At some point in the next couple months, I will write down what I think is the best 30-year fixed rate mortgage (FRM) and best adjustable-rate mortgage (ARM) available to me. The ARM may be 5/7/10 year initial period, with a 30 year loan term - I will choose just the one specific ARM that I think is best at this time.

Then, over the course of owning the home, I will track the actual cost of the mortgage I choose, and the counterfactual cost I would have had on the other mortgage. I will resolve based on which of them would have been cheaper overall in the end - resolves YES if the 30-year FRM is cheaper, NO if the ARM is cheaper.

The cost calculation will include the mortgage payments as well as opportunity cost and refinancing opportunities.

Would love to hear your insights in the comments. By the way, I am working on writing some simulation code to help me model this. I will update when I have insights from that.

Details

My cost computation will include:

• The mortgage payments

• Opportunity cost: For simplicity, I will assume that the difference in cash on hand will be invested in the Vanguard Total World Stock Index Fund (VT).

• Refinancing opportunities:

  • If at any point I refinance my actual mortgage or decide I would have refinanced the counterfactual other mortgage, I will then track the cost of the refinanced mortgage instead. This will be a best-effort thing because optimization is hard (there is a potentially-exponential tree of potential future paths).

  • If it makes things easier, I might instead calculate with a simplified model where I refinance whenever mortgage rates drop some amount (perhaps 1%) below the rate of the current mortgage.

  • The main reason for a refinancing would be to take advantage of lower interest rates to reduce the total expected future cost of the mortgage. Another reason could be cash-out refinancing to convert home equity into cash - note that the additional cash would be invested in this cost calculation, and stock market returns are generally higher than mortgage rates, so this is likely to be advantageous both in the cost calculation and in the real world in my personal situation.

Some of the key factors in which is better are:

• How much lower the initial ARM rate is than FRM - currently I'm seeing about 0.6% lower for a 7-year ARM.

• How interest rates change over time. FRM locks in an option on the current interest rate (if rates drop, then you can refinance; if rates stay the same or go up, then you can keep the FRM). ARM varies with the interest rate after the initial period (it's usually set to SOFR + some fixed margin). So generally FRM is better if rates rise, ARM is better if rates fall.

• How long I own the house: Currently, I very roughly predict a 30% chance of owning the home for less than 5 years, 30% chance of 5-20 years, and 40% chance of owning the home for 20+ years. Typically, ARMs are cheaper than FRM until some breakeven point.