Swaptions & the Massachusetts Turnpike Authority Fixed Income Analysis Class Project April 28, 2009

What Are Swaps? ● The most common are interest rate swaps ○ Floating rate swapped for fixed rate. ● Notional amounts ● Theory of comparative advantage Fixed Floating AAA 4.0% 6-m LIBOR + 0.3% BBB 5.2% 6-m LIBOR + 1.0% ● Credit Risks

What Are Swaptions? ● Option on a swap ● European Swap Options or Swaptions ● Interest Rate Option like caps/floors ● Use to hedge against interest rate increases ● Alternatives: ○ Forward/deferred swaps

Swaption Example After 6 months...

Swaption Valuation Using Black Model ● L: Notional amount ● T: When the swap begins ● n: The period of the swap ● m: Payments annually ● σ: volatility of forward swap rate ● s_k: Fixed rate of swap ● s_t: Swap rate for n-year swap starting at T ● s_0: current swap rate ● T_1, T_2, ..., T_mn: Swap payment dates ● P(0, T_i): Payoff factor at date T_i ● N(x): Cumulative normal distribution of random variable x

Value swaption paying fixed rate: ● L: Notional amount ● T: When the swap begins ● n: The period of the swap ● m: Payments annually ● σ: volatility of forward swap rate ● s_k: Fixed rate of swap ● s_t: Swap rate for n-year swap starting at T ● s_0: current swap rate ● T_1, T_2, ..., T_mn: Swap payment dates ● P(0, T_i):Payoff factor at date T_i ● N(x): Cumulative normal distribution of random variable x The following formulas and examples are from (Hull 2007)

Swaption Simplified Calculation where... Pay fixed: Receive fixed:

Swaption Calculation ● s_k = 6.2% (fixed rate of swap) ● s_0 = 6.09% (LIBOR yield is 6%/annum, continuous compounding) ● n = 3 (3-year swap) ● T = 5 (starts in 5 years) ● σ = 20% (volatility of forward swap rate) ● m = 2 (semi-annual payments) ● $100 (Principal/Notional Amount)

The value of the swaption is $2.07.

Swaption Calculation ● s_k = 4.75% (fixed rate of swap) ● s_0 =5.3201% * 68% (68% 1-m LIBOR) LIBOR yield is 6% /annum, continuous compounding) ● n = 35 (3-year swap) ● T = 5.5 (starts in 5 years) ● σ = 10% (volatility of forward swap rate) ● m = 2 (semi-annual payments) ● $207,665,000 (Principal/Notional Amount)

The value of the swaption is $2,013,694.

Using Trees to Value Swaptions Cash flows of original swap from t = 0 to t = 1.5 Exercise

Using Trees to Value Swaptions

Max ( CF, 0 )

About the Massachusetts Turnpike Authority (MTA) ● Two highway systems: MassPike and Metropolitan Highway System (MHS) ● 138-mile long, from MA to NY ● In 1997, the MA government made the MTA in charge of overseeing construction of Boston's Big Dig. ● MTA grosses about $170 million per year ● Issued $2.3 billion in 3 series bonds to finance project ○ accelerated payments began in 2009

Financial pressures ● Escalating costs (health, property, utility insurance premiums, pension, police pay) ● Underforecasted revenues ● Delayed toll increases ● Related debt service ● Center artery/Tunnel (CA/T) (Big Dig) Expenses ● Repair, investigation, remediation

Swaptions Entered into by the MTA ● Serious financial pressures led to the MTA entering into swaption agreements. ● Purpose of the swaptions: ○ additional revenue source that allowed them to: ■ avoid the need for a toll increase in 2002 to 2008 ■ achieve a 1.35 coverage ratio ■ provide a modest capital program ■ fund the Fast Lane discount program ■ to offset the fixed-rate bonds they issued ○ Total of $64 million received in additional revenue (UBS $29M,Lehman $35M) ● But assumed risks for the next 35 years!

UBS Swaptions ● Executed in May 2001 ● Five fixed-rate payer swaptions, with notional amount totaling $800 million ● MTA received $29 million premium payment ● 35 years ● MTA is the fixed-rate payer ● MTA pays UBS fixed rates of 4.75%, 4.875%, and 5%, and receives 68% of one-month LIBOR from UBS. ● Cost of termination: $400 million

Lehman Brothers Swaptions ● Executed in November 2002 ● Five fixed-rate receiver swaptions, with notional amount totaling $800 million ● MTA received $35 million premium payment ● 35 years ● MTA is the fixed-rate receiver ● Cost of termination: $30 million ● Were meant to offset the five UBS swaptions

http://www.google.com/url?sa=t&source=web&ct=&cd=2&url=http%3A%2F%2Fwww.wsjprimerate.us%2Flibor% 2Flibor_rates_history-chart-graph. htm&ei=C8PeSaLsC9XwnQeRz5W1CQ&usg=AFQjCNHqhjAsmtLnvpim3KSXeVEOwHXumA&sig2=RmL0elOoX13j mNJPE4pmUA UBS exercises swaptions 2 2 1 UBS swaption executed Lehman swaption executed

Problems from the UBS Swaptions ● Exercised in Jan 2008, Jul 2008, Jan 2009 ● MTA pays UBS fixed rates of 4.75%, 4.875%, and 5%, and receives 68% of one-month LIBOR from UBS. ○ One-month LIBOR is now ~0.33%, compared to 4.56% three months ago. This means the MTA is receiving only 0.2244%. ● The swaptions have increased MTA's fixed rate liabilities and is estimated to require $24 million in annual expenses by 2010. ● Massachusetts government temporarily backed the MTA with a "general obligation" which expired in January 2009 ○ MA government has a stronger credit rating (AA) than the MTA

Problems (continued) ● $12.1 million deficit in budget as of Jan 2009 ● Has and will need to increase tolls ranging from a 50% increase in some areas to double in others. Expected to result in $90 million additional revenue ● Reduced toll collector staff from 375 to 275 in December, plans to terminate another 80 ● At current bond rating, borrowing capital is impossible

Problems (continued) ● Bonds and swaps do not match ○ Now must pay $2 million per month in additional interest costs ● Going to refinance the bonds to variable rate to better match the bonds to the swaps: ○ Citi $229 million ○ JP Morgan $207 million ○ Morgan Stanley $185 million ○ Merrill Lynch & Co. $185 million ● Terminated the Lehman Brothers swaptions (which were never exercised) to prepare for the refinancing in December 2008 and paid Lehman $3.4 million fee ● Ongoing litigation - MTA disputes the trigger of the termination fee

Termination Fee Triggered ● Termination fee of $400 million was allegedly triggered when MTA’s insurer, Ambac Assurance Corporation, was downgraded by S&P and Moody's during the same month. ○ 9/10/2008 Fitch places MTA bonds on Rating Watch Negative (likely downgrade) ○ In November, 2008, Moody's downgraded Ambac from Aa3 to Baa1 ○ In November 2008, S&P assigned a negative outlook and proposed downgrade of Ambac from A to AA ○ UBS wrote a letter to MTA notifying of the termination fee trigger

References ● Fabozzi, Frank. Bond Portfolio Management. Hoboken: Wiley & Sons, Inc., 2001 ● "Fitch Puts Massachusetts Turnpike Authority's Metro Highway System Revs on Watch Negative." Reuters. 9 Sep 2008. 28 Mar 2009. . ● Hull, John C.. Options, Futures, and Other Derivatives. 6. New Delhi: Prentice-Hall, 2007. ● "Massachusetts Turnpike reducing toll collectors from 375 to 275." Tollroad News. 12 Dec 2008. 18 Mar 2009. . ● "Fitch Comments on Massachusetts Turnpike Auth MHS Swaptions." Business Wire. 19 Dec 2008. 18 Mar 2009. . ● "Toll Increase - Frequently Asked Questions." MTA - Turnpike News. 15 Dec 2008. 18 Mar 2009. . ● "Fitch Affirms MA Turnpike Auth MHS Sr. Bnds at 'BBB+'/Sub. Bnds at 'BBB'; Stable Outlook." The Free Library by Farlex. 28 Jul 2005. 18 Mar 2009. . ● Kaske, Michelle. "MassPike Swap Payment a Looming Threat." The Bond Buyer. 14 Jan 2009. 18 Mar 2009. . ● "Massachusetts Turnpike Authority, Financial Statements, Required Supplementary Information, and Supplementary Schedules, December 31, 2003 and 2002." KPMG. 17 Sep 2004. ● "Transportation Finance in Massachusetts: An Unsustainable System. Findings of the Massachusetts Transportation Finance Commission." 28 Mar 2007. ● "Massachusetts Turnpike Authority Request for Proposals. Legal Services for Potential Claim(s) Against Investment Bank/Swap Counterparty, Financial Advisor, Bond Insurer and/or Rating Agencies." 29 Jan 2009. ● "Ehrlich: Understanding 'swaptions' coming down the Pike." The Milford Daily News. 26 Mar 2009. 10 Apr 2009. . ● http://www.wsjprimerate.us/libor/libor_rates_history.htm