Economics 434 Theory of Financial Markets

Economics 434Theory of Financial Markets Professor Edwin T Burton Economics Department The University of Virginia

Imagine a Two Year Note: the 10s of Sept ‘11 • Pays $ 5,000 twice yearly (four times in all) and pays $ 100,000 at maturity, September 15th, 2011. • Imagine that these are four separate securities (with different risks) • This is the process of “stripping” the two year treasury to create four new securities. $ 5,000 $ 5,000 $ 5,000 $ 105,000 3/15/10 9/15/10 3/15/11 9/15/11

A simple ABS (asset backed security) $ 5,000 $ 5,000 $ 5,000 $ 105,000 3/15/10 9/15/10 3/15/11 9/15/11 Create Tranche A, B and C as new securities (“backed” by the two year treasury note). These are asset-backed securities Tranche A receives the first $ 5,000 payment Tranche B receives the second $ 5,000 payment Tranche C receives the third and fourth payments ($ 110,000 in all)

Things to note about this simple ABS • Assuming today is Sept 16, 2009, Tranche A should be equivalent to a six month Treasury bill and Tranche B should be equivalent to a Treasury year bill. • Tranche A has a duration of ½, Tranche B has a duration of 1, and Tranche C has a duration that is just slightly less than 2.

Now, Imagine a Corporate Note (Similar in structure to a Treasury 2 year note, but with a higher yield, now 6 percent not 5 percent, and the possibility of a default $ 6,000 $ 6,000 $ 6,000 $ 106,000 3/15/10 9/15/10 3/15/11 9/15/11

Defaultable Corporate Two Year Note with a 6 Coupon $ 6,000 $ 6,000 $ 6,000 $ 106,000 3/15/10 9/15/10 3/15/11 9/15/11

What if you strip the corporate note? • The first coupon payment due March 15, 2010 has ½ duration, but also has lower credit risk than the other coupon payments • Last payment, on date of maturity Sept 15, 2011, has highest duration (2), but also has highest risk of default because of the longer maturity of the payment

Now, imagine there are two corporate bonds, not one. Assume That each has a 6 coupon, but that they are from two different Companies. Each bond has payments like that shown below $ 6,000 $ 6,000 $ 6,000 $ 106,000 3/15/10 9/15/10 3/15/11 9/15/11

Now, put the two bonds together in a common “pool” Then the combined pool has the following payment schedule $ 12,000 $ 12,000 $ 12,000 $ 112,000 3/15/10 9/15/10 3/15/11 9/15/11 Now, create Tranche A and Tranche B from this pool Tranche A receives ½ of the proceeds of the pool; Tranche B Receives ½ of the proceeds of the pool. If either bond defaults, then Tranche B loses everything; Tranche A is “protected”. If both bonds default, then Tranche A and B Lose everything.

Bond ratings • Assume that bonds are rated by “probability of default” • Ratings are either AAA, BBB, or C • If default rate is less 5 percent, bond is rated AAA • If default rate is at least 5 but less than 20, then the bond is rated BBB. • Assume each bond has a 10 percent chance of default (1/10 probability of default) • Each bond would normally be rated BBB

What is the probabilty of default of Tranche A? Tranche B? Need to know in order to rate them $ 12,000 $ 12,000 $ 12,000 $ 112,000 3/15/10 9/15/10 3/15/11 9/15/11 Now, create Tranche A and Tranche B from this pool Tranche A receives ½ of the proceeds of the pool; Tranche B Receives ½ of the proceeds of the pool. If either bond defaults, then Tranche B loses everything; Tranche A is “protected”. If both bonds default, then Tranche A and B Lose everything.

Assume the two bonds are “independent” • 1/10 probability of each bond defaulting • Tranche A only fails when both bonds default • 1/10 times 1/10 = 1/100; one percent probability of default • Thus, Tranche A gets AAA rating • Tranche B fails when either bonds default • 1/10 + 1/10 – 1/100 = 19/100 • Tranche B gets BBB rating

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Economics 434 Theory of Financial Markets