Did I get my math right?

In my post Manufactured American financial crisis: all thanks to borrowers, I surmised that investors can get most their money back on creative mortgages.

But I forgot something: the loans were repackaged as securities and sold off. This changes the dynamics of the first point.

Simple model

Under a really simple model, a bank lends cash to a borrower. The borrower uses the cash to buy a house. The borrower pays the bank a series of identical payments over many years. These payments will repay the principal and provide a profit.

Suppose the borrower defaults. If the bank can recover its investment, including the principal and expenses of dealing with the default, it is out nothing except anticipated profits. It retains profit earned to the point of default, and recovered principal can be used towards a new investment.

Securitizing the loan

The problem is when you securitize a loan, where you convert it into a financial instrument. Its price will mimic bond pricing, where the bond’s price is based on expected future payments from the bond issuer.

For example, suppose a bank lent someone $200,000 at 7% yearly interest payable monthly over 30 years. That means the borrower owes $1,330.60 per month for 360 months. In nominal dollars, this is $479,016 over the life of the loan.

For the right amount, an investor can purchase the rights to this series of payments. This can be a win-win: the bank doesn’t have to wait 360 months to get all its money back, and the investor can be assured a fixed income with a known risk for 360 months.

Further suppose someone has investments returning 4% annually. Using a financial calculation called “present value,” this person would break even by purchasing the rights to the mortgage payments for $278,709.13. That is, after 360 months, the investor would end up with the same end result regardless of whether he left the $278,709.13 it in the 4% account or used it to purchase the rights to the mortgage payments. (Obviously, the investor would purchase the rights to the mortgage payments for less than “present value” to come out ahead.)


Here’s a key point: the investor paid way more than the loan’s value.

Suppose the borrower for the $200,000 7% loan defaults right after the investor purchased the loan. The most the investor could recover from foreclosure is the value of the loan. That means in a best case scenario, the investor loses almost 30% of his investment!

In real life, these investments are backed by some kind of insurance. But if masses of irresponsible borrowers default, insurance may have too many losses to pay out.

But politicians exaggerate

It’s obvious that mortgage investments could be more risky than investors anticipated. But does that added risk mean much more than lower return or a modest loss? Nah:

  1. The mortgages are still backed by homes. You can recover most of the outstanding balance of the mortgage.
  2. The vast majority of borrowers will properly pay the loan. I have yet to see any reason to believe that the vast majority of borrowers would be unable to pay their mortgages.
  3. The mortgage investments appear to be in a mix of mortgages. Mixed in with the risky loans will be a ton of perfectly good loans.

I don’t believe the hype, which is why I don’t support the “bailout.”

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