Being a blogger with a contact form, I often receive PR outreach messages. They want me to write about what they are trying to promote. I ignore most of those. Once in a while, I get something worth reading.
Andrew Kalotay Associates is a fixed income analytics and debt management advisory services company in New York. They sent me a special report they wrote for Mortgage Bankers Association, the industry trade group.
A Financial Analysis of Consumer Mortgage Decisions, Andrew J. Kalotay and Qi Fu
The 60-page report attempts to answer three common questions in getting a mortgage. Two of which are of interest to me.
1. How many points should you pay on your (fixed rate) mortgage? No point, 1 point, 2 points, or a no-cost loan with negative points?
Most of the calculators on the web, including ones created by The Mortgage Professor, use break-even analysis. They show you how long you will break even between different loans. Then they ask you “how long will you keep the house?” That’s actually the wrong question to ask. The correct question should be “how long will you keep the loan?” because you can refinance if the rate goes down.
The Kalotay and Fu paper takes a different approach. It applies “industrial strength” option pricing model to these loan decisions.
A mortgage loan in the U.S. is basically a callable bond. When a borrower gets a loan, the borrower issues a bond to the lender. The borrower is also free to call the bond at par at any time. The call option embedded in the bond has value. The value of the call option differs depending on the interest rate, interest rate volatility, and the remaining term of the loan.
Comparing different loans means comparing the APR for the loan payments, the upfront cost, and the value of the call option. Kalotay and Fu call it option-adjusted APR or APRPlus.
They created a mortgage points calculator for comparing APRPlus. I got some current quotes for a 30-year fixed rate loan from a lender and I calculated the regular APR and the APRPlus:
|Rate||Points & Fees as % of loan||APR||APRPlus|
The 5% loan is a no-cost loan. There is little upfront cost, but it has the highest rate and the highest APR. The 4.5% loan has a high upfront cost with a low APR. After adjusting for the value of the call option, the option-adjusted APRs for all these loans are practically identical.
Even after adjusting for the value of the call option, I think it still biases toward the loan with a higher upfront cost, because the typical holding period for a 30-year loan is much shorter than 30 years even without refinancing.
2. Should you refinance now?
Kalotay and Fu apply the same option pricing framework to the mortgage refinancing decision. When you refinance to a lower rate, you also reduce the value of the embedded option in the loan. The cost savings from refinancing must be sufficient to cover the loss of the option value. This is the same decision framework corporate treasurers use when they decide when to call their bonds.
Because homeowners can’t easily calculate the value of the call option in their loan, Andrew Kalotay Associates developed a mortgage refinancing calculator for us. You enter the information about your current loan and the refinancing offer. The calculator will calculate a Kalotay Refi Score (the higher the better), together with a recommended action. You will get “Don’t Even Think About It!”, “Not Yet!”, “OK, But Not Optimal”, or “Go For It!”
For example, if someone has a $200k mortgage at 5.25% with 28 years to go, refinancing to a 5.0% loan with $2,000 closing cost will get a “Not Yet!”. Cutting down the closing cost to $1,500 will get a “OK, But Not Optimal”. If the closing cost can be reduced to $950 or less, the calculator will say “Go For It!”
I like these option-aware calculators. The mortgage rates are low once again. Try them and see if you should refinance. I already sent out an e-mail to the loan officer I used last time. When the rate hits my target, they will let me know.