# How to remove the risk element from a set of fixed rate mortgage offerings?

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.)

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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