Bonds have lost significant value in recent months. As measured by the Barclays U.S. Aggregate Bond Index, a widely followed index of U.S. investment grade bonds, bonds are down over 9% year to date. In this article I will cover the sources of bond returns and I will show using bond valuation techniques how two factors (credit and interest rates) affect bond *prices*. In follow-up articles I will show how inflation affects the value of bonds and how higher rates may actually lead to better financial outcomes for investors – even when bond prices fall.

For more information, you may also be interested in two recent articles on bonds we’ve written for Forbes *Why Are Bonds Down?* And *What Should You Do About Bond Price Declines?*.

## The sources of bond returns.

*What is a bond?* A bond is simply a loan. Investors lend money to an issuer, such as a corporation or government, and in exchange for this loan the issuer promises to make interest or “coupon” payments over time and to eventually repay the loan. The “face value” or original value of the loan is often $1,000. The “coupon rate” is the amount of interest paid.

**One source of a bond’s return is yield or income return**. This is the amount which is received in the form of interest payments. For example, if a $1,000 bond pays $50 per year in interest the coupon rate is 5%, or $50/$1,000. The amount received in interest payments over the life of the bond is the income return. But there is more to the story.

**The second source of a bond’s return is capital return – or the return due to the change in a bond’s price.** As you probably know, bonds have lost a lot of value this year. If the coupon payments investors receive are positive, how is this possible? That is because the prices of bonds have declined. We can think about the total return of a bond using a simple formula:

Bond Total Return (%) = Coupon Rate (%) + Change in Price (%)

Imagine you buy a U.S. Treasury Bond for $1,000. The bond has a 5% coupon. A year later, the bond’s price has declined to $900, a change of -10%. If the price stays the same for the year, your total return would be -5%, or your 5% coupon *minus* the 10% change in price. On the other hand, if the bond price increased to $1,080 then your return for the year would be 13%, or 5% plus 8%. But what causes bond prices to fluctuate?

## How are bonds valued?

To better understand how and why bond prices fluctuate, it is helpful to know how bonds are valued. Bond valuation can be complicated, but I’ve tried to summarize the basics below.

Investors use *discounting* to value bonds. You can think of discounting as the opposite of compounding, something we are all familiar with. Compounding can help you figure out how much you would have in your savings account at the end of the year. If you have $1,000 and your interest rate on savings is 5%, you will have $1,050 at the end of the year. The math is:

present value x (1 + interest rate) = future value

or

$1,000 x 1.05 = $1,050

Discounting works the same just in the opposite direction, converting a future amount into today’s value. Discounting can help answer the question *How much would I need to invest today to have $1,050 one year from now?* Assuming the same 5% rate we can rearrange the above to discount $1,050 to calculate the required investment:

present value = future value ÷ (1 + interest rate)

or

present value = $1,050 ÷ 1.05

Discounting $1,050 by one year at a 5% rate gives us $1,000, or the amount we would need to save today to have $1,050 one year from now. Discounting is just compounding in reverse. Discounting can be used to answer even more complex questions. What if we wanted $1,050 *two* years from now? Simply divide $1,050 by 1.05 twice, or 1.05^{2}, and you get $952.

The same discounting process is used to value bonds. Investors discount a bond’s future cash flows (coupon payments + face value) to calculate how much they would be willing to pay for a bond today. Imagine a 5-year bond which promises to make 5 coupon payments of $50 each and a face value of $1,000. We can illustrate these payments over time as follows:

If we apply the same discounting method as above assuming a 5% “discount rate”, we calculate the price of the above bond to be **$1,000**. We do this by dividing each cash flow by 1 plus the interest rate raised to the number of years in the future. The table below shows all future cash flows discounted using the appropriate divisor.

The value of this bond is simply the sum of all its future cash flows discounted to today. Notice how the further a cash flow is in the future the less it is worth today.

We can conclude that the value of a bond will depend on 1) its cash flows and 2) the rate used to discount those cash flows back to today’s value. It stands to reason that bond prices will fluctuate with changes to either cash flows or the discount rate.

## Why do bond prices change?

Bond prices will fluctuate with changes to credit ratings, interest rates and inflation. We can take each of these situations in turn and using what we know about bond valuation show their effect on bond prices.

When an issuer becomes less likely to make promised payments, its **credit rating **is downgraded. Investors adjust future expected cash flows accordingly. Let’s assume that in response to a credit rating change, investors estimate that a bond issuer will only make 80% of its promised future payments. Assuming everything else remains the same, we modify our previous example by reducing all future cash flows by 20%.

The price of this bond after a credit downgrade is $800. This type of price change is an economic loss to the investor. Unless the situation changes, whether the investor sells the bond now or waits until maturity they will get less than they were promised.

Changes in interest rates also affect bond prices. The rule is *bond prices move inversely with interest rates*. But no need to worry about that. The relationship is easy to see using our bond valuation knowledge. You will recall that to discount a future value we divide it by 1 + a discount rate. When rates increase, we divide cash flows by a larger number. Voila! As rates increase, bond prices, which are just the sum of all future cash flows, decrease. In our previous example, we valued a bond using a 5% discount rate. Imagine that rates increase, leading to a higher discount rate of 8%. We can recalculate the value of our original $1,000 bond from above:

Dividing future cash flows by a larger number leads to a lower price. But has our investor lost money? You’ll notice that unlike the credit example above, the cash flows have not changed. If our investor keeps their bond, they will continue to collect all the future coupon and principal payments they were promised. **Lower bond prices due to rising rates do not result in reduced cash flows for the long-term investor. **In my next article I’ll explore how higher interest rates can make many people better off despite bond price losses.

Finally, bond prices can change due to changes in inflation. Inflation reduces purchasing power, and higher than anticipated inflation over the life of a bond will reduce its *real* return. For example, you will still receive your original $1,000 but it could buy (much) less than you anticipated. In my next article I’ll show how changes to inflation affect bond prices again using our bond valuation knowledge.

*All written content is provided for information purposes only. Opinions expressed herein are solely those of Sensible Financial and Management, LLC, unless otherwise specifically cited. Material presented is believed to be from reliable sources, but no representations are made by our firm as to other parties’ informational accuracy or completeness. Information provided is not investment advice, a recommendation regarding the purchase or sale of a security or the implementation of a strategy or set of strategies. There is no guarantee that any statements, opinions or forecasts provided herein will prove to be correct. Past performance may not be indicative of future results. Indices are not available for direct investment. Any investor who attempts to mimic the performance of an index would incur fees and expenses which would reduce returns. Securities investing involves risk, including the potential for loss of principal. There is no assurance that any investment plan or strategy will be successful.*

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