would be the total cost of creating (purchasing) such a strip portfolio?

The cost of buying this portfolio that would mimic the T-note we bought in Question 1 above would be the cost of buying the right number of each strip to duplicate the T-note.

c)      Would the strip portfolio you constructed in b) be any more or less “risky” than the Treasury Note?  Why is this important to know?

There is no difference in riskiness between T-notes and the portfolio of strips since the Government stands behind both of them equally.  If the risk level were different, it might be possible for the prices of the portfolio vs. the T-note to diverge.

d)      Now consider a situation where you already own the Treasury Note in Question 2.  What are the total proceeds you could likely get for it if you sold it?

You should remember that when you sell, you get the bid price, which is lower than the asked, so you must recalculate the price using 103:03.  The decimal equivalent is 103.0937.  Therefore, the total proceeds from the sale would be $1,030,937.50.

e)      Compare the sales price calculated in d) to the cost of the portfolio calculated in b).  Is there a difference?  Is there a profit (i.e., arbitrage) opportunity for you here? 

f)       Now consider a situation where you already own the strip portfolio that replicates the Treasury Note.  How much could you likely get for this portfolio if you liquidated it (i.e. the bid price)?

g)      Compare the sales price calculated in f) to the total price calculated in part a) of Question 1.  Is there a difference?  Is there a profit (i.e., arbitrage) opportunity for an investor here? 

It is very unusual to see a potential for arbitrage profits in a strategy this basic.  When one attempts to do the trades that one needs to accomplish the arbitrage, one may find that they are not feasible.  (The quotes in the paper are not firm transaction prices.)  But, this is a good example of the type of transactions arbitrageurs are looking to profit from.