With the recent weakness in the bond market and following several questions from clients regarding bond behavior, we thought it would be worthwhile to revisit how bonds react to changes in interest rates. Specifically, how bond *funds* behave with changes in interest rates. Spoiler…there is a silver lining for bonds after a rise in rates.

### Background

As we have indicated in most of our quarterly newsletters, bond prices move inversely to interest rates. With the unanticipated high inflationary data announced this year, interest rates have moved much higher in a short amount of time. This interest rate movement has caused most bond funds to decline in value and many investors are questioning why this happens.

To address this question, below are some bond mutual fund basics:

An individual bond represents a loan to an entity, which promises to pay the investor interest and the borrowed amount at a specified time.

A bond mutual fund is a collection of individual bonds invested for a stated goal.

Bond mutual funds are priced daily based upon the Net Asset Value (NAV), which measures value of all the assets (primarily individual bonds) owned by the fund less the fund liabilities. Each share of a bond mutual fund represents a claim on that NAV.

### Bond Mutual Fund Example

We have recently seen the NAV of many funds decline of late. This is a function of the individual bonds being repriced lower. To illustrate, let’s assume the following hypothetical bond fund and its individual components:

*At the beginning of 2022, Bond Fund XYZ began and has 10,000 shares outstanding owned by investors that contributed $400,000. Therefore, each share of Bond Fund XYZ is worth $40 (assets/shares = $400,000/10,000 shares = $40). On day 1, it purchased $100,000 each of Bond A,B,C, and D at par (the value that is paid back at the end of the bond’s life). The prevailing coupon rate is 3% (and yield to maturity) for all bonds at the time of purchase. *

*Bond A – 1-year, 3% annual coupon bond maturing in 2023 *

*Bond B – 2-year, 3% annual coupon bond maturing in 2024 *

*Bond C – 3-year, 3% annual coupon bond maturing in 2025 *

*Bond D – 4-year, 3% annual coupon bond maturing in 2026 *

Now let’s assume prevailing interest rates rose to 4% immediately after purchase. We would expect the value of the bond fund to decrease, and we can calculate to what extent. All the bonds would be expected to yield 4%, reflecting the new prevailing interest rate.

The formula to calculate bond prices is based on the coupon rate, the coupons and principal (and the time they are received), and the discount rate. Here is an example of the equation to calculate the expected price for the 3-year bond. In our example we will use the new prevailing interest rate as the discount rate (note: in practice the discount rate may be modified for various factors).

Calculating the pricing for the individual bonds using the methodology above, we would expect the value for each bond holding to be approximately:

Bond A = $99,038 ($100k original investment – 0.94% decrease)

Bond B = $98,114 ($100k original investment – 1.9% decrease)

Bond C = $97,225 ($100k original investment – 2.8% decrease)

Bond D = $96,370 ($100k original investment – 3.6% decrease)

**Total =$390,747 ($400k original investment – 2.3% decrease)**

Since there are still 10,000 shares outstanding, we would expect the share price to now be $39.07 or a 2.3% decline from the original $40 price. This is reflective of the underlying decrease in each price of the bonds. Note the longer the time to maturity, the larger the effect of the interest rate change on the price of the bond.

**It is important to note that none of the contractual terms of the bond have changed in the example. The only variable **that **changed was the prevailing discount rate used (i.e., prevailing interest rate). All four bonds should continue to make the 3% coupon payments and pay back the borrowed principal in the end, despite the loss reflected on paper. **

### Interest Rates Jump from 3% to 4% - Future Returns

Now let’s assume that interest rates stay constant at 4% until the last bond matures after year 4. Recall that all bonds are redeemed at par, and we will assume any bonds maturing will be reinvested into new bonds with a coupon rate reflecting the prevailing interest rate.

Here is a graphical example of how we might expect the bond fund’s valuation to behave versus a scenario where interest rates stayed constant at the original 3%:

As you can see in the graph above, when there is an immediate increase in interest rates the fund valuation drops by about 2.3%. However, if interest rates don’t change and proceeds from bond maturities are invested at the prevailing rate, we expect the value of the fund to earn back what was lost from the initial interest rate shock. This is driven by the fact that all bonds in this hypothetical “fund” have a stated amount they will pay back when they mature.

When interest rates rise, the total return of a bond is based a combination of the coupon and the price appreciation. To illustrate, Bond A, from the previous example, is a 1-year bond with a 3% coupon. Bond A’s value dropped to $99,038 when rates initially changed to 4%. An investor will still receive the 3% coupon over the year and will also receive a price appreciation since the investor expects to get their initial loan of $100,000 back when the bond matures.

*Total Return over 1 year = (Ending Value + Interest)/Beginning Value – 1*

*Total Return over 1 year = ($100,000+3,000)/$99,038 - 1 = 4.00%*

Note that the total expected return of this bond over the year matches the prevailing interest rate. This makes sense because on any day, an investor would be indifferent if they purchased a new 4% bond at $100,000 or a discounted 3% bond at $99,038.

### Summary

In our hypothetical example, we simplified the analysis to demonstrate how bond funds can behave after a rise in interest rates. While lowering bond prices initially, the rise in interest rates can improve** **expectations of future returns, since investors can expect newer bonds to pay out the new higher prevailing rate. On the other hand, if interest rates fall, bond mutual funds increase in price initially, but then be expected to earn the prevailing interest rate. These returns are dependent on the future path of interest rates.

Of course, an investor would have been better off if they had waited for the rise in interest rates before investing, but much like the stock market, interest rate moves are difficult to accurately predict ahead of time. The Federal Reserve has stated they are expecting to raise interest rates, but keep in mind they are most focused on the overnight lending rate to member banks, which does not necessarily change interest rates for all bond maturities. Therefore, we believe the best course forward is to maintain a long-term focus and stay committed to your long-term plan.

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