## Price versus Market Discount Rate (Yield-to-maturity)

The price of a fixed-rate bond will fluctuate whenever the market discount rate changes. This relationship could be summarized as follows:

- When the market discount rate increases, the bond’s price decreases (inverse effect).
- When the market discount rate decreases, the bond’s price increases (inverse effect).

However, the percentage price change is greater in absolute value when the market discount rate goes down than when it is up due to the convexity effect. We will see why this is true when we learn to interpret and calculate convexity in the reading on *Understanding Fixed-Income Risk and Return*.

**Price versus Maturity**

When a bond is redeemed, at maturity, the bondholder receives the bond’s par value from the issuer. As a result, the bond’s price converges (moves closer) to the par value as the bond nears maturity. It is actually easy to see why this happens. As maturity nears, bondholders are almost assured of receiving the par amount and will therefore not part ways with the bond unless they are offered a price closer and closer to the par value. Buyers are also unwilling to pay much of a premium for a bond nearing maturity because they stand to receive only the par value when the bond is redeemed.

All else equal, generally, the price of a longer-term bond is more volatile than that of a shorter-term bond. Think of a company that has issued a 30-year bond. There are high chances that interest rates, and hence bond prices, will vary quite a bit throughout the 30-year period. The price of a different bond that matures in a few months would show less price volatility as interest rates are unlikely to change a whole lot in such a short period of time. Besides, with a short-term bond, bondholders are almost assured of being paid off.

**Price versus Coupon Rate**

When the coupon rate is greater than the market discount rate, the bond is priced at a premium above par value. When the coupon rate is less than the market discount rate, the bond is priced at a discount below par value.

All else equal, the price of a lower coupon bond is more volatile than that of a higher coupon bond. The smaller the coupon, the greater the interest rate risk

QuestionA bond’s price is forecasted to increase by 4% if the market discount rate decreases by 100 basis points. If the bond market’s discount rate increases by the same amount, the bond price will

most likelychange by:A. 4%.

B. Less than 4%

C. More than 4%

SolutionThe correct answer is B.

The bond price is most likely to change by less than 4% as the relationship between the bond’s price and the market discount rate is not linear (convexity effect).

*Reading 52 LOS 52b: *

*Identify the relationships among a bond’s price, coupon rate, maturity, and market discount rate (yield-to-maturity)*