# Bond Math & Negative Convexity

## Here’s Why Your Mortgage is Valuable.

A little bond math to illustrate why the debt you’ve borrowed may be one of your greatest assets

As a real estate investor, you may not immediately think of your loans taken out as being favorable to you. However, the debt you borrowed over the last two years is actually one of the greatest assets in your portfolio. Why is that?

Over the last year, the 30-year fixed mortgage rate has climbed aggressively, more than doubling from 3.1% to almost 7%. If you were a lender, it has been a terrible year.

Mortgages with similar characteristics like loan size, loan-to-value (LTV), FICO credit scores get pooled together and traded in the market between banks, insurance companies, mortgage REITs, etc. These loans illustrate how much prices have aggressively moved down over a short period of time.

Let’s take a look at some basic bond math to determine how the value of your loan has changed dramatically, while diving into a unique feature of mortgages.

## How To Determine Bond Value

To understand the price changes and quantify why lenders are hurting, let’s review a hypothetical example:

The loans you take out in your real estate business are simply bonds secured by real estate (usually owned by an entity that buys mortgages, like banks or insurance companies).

Let’s say a bondholder is holding a \$100,000 loan and the interest rate is 6%, which is what it was at origination. But a lender can make virtually the same loan in the market now with similar terms at 7.5%. So why would another buyer buy this loan and only receive 6%, when the current market rate could be 7.5%?

To compensate, the bondholder is going to put a discount on the bond and sell it for less than \$100,000. What’s the right discount that the bond should trade at?

Looking at the 6% original interest rate and the current market interest rate of 7.5%, you calculate a difference of 1.5% every year. This difference is what would be left on the table if you were to buy a loan offering 6%, even though the current market is at 7.5%. Then you consider how long this loan will stay outstanding – let’s say that it will pay off in 5 years. So over that period of time, 1.5% * 5 years = 7.5%

The discount on the loan price should be 7.5% and the bond price would be 100% – 7.5% = 92.5% of face value, which is the same as 92.5 cents on the dollar. That is the price a bond buyer would be willing to pay for this loan.

This loan price has dropped from 100 (par) at origination to 92.5 cents on the dollar.

You’ll notice that two main factors determine pricing: the interest rate (bond yield) and the amount of time the loan would be outstanding before it’s repaid (duration). Now let’s apply this to mortgages.

## US Mortgages: Uniquely Favorable to Homeowners

Structurally mortgages are an incredible deal for American homeowners. We decided as a country that for the benefit of American society, homeowners could take out long-term, 30 year fixed rate mortgages. Not only that, but homeowners wouldn’t be locked in because they have the option to move or refinance at any time.

This is an amazing one-sided transaction favorable to the borrower, which does not happen in commercial transactions. It’s only available to the American homeowner. In some situations, the lender really ends up losing.

### Increasing Duration

For the past 20 – 30 years, we’ve had declining interest rates. Homeowners have either moved for personal reasons or refinanced roughly every five to seven years because they had the opportunity to get a lower rate. Because of that free option to refinance, these 30 year loans have been paying off, on average, at a duration of every five to seven years.

However, in a rising interest rate environment, homeowners won’t give up the low interest rate they locked in for 30 years that easily. Maybe they’ll stay in a house for longer or choose not to refinance because rates are only going higher.

The mortgage interest rate that used to be 3.5% is now 7%, and the bigger that gap gets, the longer a homeowner will stay in the loan. That means that instead of mortgages paying off every five to seven years, it takes longer – perhaps 10 or 12 years, which is a lengthier duration than it was in the last 20 or 30 years.

### Negative Convexity: Why Bondholders are Hurting

Mortgage bondholders are getting hurt on both dimensions that factor into bond pricing – the bond price is dropping because interest rates and the opportunity cost to capital is increasing, while the borrower is simultaneously able to keep that loan for a longer period of time.

This phenomenon where bond prices are dropping and the duration is getting longer is known as negative convexity, which refers to the shape of the graph plotting bond yields versus prices.

As an example, mortgages originated back in December were worth par, or 100% of face value. Now they’ve gone from being worth 100% down to 62%. Credit quality is not an issue, but if a lender originated a loan at par last December, they have lost 38% because now it’s worth 62%. As a result, volatility and situational distress has started to creep into the economy based on this violent increase in rates. It’s a horrific environment to be lending in and bond buyers have been getting destroyed.

American mortgages uniquely have this feature of negative convexity, which makes them dangerous for bondholders or lenders in a rising interest rate environment. Understandably, mortgage buyers and lenders have become a bit gun-shy. On the other hand, as a real estate investor, you can think of the price changes as how much you’ve effectively made on the loans taken out last year.Looking to finance your next purchase? Dominion offers competitive rates for rental, fix & flip, ground-up construction, and multifamily bridge loans.

Published December 28, 2022