Introduction

In this chapter, we delve into the critical concept of carry roll-down scenarios in bond analysis. Carry roll-down refers to the expected profit or loss on a bond position due to holding it for a specific period. We will explore four common assumptions in carry roll-down scenarios: realized forwards, unchanged term structure, unchanged yields, and realized expectations of short-term rates. Understanding these assumptions is vital for accurately assessing the potential changes in the value of a bond position. We will also learn how to calculate carry roll-down under each of these assumptions.

Realized Forwards

One common assumption is that forward rates embedded in the yield curve are realized. Forward rates are the market’s expectations of future interest rates. If we assume these forward rates will be realized, then the carry roll-down is straightforward. It’s the difference between the initial yield and the yield at the end of the holding period.

Example: Suppose you hold a bond with an initial yield of 4%, and the market’s expectations are that yields will increase by 0.5% over the next year. If these expectations are realized, the carry roll-down would be 0.5%, resulting in a new yield of 4.5%.

Unchanged Term Structure

Another assumption is that the term structure of interest rates remains constant over the holding period. This means that the yield curve doesn’t change shape; it just shifts up or down uniformly.

Example: If you hold a bond with a yield curve that is flat at 4% for all maturities, and it remains flat at 4% over your holding period, the carry roll-down would be zero since the shape of the curve didn’t change.

Unchanged Yields

In this scenario, we assume that yields across all maturities remain constant during the holding period. This is a simplified view, but it helps in understanding the impact of yield changes.

Example: If you hold a bond with a 5% yield, and the yield stays at 5% over your holding period, there is no carry roll-down.

Realized Expectations of Short-Term Rates

This assumption involves the realization of market expectations regarding short-term interest rates. It means that the expected changes in short-term rates actually occur during the holding period.

Example: Suppose the market expects short-term rates to rise by 0.25% in the next three months, and you hold a bond. If this expectation is realized, the carry roll-down would incorporate this 0.25% increase.

Calculating Carry Roll-Down

The formula to calculate carry roll-down is straightforward:

Carry Roll-Down=Yield at End of Holding Period−Initial Yield