Bond Carry and Roll-Down Returns on an Unchanged Yield Curve
Summary
The document compares buying a one-year Treasury and holding it to maturity with buying a three-year Treasury and selling it after one year, assuming the yield curve stays unchanged and funding costs are zero. It explains that the longer bond earns its higher initial yield during the first year, then may be sold at a premium after its remaining maturity shortens to two years, where the unchanged curve has a lower yield.
Using the stated yields, one answer estimates 0.24% return for the one-year bond and 1.30% for the three-year strategy, combining 0.80% carry with an estimated 0.50% price gain. This is an illustrative calculation, not a general guarantee: actual returns depend on bond cash flows, pricing conventions, funding, transaction costs, and whether the curve truly remains unchanged. The discussion also notes that very short-maturity bond prices can behave unusually near maturity.
Key ideas
- An upward-sloping yield curve can make a longer bond earn more carry than a short bond.
- If yields remain unchanged, a bond may gain price as it rolls toward a lower-yield maturity point.
- The example estimates 0.24% return for the one-year bond and 1.30% for the three-year bond sold after a year.
- The comparison assumes zero funding cost and an unchanged yield curve.
- Short-maturity pricing can be affected by market funding and arbitrage activity.
Tags
Full text
# Will rolling-down-yield-curve bond strategy work if interest rates remain unchanged? # Will rolling-down-yield-curve bond strategy work if interest rates remain unchanged? Suppose I have 2 strategies; A) Buying A One Year Bond And Holding To Maturity (Buy & Hold To Maturity) B) Buying A 3 Year Bond and Selling After One Year (Rolling Down The Yield Curve) Assume that the 1 year treasury yield to be 0.24%, the two year 0.55%, and 3 year to be .80%. The cost of funding is assumed to be zero. During the next one year, interest rates do not move at all. Which strategy will be more profitable? Some bond mathematics, if possible, would be useful. I understand strategy B will be more profitable if interest rates go down later. I am wondering what happens if interest rates remain static. ## Answer by rrg (score 3, accepted) https://quant.stackexchange.com/a/30390 Strategy (B) will always win. In most simple sense, you are achieving a yield of 0.80% for investment in the first year, and sell-buying back at 0.80% for investment in the second year (because as you state the yield curve has not moved). This is known as carry. There is an indirect gain through price-roll, too. Strategy (A) will perform poorly. In your scenario, the yield curve is monotonically increasing (upward sloping). The initial yield is 0.24% [clearly 56bp less carry than (B)], and the roll-down is relatively modest. Bond prices tend to behave oddly in the final days/weeks of trading, as a variety of market participants fund and arbitrage in very different ways. Have a look at money market instruments to discover more. ## Answer by dm63 (score 2) https://quant.stackexchange.com/a/31568 Strategy A: You borrow at 0% and invest at 0.24% for one year, so you make 0.24% total return. Strategy B: You borrow at 0% and invest for one year at 0.80%, making 0.80%. You then sell the 0.80% bond at a yield of 0.55% (it is now a 2yr bond, whose yield must be 0.55% if rates are unchanged). The price of this bond will be 100.50%, since you are getting an extra 0.25% for an additional 2 years. Hence your overall profit is 0.80% + 0.50% = 1.30% Therefore Strategy B is much better , assuming rates do indeed stay unchanged.
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