Volatility of Bond Prices in the Secondary Market

Bond prices fluctuate in the secondary market just like any other security. The main cause of changes in bond prices is changing interest rates. When interest rates rise, bond prices fall, and when interest rates fall, bond prices rise. However, how much bonds change in price with interest rates depends primarily on 3 factors: maturity, yield, and the credit rating of the issuer.

Maturity

The greater the length of the bond's remaining term, the more sensitive it will be to changes in interest rates. Thus, a 1-year bond will change less than a 10-year bond or a 30-year bond, but it will have the same sensitivity to interest rates as a 30-year bond with 1 year to go until maturity. Thus, bonds with longer remaining terms will be more volatile than those with less time until maturity.

Why should this be? Because the present value of the interest payments and of the principal diminish as interest rates rise; likewise, the present value increases when interest rates decrease; likewise for the length of time remaining until maturity—the greater the bond's term, the lesser the present value of the bond's payments. Because the present value of any future payment is inversely proportional to length of time and to interest rates, rising interest rates will cause the prices of bonds with long remaining terms to drop more than those with shorter remaining terms. On the other hand, if interest rates drop, then the present value of each payment increases proportionately.

Another relationship between bond pricing and maturity is that, with all other factors assumed to be constant over the term of the bond, a premium bond will continuously decrease in price until it reaches par value at maturity; likewise, a discount bond will continuously increase in price to par value until maturity. A bond sells for a premium because the present value of all of its payments are greater than for a bond selling for par value, but this sum of present values decreases with each coupon payment. For the same reason, a bond sells at a discount because the coupon rate it pays is less than the prevailing interest rates, or, in the case of a zero coupon bond, it has no coupon payments at all. Thus, for a discounted bond, much or all of the present value of the bond comes from the present value of the final or only payment, and this present value increases as the date for the final payment approaches.
Graph of price changes for discounted and premium bonds.

Yield

Bonds with higher yields will be less volatile than bonds with low yields. Bonds with yields well above prevailing interest rates are sometimes called cushion bonds, because these bonds help to cushion against falling prices. When a bond's yield is already high, then changes in interest rates will have less effect on its price than a bond with a lower yield. Thus, if interest rates increase by 1%, or 100 basis points, then the price of a bond with a yield of 10% will drop less than a bond with a yield of 4%, because 1% is only 1/10th of 10%, but ¼ of 4%.

Another factor is that the present value of a bond's payment stream is higher for a higher yielding bond, because an investor receives more money in a given time period with the high-yielding bond than with the lower-yielding bond. For this reason, zero coupon bonds have the most volatility for a given discount, because the only payment is received at the end of the bond's term.

Credit Rating

The better the credit rating of the bond's issuer, the less sensitive the bond's price will be to interest rates. Vice versa, when the credit rating of the issuer is low, the bond's price will move more than one with a better credit rating.

A lower credit rating increases a bond's volatility because higher interest rates will hurt a company in poor financial shape more than one in good financial health. Thus, bonds with a lower credit rating will drop in price faster when interest rates rise. Since lower interest rates will help a financially distressed company more than it will help a healthy one, falling interest rates will cause the bonds of lesser credit quality to rise faster.

Current Interest Rates

Fixed
Income
Security
Prices
Fixed income security prices decline when interest rates rise, and vice versa.Prevailing
Interest
Rates

When the prevailing interest rates are high, the price of bonds changes less, because a given change in interest rate is more significant when interest rates are low than when they are high. If interest rates rise by 1%, then this will be a 20% increase when the prevailing rates are 5%, but only a 10% increase when prevailing rates are 10%.

Duration—the Measure of a Bond's Volatility

Duration is the average time it takes to receive all cash flows from a bond or other asset. It is a mathematical formula that calculates a bond's volatility independently of its maturity and yield, for a particular current interest rate, which allows an easier comparison of different bonds. Duration is measured in years, and is equal to the volatility of a zero coupon bond with a term equal to the duration. By reducing bonds to an equivalent zero, it becomes easy to see which is more volatile—the greater the duration, the more volatile the bond. Duration increases with a lower yield and longer maturity.

The formula for duration, first published by Frederick Macaulay in 1938, sums the present value of each interest payment multiplied by the time until that payment is received, and divides it by the sum of the present value of each payment.

Formula for Duration (Macaulay Formula)
T

t=1
t * Ct
(1+y)t
  • D = Macaulay duration
  • t = time until payment in years
  • T = total number of payments
  • Ct = cash flow at time t
  • y = bond yield until maturity
D =
T

t=1
Ct
(1+y)t
Note that the denominator is equal to
the sum of all cash flows discounted
by the yield to maturity which equals
the bond's price.

The Macaulay formula is valid only if all expected cash flows are received. However, it is not accurate with bonds with embedded options or that are callable, because cash flows can change depending on the interest rate. The effective duration, although more difficult to calculate, takes possible changes in cash flow into account.

Macaulay duration is measured in years, but it can be modified to better reflect the change in bond prices due to changes in interest rates. This modified duration is called, naturally enough, modified duration, which is a better measure of how much a bond's price will change for a change of 100 basis points in interest. For instance, the price of a bond with a modified duration of 5 will drop about 5% if the market interest rate increases 1%, or will increase by 5% if the rate drops by the same amount.

Modified Duration Formula
Modified duration formula.
  • Dm = Modified Duration
  • DMac = Macaulay Duration
  • y = yield to maturity
  • k = number of coupon payments per year

A common bond strategy is use duration to adjust bond portfolios to maximize profits from an expected change in market interest rates. If a bond manager believes that bond prices will rise (interest rates fall), then he will lengthen the duration of the portfolio to increase profits. Profits increase because bonds with longer durations rise in price faster because of the longer effective maturities. By the same reasoning, if bond prices are expected to fall (interest rates rise), then a portfolio can be better protected by shortening its duration, which shortens the effective maturity of the portfolio, making it less responsive to increases in interest rates.

Convexity—How Duration Changes with Current Interest Rates

While modified duration can predict how much a bond's price will change for a given change in interest rate, this change actually depends on what the current interest rate actually is. In other words, duration is different for any given bond at different current interest rates. Thus, the duration for a bond when current interest rates are 4% will be different from the duration for the same bond when rates are 6%. Convexity measures the rate of change of duration, or the rate of change of a bond's volatility, to changes in current interest rates.

Convexity, like duration, usually increases with lower yield and longer maturity. Straight bonds always have positive convexity, because cash flows are unaffected by changes in interest rates. However, some bonds, notably callable bonds and mortgage-backed securities, will probably have reduced cash flows when interest rates drop, because of callbacks and prepayments of interest. These bonds exhibit negative convexity.