# 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.

• What are your costs of funding? – Phil H Sep 19 '15 at 6:35
• The cost of funding is assumed to be zero. – curious Sep 19 '15 at 6:43

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.

• Qn:To what extent do you win from roll-down only if you sell it before par/0% is reached? – rrg Oct 4 '16 at 22:09

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.