In last week’s post we looked at some of the pros and cons of paying off your mortgage (most of them were pros). An argument for not paying off your mortgage was that if interest rates rise you may eventually be in a positive arbitrage position – earning at a higher rate on bonds than you are borrowing on your mortgage. While this is true, it misses a critical point that we will discuss today.

**Bond Math**

Bond prices are dependent on interest rate changes, and vice versa. If the price of a bond goes up, the interest rate earned (coupon payment divided by the bond price) goes down; conversely, if the price of a bond goes down, the interest rate earned goes up. Over the last 30 years, we have been in a decreasing interest rate environment; this has proved to be a great investment for those that purchased bonds 30 years ago and held them to maturity.

Let’s look at a basic example of how the math looks for bonds in a rising rate environment. Let’s say you have a simple 5-year bond you bought for $1,000 that pays an annual interest rate of 2% per year, or $20. One year goes by and now the going market rate on a 4-year bond is 5%. If you were going to sell your bond you could no longer get the $1,000 you paid for it as it only pays a coupon of $20 a year, or 2%. Comparable bonds are paying a $50 coupon per year. In order to capture a yield to maturity of 5%, you would only be able to sell your bond for $894 – a $106 loss!

It is true that if you do not sell the bond, you do not have to take the capital loss; however, you would continue to earn the 2% interest – not the current market rate of 5%. In fact if you own a bond fund you will see the change in fund’s net asset value (NAV): the value of the fund will drop.

**A Mortgage Example**

Brad has $1,000,000 in his 401K. He is nearing retirement and has a 60/40 split between stocks and bonds with $400,000 invested in the total US bond market ETF BND. He also has a $400,000 mortgage with an interest rate of 4.5%. Currently, BND is paying an interest rate of 2.1%. This means he is borrowing money at 4.5% and lending back out to the market at 2.1%. Hardly a smart strategy.

In addition to being in a negative arbitrage position, since he is lending money and borrowing money at the same time they essentially cancel each other out. Contrary to most people’s thinking, if you buy the same amount of bonds with one hand (your bond fund) and sell bonds with the other hand (your mortgage) your portfolio is essentially at a 0% bond exposure. His actual portfolio is 100% in stocks. This might not be the risk tolerance he believes is appropriate.

Let’s say Brad is confident interest rates will rise in the future and decides to keep his mortgage. In fact, Brad needs interest rates to rise about 3% in order for his strategy to make sense. However, as noted above rising rates will reduce the value of his bond portfolio. Chris Philips of Vanguards Investment Strategy Group said that if rates rose 3% over a 1-year period, then he would expect BND to lose about 12.8% in Net Asset Value, a loss of $51,200 for Brad! It will take a long time for Brad to make up that loss, despite the fact he will now be in a positive arbitrage position.

After realizing this, Brad decides to just skip bonds all together and wait for interest rates to rise. If he decides to invest in stocks instead he is not only taking on too much risk close to retirement, but he is also heavily leveraged. He is essentially borrowing money from the bank (his mortgage) to invest in stocks. If he leaves the money in cash instead he runs the risk of not earning any interest if rates stay low. For the last 5 years the annual return on 1-month treasury bills has been below 1%, where the average annual return has been about 3.5% since 1927. Surely interest rates will rise at some point in the future; however, the annual return of 1-month treasury bills stayed below 1% over a 16-year period from 1934-1949. There is no reason rates can’t stay low for a long time.

**Conclusion**

While it’s true that if rates rise in the future, it may make sense to hold a mortgage and invest in bonds. This decision must take into account the fact that if you own bonds as part of your current investment plan, not only do the mortgage and bonds essentially cancel each other out, but you will lose value in your bond funds while waiting for rates to rise. It is crucial to develop a sound and comprehensive investment strategy that takes into account any mortgages and other debt in order to ensure proper diversification and understanding of overall risk.