# Roll Returns vs Total Returns

Very basic question I'm confused about :

Is there a formula that relates total return of a bond as a function of yields and its roll down returns?

I mean ignoring reinvestment risk, would the total return of a bond be roll down return + yield?

Yes I think you can say that the total return for a bond over a period equals to first order the sum of

A) yield

B) change in yield over the period * dv01 of the bond.

The question is, what assumption to make about the change in yield. The term roll down pnl is usually defined to mean that the yield curve remains constant over the period. For example, if it’s a 5yr bond and the period is one month, then the yield of the bond at the end of the period is equal to the yield of a 4yr11mo bond at the beginning of the period.

Of course the actual change in yield will not in general be equal to the above calculation.

• So in general Total Return is (1) Yield, plus (2) Rolldown, plus (3) A residual due to "not as expected movement of the yield curve". (I am not sure if (3) has a name). Commented Jul 6, 2019 at 16:20
• Thank you for the answer @alex C I think the term is known as valuation change. Valuation change and roll down return cancel each other if forward rates are realised in the future and total return is yield only. Commented Jul 6, 2019 at 17:02
• I believe that if forward rates are realized, the total return on a bond equals the short term interest rate , not the yield.
– dm63
Commented Jul 6, 2019 at 22:32

Total return approximately equal to the sume of three components:

• issue OAS + rolldown = carry

• mark to market OAS

• falling angel cost if you are investing IG-only

• So for a treasury with 0 OAS, the total return would be just the rolldown? Commented Jul 3, 2019 at 12:35
• Correct, if you hold untill maturity, otherwise you Need to consider OAS evolution Commented Jul 3, 2019 at 14:02
• Shouldn't it be yield + roll down. Because roll down returns are in the range of 0.3% Commented Jul 4, 2019 at 7:54
• OAS is the spread measure, while with yield one means the return rate but they are eventually equivalent, it only depends on how you set the original problem Commented Jul 4, 2019 at 11:13