Return on fixed-income securities depends on whether the interest and principal are received in full on specified dates, what is the rate at which coupons are reinvested and how interest rates have affected the price of the security. Duration and convexity are two measures that study how prices change with reference to changes in interest rates.

## Sources of fixed-income return

Return on a fixed income instruments comes from (a) receipt of **coupons and principal** on the scheduled dates, (b) **reinvestment of coupons**, and (c) any **gain and loss on the sale** of the bond prior to maturity.

The rate of return is also affected by whether the bond is issued on a discount or premium. Amortization of discount makes up for the deficient coupon rate and amortization of premium takes away the effect of excessive coupon rate such that the realized return for a buy-and-hold investor is exactly equal to the yield to maturity.

## Yield to maturity as a measure of fixed-income return

The yield to maturity of a bond measures an investor’s return if the following assumptions hold:

- The investor holds the bond to maturity.
- There is no default by the issuer.
- The coupon payments are reinvested at the same interest rate i.e. the yield to maturity.

An investor which holds the bond till maturity realizes the **yield to maturity** if all the above conditions are met. Similarly, for an investor who purchases a bond but sells it mid-way, the **horizon yield**, the *annualized* holding period return from the purchase date to the sale date is equal to the yield to maturity if the coupon rates at reinvested at the same rate and there is no gain or loss on the bond.

The interest income comes from receipt of coupons and their reinvestment and any associated amortization of discount or premium over time.

Any capital gain or loss comes from a change in the value of the security, which results from a change in the yield to maturity.

## Types of interest rate risk: coupon reinvestment risk and market price risk

An investor faces two types of interest rate risk: **coupon reinvestment risk** and **market price risk**, which are *inversely* related. For example, if market interest rates increase, the reinvested value of the coupons increases because they can be invested at the higher market rate, but the value of the security falls because, at the high market discount rate, the lower coupon rate is not attractive. Whether the coupon reinvestment risk matters more, or the market price risk depends on the investment horizon of the investor.

If an investor has a **short-term horizon**, the benefit of high reinvestment income will be much lower as compared to the adverse movement in value of the bond and the realized yield of such investor will be less than the yield to maturity. However, if an investor has a **long-term horizon**, the high reinvestment income from a high market interest rate will matter much more than the adverse effect of the high market rate on the value of the security. In other words, reinvestment rate risk is more of a consideration when an investor has a long-term horizon and market price risk matters more when he has a short-term horizon.