### Leverage and Derivative of Mortgage Debt

January 06, 2008
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In Six Degrees of Leverage Part I I showed how a modest change of interest rate changes the effective yield on a hypothetical 10 utility bond. Because rates declined from 6% to 4.5%, the bond was priced up so the yield would be 4.5% and because of selling early the yield ended up being 8.3%.

One thing that I don't remember looking at in that series is the leverage if a mortgage if the price of a mortgage is priced to reflect current rates, or just different rates. I was reading John Mauldin 2008 forecast and he said something about some derivatives having 3 times the face value. I am not going to profess to understand the complexity of the things the financial industry has done, but I suspect that some of this bad mortgage debt has also been repriced somewhere along the line to reflect current yields, and this post is calculating the principal some of those terrible mortgages may have been sold for somewhere in this mess.

My reading on the municipal funds that got into trouble with CDOs was that their yield was about 5.5%, so this is the rate that I will use to re-price these 30 year mortgages. There is some of this crazy stuff that was priced at 1 and 2%, but my reading shows that these were not that common, and a rate around 6% was more common. Some of it is being repriced to as much as 12% for the last 25 years.

On a 30 year mortgage, especially if the starting rate was low, there would be very, very little principal paid back during the first 5 years. Say you had $100k at 6% for 30 years. The monthly payment would be about $600. At the end of 5 years you would still owe about 92,900. If it reset to 12% your payments would increase to about $952/month. Even though the payment started at $593, the average payment over the mortgage would end up being $892. To have a constant payment for 30 years the rate would have been 10.4%, so the effective rate tends to be closer to the reset rate than the starting rate.

For simplicity I am just going to use a constant rate over the life of a 30 year mortgage and calculate a purchasing price for the debt to re-price the yield to 5.5% for a $100k mortgage.

Rate (%) | Total Payment (for $100k Mortgage) | Priced at 5.5% yield |

3 | 151,000 | 74,700 |

3.5 | 161,000 | 79,500 |

4 | 171,000 | 84,500 |

4.5 | 181,000 | 89,500 |

5 | 191,000 | 94,700 |

5.5 | 202,000 | 100,000 |

6 | 213,000 | 105,500 |

6.5 | 224,000 | 111,100 |

7 | 236,000 | 116,700 |

7.5 | 248,000 | 122,500 |

8 | 260,000 | 128,300 |

8.5 | 272,000 | 134,400 |

9 | 284,000 | 140,300 |

9.5 | 296,000 | 146,400 |

10 | 309,000 | 152,600 |

What I understand in this mess is that even prime loans are resetting at higher rates, so they may not be resetting to 12% like a subprime loan, but they maybe resetting to 8 or 9 percent. A reset to 8% gives an effective rate over the life of the mortgage of about 7.5% and if that prime mortgage was repriced to yield 5.5%, well there is about 22% extra being charged to an investor than what the borrower got.

Without making a new table, say it had a teaser rate of 3% and was resetting to 12%. These things were rated AAA so there would have been the ability to reprice them to yield 5.5%. In this case the difference is 104%.

The incentives to keep homeowners in their homes and to work out new financing arrangements to prevent foreclosures resets the effective rate down. Reducing the effective rate by 2% re-prices the principal down by about 20%.

It does make me question just what was it that hedge funds were doing that enabled them to make those insane rates of return. Would anyone reading this actually pay $122k for $100k of debt and give the bank $22k for their services and then hope to collect over the next 30 years?

But somehow with their financial scythe they've managed to create something valued at 3 times the face value. It does explain how it is that some of these things have gone to zero value...