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# Carry-roll-down, realized forwards and unchanged term structure -Not able to understand the timeline

#### Tarun Kaushal

##### New Member
Subscriber
Hi David

Can you please explain the realized forward concept by a timeline diagram. I am unable to understand the solution given in Tuckman Practise Question 317.1 and 317.2. I am unable to deduce the timeline correctly. I have already looked at the posts related to this topic in the forum and i am still not able to visualize the timelines.

Hoping for a quick reply.
Thanks..

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
Hi @Tarun Kaushal

Here is the assumption set under 317.2

The initial state is given by:
Bond price = $102.80 with maturity of 1.5 years and therefore three semi-annual cash flows:$1.1875 coupon
$1.1875 coupon$101.1875 final cash flow

Forward rates (forward rate curve) are:
F(0.5) = 0.20%
F(1.0) = 0.50%
F(1.5) = 0.80%

Finally, this bond's yield is (calculator) given by 3 N, -102.8 PV, 1.1875 PMT, 100 FV --> CPT I/Y * 2 = 0.4990%

The three scenarios concerns which assumption(s) we make if we model forward six months (+0.5 years) in time, when there will be only two cash flows remaining. There are three alternatives given by Tuckman:

(1) unchanged term structure is just the assumption that forward curve is static
F(0.5) = 0.20%
F(1.0) = 0.50%

(2) realized forwards would assume instead that the forward rates "predicted" the future:
F(0.5) = 0.50%; the previous one year rate becomes, in six months, the new six month rate
F(1.0) = 0.80%; the previous 1.5 year rate becomes, in six months, the new one year rate

(3) unchanged yields assumes the yield of 0.4990% remains the same

I hope that helps,

For future discussion, the source is located here at https://www.bionicturtle.com/forum/...d-forwards-and-unchanged-term-structure.6941/

Last edited:

#### Tarun Kaushal

##### New Member
Subscriber
Thanks for your prompt reply. However, i am still confused as to whether these dates are corresponding to ending period or the starting period ? and please explain how the spot rates are being deduced .. ?

Thanks..

#### David Harper CFA FRM

##### David Harper CFA FRM
Staff member
Subscriber
The initial state is settlement: 5/31/2013; at that time, the bond matures on 11/30/2104
The scenarios concern + 0.5 years (six months), so we are talking about the three different scenarios (assumptions) on 11/30/2103
Re spot rates: these are forward rates, spot rates aren't deduced. They can be inferred via usual relationships, thanks