Refresher Reading. Functional cookies , which are necessary for basic site functionality like keeping you logged in, are always enabled. Allow analytics tracking. Analytics help us understand how the site is used, and which pages are the most popular. Read the Privacy Policy to learn how this information is used. It is important for analysts to have a well-developed understanding of the risk and return characteristics of fixed-income investments.

Beyond the vast worldwide market for publicly and privately issued fixed-rate bonds, many financial assets and liabilities with known future cash flows may be evaluated using the same principles. The starting point for this analysis is the yield-to-maturity, or internal rate of return on future cash flows, which was introduced in the fixed-income valuation reading. The return on a fixed-rate bond is affected by many factors, the most important of which is the receipt of the interest and principal payments in the full amount and on the scheduled dates.

Assuming no default, the return is also affected by changes in interest rates that affect coupon reinvestment and the price of the bond if it is sold before it matures. Measures of the price change can be derived from the mathematical relationship used to calculate the price of the bond.

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The first of these measures duration estimates the change in the price for a given change in interest rates. The second measure convexity improves on the duration estimate by taking into account the fact that the relationship between price and yield-to-maturity of a fixed-rate bond is not linear. Section 2 uses numerical examples to demonstrate the sources of return on an investment in a fixed-rate bond, which includes the receipt and reinvestment of coupon interest payments and the redemption of principal if the bond is held to maturity.

The other source of return is capital gains and losses on the sale of the bond prior to maturity. Section 2 also shows that fixed-income investors holding the same bond can have different exposures to interest rate risk if their investment horizons differ. Discussion of credit risk, although critical to investors, is postponed to Section 5 so that attention can be focused on interest rate risk.

Section 3 provides a thorough review of bond duration and convexity, and shows how the statistics are calculated and used as measures of interest rate risk. Although procedures and formulas exist to calculate duration and convexity, these statistics can be approximated using basic bond-pricing techniques and a financial calculator.

## BUS202: Principles of Finance

Commonly used versions of the statistics are covered, including Macaulay, modified, effective, and key rate durations. Section 4 returns to the issue of the investment horizon. When an investor has a short-term horizon, duration and convexity are used to estimate the change in the bond price.

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In this case, yield volatility matters. In particular, bonds with varying times-to-maturity have different degrees of yield volatility. When an investor has a long-term horizon, the interaction between coupon reinvestment risk and market price risk matters. The relationship among interest rate risk, bond duration, and the investment horizon is explored.

A summary of key points and practice problems in the CFA Institute multiple-choice format conclude the reading.

This reading covers the risk and return characteristics of fixed-rate bonds. The focus is on the widely used measures of interest rate risk—duration and convexity. These statistics are used extensively in fixed-income analysis. The following are the main points made in the reading:. The three sources of return on a fixed-rate bond purchased at par value are: 1 receipt of the promised coupon and principal payments on the scheduled dates, 2 reinvestment of coupon payments, and 3 potential capital gains, as well as losses, on the sale of the bond prior to maturity.

The total return is the future value of reinvested coupon interest payments and the sale price or redemption of principal if the bond is held to maturity. The horizon yield or holding period rate of return is the internal rate of return between the total return and purchase price of the bond. Coupon reinvestment risk increases with a higher coupon rate and a longer reinvestment time period.

Capital gains and losses are measured from the carrying value of the bond and not from the purchase price. The carrying value includes the amortization of the discount or premium if the bond is purchased at a price below or above par value.

The carrying value is any point on the constant-yield price trajectory. Interest income on a bond is the return associated with the passage of time. Capital gains and losses are the returns associated with a change in the value of a bond as indicated by a change in the yield-to-maturity. The two types of interest rate risk on a fixed-rate bond are coupon reinvestment risk and market price risk. These risks offset each other to a certain extent.

An investor gains from higher rates on reinvested coupons but loses if the bond is sold at a capital loss because the price is below the constant-yield price trajectory. An investor loses from lower rates on reinvested coupon but gains if the bond is sold at a capital gain because the price is above the constant-yield price trajectory. Market price risk dominates coupon reinvestment risk when the investor has a short-term horizon relative to the time-to-maturity on the bond. Coupon reinvestment risk dominates market price risk when the investor has a long-term horizon relative to the time-to-maturity —for instance, a buy-and-hold investor.

Bond duration, in general, measures the sensitivity of the full price including accrued interest to a change in interest rates.

### Bond Pricing

Macaulay duration is the weighted average of the time to receipt of coupon interest and principal payments, in which the weights are the shares of the full price corresponding to each payment. This statistic is annualized by dividing by the periodicity number of coupon payments or compounding periods in a year. Modified duration provides a linear estimate of the percentage price change for a bond given a change in its yield-to-maturity.

Approximate modified duration approaches modified duration as the change in the yield-to-maturity approaches zero. Effective duration is very similar to approximate modified duration. Bonds with an embedded option do not have a meaningful internal rate of return because future cash flows are contingent on interest rates.

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## Bond (finance) | Revolvy

Therefore, effective duration is the appropriate interest rate risk measure, not modified duration. The effective duration of a traditional option-free fixed-rate bond is its sensitivity to the benchmark yield curve, which can differ from its sensitivity to its own yield-to-maturity.

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What Is Pull to Par? Key Takeaways Pull to par refers to the tendency for a bond's price to approach its par value as it approaches its maturity date. Discount bonds that trade below par will see their value rise as maturity approaches. Premium bonds, on the other hand, will see their value fall towards par value.

Compare Investment Accounts. The offers that appear in this table are from partnerships from which Investopedia receives compensation. Accrued Market Discount Accrued market discount is the gain in the value of a discount bond expected from holding it for any duration until its maturity. Factors that Create Discount Bonds A discount bond is one that issues for less than its par—or face—value, or a bond that trades for less than its face value in the secondary market. Just as with buying any other discounted products there is risk involved for the investor, but there are also some rewards.

Par Value Par value is the face value of a bond, or for a share, the stock value stated in the corporate charter. It is important for a bond or fixed-income instrument because it determines its maturity value as well as the dollar value of coupon payments. Introduction to Accretion of Discount Accretion of discount is the increase in the value of a discounted instrument as time passes and the maturity date looms closer. Bond Discount Bond discount is the amount by which the market price of a bond is lower than its principal amount due at maturity. Partner Links. Related Articles. Fixed Income Essentials When is a bond's coupon rate and yield to maturity the same?

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