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Currently I'm learning about the principles of corporate finance. More specifically I'm learning about valuing bonds. I have the follow question:

Is the yield on high coupon-bonds more likely to be higher than on low-coupon bonds when the term structure is upward or downward sloping?

From the theory I learned that the yield is the expected return that investors get from the bonds. That means that in upward sloping investors can expect a higher return if they invest in long-term bonds. Alternatively with downward sloping investors can expect a higher return if they invest in short-term bonds.

I'm not really sure about the high-coupon and low-coupon definition, but I assume that a high-coupon bond has a higher coupon rate and vice versa.

To answer the question these concepts need to be linked together. Unfortunately I don't see how.

My question is:

How are the yields of high-/low- coupon bonds connected to the structure term?

Answer from the book:

Downward sloping. This is because high-coupon bonds provide a greater proportion of their cash flow in the early years.

Side question:

Why do high-coupons provide a greater proportion of their cash flow in the early years? Why is this? I thought that the cash-flow of coupons stays fixed, since the coupon rate stays fixed. Besides, if high-coupon bonds provide a greater proportion of their cash flow in the early years. What is the connection with downward sloping?

A lot of questions, but I hope that somebody could help me out! That would be really appreciated.

Kinds regards, Tim

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2 Answers 2

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Yield to Maturity (YTM) is a complex average of the spot rates, which is weighted by the cash flows. What that means is that the YTM of the bond will be centered around the spot rate of the year that the highest proportion of cash flows are received. For a bond this is the year of maturity, where the biggest proportion of cash flows are received.

  1. When the coupon rate of a bond increases (regardless of the term structure), the proportion of cash flows from the bond get shifted towards the left (left being the early years and right being the later years). You can check this in an excel by tabulating the PV of Cash flows from two bonds at different coupon rates. The proportion of cash flows in the first few years are relatively higher for higher coupon bonds than lower coupon bonds.
  2. From the above point, you can infer that increasing the coupon rate for a bond (regardless of term structure) shifts the YTM towards the left (relatively speaking) ie. towards the initial years. Relatively higher weight to the initial years
  3. So when the term structure is upward sloping ie. Lower spot rates at the left compared to the right, increasing the coupon rate shifts the YTM to the left. So YTM falls
  4. When the term structure is downward sloping ie. Higher spot rates at the left compared to the right, increasing the coupon rate shifts the YTM to the left. So YTM increases.

This is an intuitive way of understanding the concept. You could tabulate all this in an excel and see for yourself. The conclusion would be the same.

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High-coupon bonds, which have higher interest rates, often provide a greater proportion of their cash flow in the early years for a few reasons.

First, the coupon rate determines the periodic interest payments received by bondholders. Since high-coupon bonds have higher coupon rates, they generate larger coupon payments. So, in the early years, when these payments are a fixed percentage of the bond's face value, the cash flow from coupons is naturally higher.

Second, the cash flow from coupons stays relatively fixed, as you mentioned, but the proportion it represents changes over time. As the bond approaches maturity, the interest payments become a smaller percentage of the total outstanding principal since more principal has been repaid. This causes the proportion of cash flow from coupons to decrease over time, making the early years more significant.

Now, regarding the connection with a downward sloping curve, it's important to understand the yield curve. The yield curve plots the interest rates of bonds with varying maturities. As time progresses, the shape of the yield curve can change. When short-term interest rates are higher than long-term rates, the yield curve has a downward slope.

In such cases, high-coupon bonds tend to have shorter maturities, and their cash flow is concentrated in the earlier years. As a result, investors may prefer these bonds to capture higher interest payments in the short term. This preference for higher cash flow in the early years contributes to the proportionality of cash flow being higher in the beginning of high-coupon bonds.

Ultimately, the higher cash flow in the early years for high-coupon bonds is a combination of their higher coupon rates, the fixed percentage nature of coupon payments, and their alignment with the shape of the yield curve when it slopes downward.

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