# Understanding Sources of Return in Fixed Income | CFA Level I Fixed Income

Let’s dive into the world of fixed income securities and explore the risks and returns associated with fixed-rate bonds. We’ll use numerical examples to illustrate the three sources of return on a fixed-rate bond investment:

• Coupon and principal payments.
• Reinvestment return. This is the return from reinvesting coupons at prevailing interest rates.
• Potential gain or loss on the sale of the bond.

Two main factors can affect returns from these sources:

1. Prevailing interest rate after the purchase of the bond
2. Credit quality of the bond

## Interest Rate Risk and Return

For a start, we’ll focus on interest rate risk, assuming the credit quality remains good. Let’s study the effect of market price risk and reinvestment risk on returns to investors by comparing two investors: Melvin, a buy-and-hold investor, and Sally, a bond trader.

Scenario: Both Melvin and Sally buy a \$1000 par bond with 3 years to maturity that pays an 8% annual coupon, at a market price of \$1081.70.

Calculate the yield-to-maturity (YTM) of the bond when they made the purchase:

Formula: N = 3, PV = -1081.70, PMT = 80, FV = 1000 Solution: YTM = 5%

Let’s examine returns under different scenarios:

### 1. No change in interest rates

Both Melvin and Sally will earn a rate of return equal to the YTM at the purchase (5%), regardless of when the bond is sold or redeemed.

### 2. Increase in interest rates (YTM increases to 7%)

Melvin: Annualized rate of return = 5.14% (higher than 5% YTM at purchase)

Sally: Annualized rate of return = 4.22% (lower than 5% YTM at purchase)

### 3. Decrease in interest rates (YTM decreases to 4%)

Melvin: Annualized rate of return = 4.93% (lower than 5% YTM at purchase)

Sally: Annualized rate of return = 5.4% (higher than 5% YTM at purchase)

Buy-and-hold investors: The change in return due to a change in interest rate is solely because of the change in reinvestment return. The rate of return has a direct relationship with market interest rates.

Bond traders: The rate of return is affected by both market price risk and reinvestment risk. The net effect on the rate of return depends on which component experiences greater change. In our examples, market price risk dominates over reinvestment risk, meaning the rate of return has an inverse relationship with market interest rates.

## Effect of Investment Horizon for Bond Traders

• If the investment horizon is long, coupon reinvestment risk dominates, and the rate of return has a direct relation to market interest rates.
• If the investment horizon is short, market price risk dominates, and the rate of return has an inverse relation to market interest rates.

An investor with an investment horizon to hold a bond till maturity should mainly be concerned with reinvestment risk. They should hope for market interest rates to increase, allowing them to reinvest coupons at higher rates.

Similarly, an investor with a long investment horizon should also be concerned with reinvestment risk, as market price risk affects their returns to a lesser extent.

However, an investor with a short investment horizon should be more concerned with market price risk, as reinvestment risk affects their returns to a lesser extent. They should hope for market interest rates to decrease, leading to higher capital gains on the sale of the bond.

In conclusion, understanding the impact of interest rate risk on an investor’s returns is crucial for making informed investment decisions. Stay tuned for our next lesson on measuring interest rate risk.

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