Why Do ARMs Use Additive Interest Markups?

Adjustable-rate mortgages in the United States and comparable mortgages in other countries generally use an additive risk markup over the pricing base. For example, the interest rate might be "cost of funds to the lender" plus 3% or the Treasury bond rate plus 2%. In all cases the number after the "plus" serves as a risk premium or markup, whereas the pricing base is a proxy for the riskless rate or the cost of the funds. The question here is why each formula uses an additive risk markup. The question is interesting because under an additive markup, the lenders′ return to risk is not constant across states of nature. Specifically, the return to risk falls as interest rates rise. It can be shown that a constant return to risk requires an alternative pricing formula of the sort 1 + R = (1 + base) · (1 + markup) = 1 + base + markup + markup · base. That is, nonvarying returns on risk require both additive and multiplicative components in the pricing formula. While multiplicative or multiplicative-cum-additive pricing is not uncommon in commercial lending, it is virtually nonexistent in mortgage pricing. In this paper an explanation for the practice of additive pricing is offered. It is based on the hedging qualities of the various pricing formulas for lenders and borrowers. We show that additive mortgage pricing is generally preferred by home-buyers because of the cyclical relationship between housing and interest rates. When market rates rise, housing prices tend to fall (or at least rise less rapidly). Hence a pricing formula that results in a drop in the risk component paid by the borrower (in those states of nature) possesses natural hedging advantages. For the lender, there is also an advantage to such an arrangement. In effect, the additive formula causes the risk component to rise and fall together with the cyclical value of the collateral. Thus the overall risk of default may be lower for any given expected return or markup. In addition, the additive formula may be superior in terms of hedging other risks stemming from other items in the lender′s portfolio. These hedging implications hold for all choices of index base, although the base choice itself also has implications for risk exposure and hedging.