Why Mortgage Investors Accept Negative Convexity Risk

Summary

The document explains why investors may hold fixed rate mortgage securities despite their negative convexity. When rates fall, borrowers can refinance, limiting the investor’s benefit from higher bond prices; when rates rise, borrowers are more likely to keep their loans, leaving investors with securities that have fallen in value. The investor’s compensation is a higher yield for bearing this prepayment-related risk.

The answer illustrates the yield premium with a comparison among Treasury and government-guaranteed mortgage rates. It argues that the premium is not compensation for default risk in the cited government-guaranteed mortgage example. The explanation is brief: it identifies the risk and the broad source of compensation, but does not quantify expected prepayments, show how to value the embedded option, or assess whether the quoted spread is adequate. The rates are a snapshot from the original discussion, not a general or current estimate.

Key ideas

• Fixed rate mortgages expose investors to negative convexity because borrowers can refinance when rates fall.
• When rates rise, borrowers may keep their loans, leaving investors exposed to falling mortgage bond values.
• Investors are compensated for bearing this prepayment risk through a yield premium.
• A government guarantee can reduce default risk without removing prepayment and interest rate risk.

Tags

# Why would anyone want to own a mortgage?


# Why would anyone want to own a mortgage?












A fixed rate mortgage has negative convexity. If interest rates fall, the borrower will prepay the mortgage and refinance at the lower rate. If interest rates rise, the borrower will keep the loan but the holder of the mortgage will now have a bond that is worth less. All of the advantages are conferred to the borrower and not the lender.

I can see why a bank who originated the loan would like to collect the origination fees but want to get it off of their balance sheet as soon as possible. But why would an investor want to own such an instrument? The only hope is that interest rates stay where they are and then they might collect a small credit spread and get their money back at maturity (provided the borrower does not default). However, if rates move either up or down, the investor loses by buying a mortgage. Why would anyone want to own such an instrument?

## Answer by dm63 (score 7)

https://quant.stackexchange.com/a/82207

Investors buy mortgage bonds because they get paid for taking the negative convexity risk. For example right now the 10yr UST is at 4.3%, the 30yr UST at 4.65% but the 30yr GNMA mortgage is at 5.5%. This is not related to default risk (GNMA is fully guaranteed by the US Government).

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.