The paper "The Cash Flows of the Callable Bond" is a wonderful example of an assignment on macro and microeconomics. Part 1 – A. Creation of Synthetic Bonds The cash flows of the callable bond which is valued at $4.2 billion in shown in Table 1 in the Appendix. The information in the table indicates that after the initial investment of $4.2 billion, interest payments of 4.125 which equates to $173.25 million are payable semi-annually. The net cash flow which is the interest over the five-year period equates to a total of $1,732.5 million.
The present value of these amounts is shown in the last row which indicates the present value cash flow (PVFCF). In order to capitalize on the mispricing in the bond market, Ms. Thompson discussed two options. One option involves creating a synthetic bond with the $4.2 million callable bonds. This bond would pay the same interest as the May’ 00-05’ callable bond. The amount of 12% of May 05’ bonds required to match the coupon payments of the callable bond is as follows: X × 12% × 100 = 8.25% × 100 X × 12 = 8.25 Dividing both sides by 12 yields: X = 8.25/12 Therefore, X= 0.6875 The fraction of 12% May 05’ treasury bonds required is 0.6875.
Therefore, the fraction of treasury STRIP required to pay the principal amount at maturity is 0.3125 (1 – 0.6875). The asking price and bid price of the May 05’ synthetic bond is therefore calculated as follows: Ask price = 0.6875 × 129.901 + 0.3125 × 30.312 = 98.78 Bid price = 0.6875 × 129.7188 + 0.3125 × 29.91 = 98.53 The alternative option would involve 8.875% May 00’ . A similar calculation as that used in the previous option.
The following calculations provide information on the fraction of 8.875% May 00’ noncallable Treasury bonds and May 00’ Treasury STRIPS required to match the 8.25% May 05’ interest payments and principal payment at maturity. X × 8.875% × 100 = 8.25% × 100 X × 8.785 = 8.25 Dividing both sides by 8.875 yields: X = 8.25/8.875 Therefore, X= 0.9296 The fraction of 8.875% May 00’ treasury bonds required is 0.9296. Therefore, the fraction of treasury STRIP required to pay the principal amount at maturity is 0.0704 (1 – 0.9296). The asking price and bid price of the May 00’ synthetic bond is therefore calculated as follows: Ask price = 0.9296 × 104.5 + 0.0704 × 46.656 = 100.43 Bid price = 0.9296 × 104.375 + 0.0704 × 46.25 = 100.28 Part 2 – Case for Mispriced Callable Bonds The May ’ 00 – ’ 05 callable Treasury bond is overpriced.
The information in Table 2 in the Appendix indicates this. Investors can sell the May ’ 00 – ’ 05 callable Treasury bond at the bid price of $101.125 and buy the cheaper priced synthetic bond at the bid-ask price of 98.78.
The profit on the transaction would be worth 2.2345 per share or $98.49 million. If both the callable and the synthetic bond had the same price the investor should prefer to buy the synthetic bond. The reason is that when the interest rate on a callable bond falls the government is likely to call the bond since they will be able to refinance it at a lower rate of interest. The May ’ 05 bond should, therefore, be worth more because it is a noncallable Treasury bond and therefore provides the government with an option.
The May ’ 00 synthetic bond is also worth more than the May’ 00 – ’ 05 callable bond because when the level of an interest rate rises the government will not call the callable bond since it is at a lower rate. Part 3 – The Case of a Bond Trader Who Does Not Currently Own the Callable Bond Part 4 – Varying Scenarios Part 5 Fall in the Price of Callable Bond by 150bps in One Year If the price of the callable bond falls by 150 basis points below that of the synthetic bond with the corresponding maturity then the (asked) yield-to-maturity of the synthetic bond which was constructed using the May ’ 05 noncallable bond and the May ’ 05 STRIP would be as follows: Yield– to-Maturity (YTM) is the rate of return on the bond if it is held until it matures.
It is found using the equation for value of the bond Vb, in which rd is the return. Vb = 98.78 = (8.875/2)/(1+ rd/2)1 + (8.875/2)/(1+ rd/2)2 + (8.875/2)/(1+ rd/2)3+ (8.875/2)/(1+ rd/2)4 + (8.875/2)/(1+ rd/2)5 + (8.875/2)/(1+ rd/2)6 + (8.875/2)/(1+ rd/2)7+(8.875/2)/(1+ rd/2)8 + (8.875/2)/(1+ rd/2)9 + (8.875/2)/(1+ rd/2)10 YTM = rd= 4.595% YTM (ask) synthetic May’ 05 is 4.595% The YTM (bid) on the synthetic May ’ 05 bond is Vb = 98.53 = (8.875/2)/(1+ rd/2)1 + (8.875/2)/(1+ rd/2)2 + (8.875/2)/(1+ rd/2)3+ (8.875/2)/(1+ rd/2)4 + (8.875/2)/(1+ rd/2)5 + (8.875/2)/(1+ rd/2)6 + (8.875/2)/(1+ rd/2)7+(8.875/2)/(1+ rd/2)8 + (8.875/2)/(1+ rd/2)9 + (8.875/2)/(1+ rd/2)10 YTM = rd = 4.627% If the callable bond one year from now is 150bps below that of the synthetic bond with the corresponding maturity the expected asked price of the synthetic bond and the bid price of the callable bond one year from now is as follows: Asked price of synthetic bond one year from now: Vb = 98.78 = (8.875/2)/(1+ rd/2)1 + (8.875/2)/(1+ rd/2)2 YTM = rd= 5.097% The bid price of the callable bond one year from now using the bond valuation formula is: Vb = 99.61 = (8.25/2)/(1+ rd/2)1 + (8.25/2)/(1+ rd/2)2 YTM = rd= 4.338% A higher rate means that the returns are better.
Even as the price of the callable bond falls below par value the yield is less than that of the synthetic May ’ 05 synthetic bond because it is still overpriced.
Use of $10 Million Loan Assuming no securities are owned and $10 million is borrowed on the repo market to perform the transaction in order to exploit the arbitrage opportunity and assuming other securities can be posted as collateral. Since I own no securities then I would borrow some and collateralize it using the $10 million loan. I would then sell the security in a short sale. I would, therefore, have to pay the interest of 4.125 semi-annually until I am ready to return the bond.
When that time comes I would enter the market and purchase the bond if it is not overpriced or I would enter into a similar borrowing arrangement with another bondholder. Buy-and-Hold Strategy If I use a buy-and-hold strategy for one year, my arbitrage profit would be calculated as follows: Repurchase Arrangements Description $mn Interest Repo Market Loan 10 (527000) Borrow 8.25 May 00' - 05' 10 (825000) Sell short 8.25 May 00' -05' Callable bond 10.04 828300 Net Profit/loss (523700) Figure 1 Much of the information in Figure 1 would result in a profit if I had investments of my own.
The difference between long-term borrowing and short sales indicates that borrowing bonds and selling them short has major benefits but the cost of the funds used to so may outweigh the benefits which are the case in Figure 1, the result been a loss of $523,700. Attribution Analysis Most of the profit under section (a) can be attributed to directional value trading as it is assumed that the callable bonds are overvalued when compared with the synthetic bonds. This mispricing is expected to be corrected in the future.
ReferencesEdleson, M.E and Tufano, P. Arbitrage in the Government Bond Market? Boston: Harvard Business School. 1995. Print.