# The Relationship Between Interest Rates and Bond Prices The discount rate for calculating the present value of the cash flows is the bond’s yield. Duration measures how long it takes, in years, for an investor to be repaid the bond’s price by the bond’s total cash flows. At the same time, duration is a measure of sensitivity of a bond’s or fixed income portfolio’s price to changes in interest rates. In general, the higher the duration, the more a bond’s price will drop as interest rates rise (and the greater the interest rate risk). As a general rule, for every 1% change in interest rates (increase or decrease), a bond’s price will change approximately 1% in the opposite direction, for every year of duration.

Remember, lower bond prices mean higher yields or returns available on bonds. Conversely, falling interest rates will result in rising bond prices, and falling yields. Put simply, ultrashort-term bond funds are best for investment objectives with less than a one-year time horizon. This is because the yields for ultrashort-term bond funds are much lower on average than short-, intermediate-, and long-term bond funds. Because of their low sensitivity to interest rates, some investors like to use ultrashort-term bond funds when interest rates are rising.

### How is bond duration calculated?

The formula for the duration is a measure of a bond’s sensitivity to changes in interest rate and it is calculated by dividing the sum product of discounted future cash inflow of the bond and a corresponding number of years by a sum of the discounted future cash inflow.

Because bonds with shorter maturities return investors’ principal more quickly than long-term bonds do. Therefore, they carry less long-term risk because the principal is returned, and can be reinvested, earlier. For example, if rates were to rise 1%, a bond or bond fund with a 5-year average duration would likely lose approximately 5% of its value. However, the “discount” in a discount bond doesn’t necessarily mean that investors get a better yield than the market is offering. Instead, investors are getting a lower price to offset the bond’s lower yield relative to interest rates in the current market.

### What is Duration Bond?

Duration is an approximate measure of a bond’s price sensitivity to changes in interest rates. If a bond has a duration of 6 years, for example, its price will rise about 6% if its yield drops by a percentage point (100 basis points), and its price will fall by about 6% if its yield rises by that amount.

Inflation reduces the purchasing power of a bond’s future coupons and principal. As bonds tend not to offer extraordinarily high returns, they are particularly vulnerable when inflation rises. Inflation may lead to higher interest rates which is negative for bond prices. Inflation Linked Bonds are structured to protect investors from the risk of inflation. The coupon stream and the principal (or nominal) increase in line with the rate of inflation and therefore, investors are protected from the threat of inflation.

Understanding bond duration can help investors determine how bonds fit in to a broader investment portfolio. In contrast, the modified duration identifies how much the duration changes for each percentage change in the yield while measuring how much a change in the interest rates impact the price of a bond. Thus, the modified duration can provide a risk measure to bond investors by approximating how much the price of a bond could decline with an increase in interest rates. It’s important to note that bond prices and interest rates have aninverse relationshipwith each other. Duration measures the time it takes to recover half the present value of all future cash flows from the bond.

If interest rates increase by 1%, additional investors in the same bond will now demand a 6% rate of return. Because the bond interest payments are fixed each year, the market price of the bond will decrease to increase the rate of return from 5% to 6%.

Duration and maturity are key concepts that apply to bond investments. Effective duration and average maturity apply if you have a portfolio consisting of several bonds. While maturity refers to when a bond expires, or matures, duration is a measure of the bond’s price sensitivity to changes in interest rates.

If a bond has a duration of five years and interest rates increase 1%, the bond’s price will drop by approximately 5% (1% X 5 years). Likewise, if interest rates fall by 1%, the same bond’s price will increase by about 5% (1% X 5 years). Still, zero-coupon bonds have unique tax implications that investors should understand before investing in them. Even though no periodic interest payment is made on a zero-coupon bond, the annual accumulated return is considered to be income, which is taxed as interest. The gain in value is not taxed at the capital gains rate but is treated as income.

## Modified Duration

For example, if a corporate bond is trading at \$980, it is considered a discount bond since its value is below the \$1,000 par value. As a bond becomes discounted or decreases in price, it means its coupon rate is lower than current yields. With coupon bonds, investors rely on a metric known as “duration” to measure a bond’s price sensitivity to changes in interest rates. Bond duration is a way of measuring how much bond prices are likely to change if and when interest rates move. In more technical terms, bond duration is measurement of interest rate risk.

## How Duration Works

• With coupon bonds, investors rely on a metric known as duration to measure a bond’s price sensitivity to changes in interest rates.
• Investors can convert older bond prices to their value in the current market by using a calculation called yield to maturity (YTM).

Ultrashort-term bond funds can be smart choices for investors who want better potential short-term yields than money market accounts but less market risk than short-term bond funds with longer maturities. Before buying, though, investors should understand the advantages and disadvantages of this fixed-income investment type, along with the best market conditions for investing. Duration risk, also known as interest rate risk, is the possibility that changes in borrowing rates (i.e. interest rates) may reduce or increase the market value of a fixed-income investment. Duration risk is easier to understand through an example, and we’ll walk through one below. But in plain English, interest rates may change after you invest in a bond.

A bond with a long time to maturity will have larger duration than a short-term bond. As a bond’s duration rises, its interest rate risk also rises because the impact of a change in the interest rate environment is larger than it would be for a bond with a smaller duration. Generally, rising interest rates will result in falling bond prices, reflecting the ability of investors to obtain an attractive rate of interest on their money elsewhere.

Investors can convert older bond prices to their value in the current market by using a calculation called yield to maturity (YTM). Yield to maturity considers the bond’s current market price, par value, coupon interest rate, and time to maturity to calculate a bond’s return. The YTM calculation is relatively complex, but many online financial calculators can determine the YTM of a bond. The Macauley duration is the weighted average time to receive all the bond’s cash flows and is expressed in years. A bond’s modified duration converts the Macauley duration into an estimate of how much the bond’s price will rise or fall with a 1% change in the yield to maturity.

With coupon bonds, investors rely on a metric known as duration to measure a bond’s price sensitivity to changes in interest rates. The duration accomplishes this, letting fixed-income investors more effectively gauge uncertainty when managing their portfolios.

Conversely, modified duration measures the price sensitivity of a bond when there is a change in the yield to maturity. The effective duration shows how sensitive a bond is to changes in market returns for different bonds with the same risk. By accurately estimating the effect of a market change on bond prices, investors can construct their portfolio to capitalize on the movements of interest rates. Also, it can help them manage their future cash flows and protect their portfolios from risk. Investors that are comparing different managed funds or market indices can also look at the portfolio’s average duration which is the weighted average timing of cashflows of all the bonds in the portfolio.

## Duration Strategies

Meanwhile, falling interest rates cause bond yields to also fall, thereby increasing a bond’s price. Macaulay duration and modified duration are chiefly used to calculate the durations of bonds. The Macaulay duration calculates the weighted average time before a bondholder would receive the bond’s cash flows.

While the two concepts are related, they also differ significantly. Macaulay duration finds the present value of a bond’s future coupon payments and maturity value.

Fortunately for investors, this measure is a standard data point in most bond searching and analysis software tools. Because Macaulay duration is a partial function of the time to maturity, the greater the duration, the greater the interest-rate risk or reward for bond prices. Yields on zero-coupon bonds are a function of the purchase price, the par value, and the time remaining until maturity. However, zero-coupon bonds alsolock inthe bond’s yield, which may be attractive to some investors.

Bond yields and bond prices have an inverse, or opposite, relationship. As interest rates increase, the price of a bond will decrease, and vice versa. A bond that offers bondholders a lower interest or coupon rate than the current market interest rate would likely be sold at a lower price than its face value. This lower price is due to the opportunity investors have to buy a similar bond or other securities that give a better return. Low-coupon and zero-coupon bonds, which tend to have lower yields, show the highest interest rate volatility.

This allows investors using managed funds to find funds with greater or lower sensitivity to interest rate changes and therefore they can assess the risk or volatility of the portfolio. Investors interested in short-term returns have numerous options to consider when looking at the market.

Conservative investors tend to like ultrashort-term bond funds because they have less interest-rate sensitivity than short-term bond funds but will typically have higher yields than money market funds. However, ultrashort-term bond funds have lower relative average returns over the long run than short-term bond funds and much lower returns than intermediate-term bond funds and long-term bond funds.

They may not be a smart investment when interest rates are high and at risk of falling, however. As with any investment, market conditions at the time of investing should play a significant role in determining your strategy. Changes in interest rates affect bond prices by influencing the discount rate. Inflation produces higher interest rates, which in turn requires a higher discount rate, thereby decreasing a bond’s price.

Posted on 25.05.2020Categories Bookkeeping 101