Kept waiting in the bank yesterday, with no paint to watch dry, I found myself staring at the mortgage rates. (These are all annual interest rates):

  • Variable: 2.475%
  • 1 year: 2.90%
  • 2 years: 3.05%
  • 3 years: 3.15%
  • 5 years: 3.30%
  • 7 years: 3.35%
  • 10 years: 3.65%
  • 15 years: 4.25%
  • 20 years: 4.70%

The longer the fixed rate the higher the interest rate; no surprise there, as the bank wants its reward for taking on the risk of rate movements. But the chart of those prices is neither a straight line, nor a simple curve, so it must represent more than risk. (?) Does it represent this bank's predictions of how the central bank's benchmark interest rate will move?

If so, how do I extract their prediction from that data? I.e. how do I remove the fixed-rate risk element. (BTW, the current benchmark interest rate is 0.00%, which may affect the calculations, as rates can only move in one direction.)

As these are rates offered to consumers, could there there also be an element of marketing here? E.g. is the 7 year rate artificially low because they want to tie more people into the 7 year rate than the 5 year rate?

(Rates are from Tokyo Mitsubishi UFJ bank; benchmark rate is from Bank Of Japan.)


Mortgage prices involve the following elements

  • The cost of funds to the bank
  • The risk of default by the borrower
  • The price of any embedded optionality in the mortgage
  • Anticipated administration costs
  • Upfront payments (known as "points")

To first order, there isn't actually any premium associated with the risk of rate movements, because the bank can hedge those away by taking opposing positions in the swaps markets. Higher-order rate risk effects related to optionality do exist.

The cost of funds to the bank is essentially "the" risk-free rate plus a premium associated with the bank's own potential for default. In the USA most mortgages are actually priced against FNMA's cost of funds, because most mortgages are securitized and sold to that agency. Tokyo Mitsubishi would have a relatively low default risk and cost of funds like Fannie Mae.

Different countries have different customs about optionality. In the USA, almost all mortgages allow the buyer to prepay without penalties but that's not the case in the UK. Traditionally US mortgages had tended to be fixed-rate, so the embedded prepayment option enjoyed by the homeowner can be valuable.

Floating rate mortgages, more common in the USA in the last decade and in Europe for many decades, entail less interest-rate risk for the issuer but the optionality of gradual rate increases, caps, and floors can be complicated. In practice lot of that optionality is just plain ignored when setting the prices, particularly since borrower default is a more important element and simultaneously difficult to measure or estimate.

  • $\begingroup$ Thanks for the interesting answer Brian, though it left me confused: if there is no risk premium involved, why do the fixed rates go up the longer the term? Or do you mean there is nothing for me to remove and it is "pure" prediction about the way this bank thinks the BOJ benchmark rate will go? E.g. that it will go from 0.00% to 0.425% in the next year. $\endgroup$ – Darren Cook Feb 9 '12 at 0:04
  • $\begingroup$ Risk-free rate curves in western countries do generally increase with tenor, though not all the time. (When they don't it is called an "inversion"). From the mortgage issuer point of view there is not any rate risk due to the ability to hedge in teh swaps market, so rate risk does not come into the calculation of mortgage rates -- it is wholly priced into the curve. Somewhere down the line, of course, someone does take the short-to-long rate risk, and there is a volatility and associated premium there that tilts the curve up. $\endgroup$ – Brian B Feb 10 '12 at 15:33

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