Does paying off a mortgage early affect future loans?
From my understanding, mortgages are considered riskier investments than most other loans because the borrowers can repay early with little to no extra cost. If I hold a 6% bond and the rate on new issues drops to 3%, then my bonds are worth more because they pay more than the new issues. If I hold a 6% mortgage and the rate for new loans drops to 3%, my borrower will probably just refinance (thus the invention of the CMO). Even without changing interest rates, the duration of a mortgage is never as certain as that of other bonds.
In light of this, would lenders see me as a higher risk if I have a history of paying off mortgages early?
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In short, no. The vast majority of "regular" or traditional (Conv/Govt) mortgages are originated by specialty lenders and brokers and are sold in the secondary market to provide yield on bank balance sheets (think Chase or BoA) or to be securitized into MBS. The investors in the secondary market have a very good grip on the prepayment risk associated with a drop in mortgage rates and use pricing or yield to offset this, which is why you so often hear of borrowers paying points and lender fees. None of these originators are allowed to assess you as a higher risk because you paid off a mortgage early.
That being said, most originators are hit with a clawback penalty if you payoff your loan within 6-9 months, meaning that the originator has to repay all commissions and fees to the buyer of the loan if you payoff the loan within that period. I mention this because if you're working with a lender or broker and tell them up front that you intend to payoff your loan in a few months, they probably arent going to waste time on you because they dont want to work for free. They arent really allowed to turn you away, but they will push you away with terrible loan pricing and intentionally bad service.
Investment mortgages, like DSCR loans for investment properties, typically come with prepayment penalties (PPP) to protect against prepayment risk and the keep portfolio CPR in line. Three years is the standard PPP, but 0-5 year options are usually available. If you elect a PPP shorter than 2-3 years in most cases, the lender is simply going to collect that fee A) upfront as points rather than as a PPP, or B) with yield, meaning a much higher rate.