## FRM- Realised Forward rates

anbu.edu
Finance Junkie
Posts: 205
Joined: Mon Feb 04, 2013 3:35 pm

### FRM- Realised Forward rates

A \$100 par bond that pays a semi-annual coupon with coupon rate of 6.0% settles on
5/31/2013 and matures in 1.5 years on 11/30/2104. The price of the bond is \$107.44 as the
six month forward rates are 0.5%, 1.0%, and 1.5%, where each forward rate is the sum of a
term structure rate and a constant spread of 30 basis points:

After six months, as of 11/30/2013, excluding the cash carry (i.e., excluding the coupon),
which is nearest to the carry-roll-down after six months under an assumption of realized
forwards?

a) a. -\$2.73
b) b. -\$0.55
c) c. +\$1.89
d) d. +\$2.40

Ans
"Realized forwards" refers to the assumption that the anticipated forward rates are
realized: in six months, on 11/30/2013, the forward rates will be realized:
 as of 11/30/2013, the six-month spot rate will be 1.0%
 as of 11/30/2013, the six-month forward rate will be 1.5%
Therefore, in six months, the bond will have a one-year maturity and its price will be a
function of the realized forward rates:
\$3.00/(1+1.0%/2) + \$103/[(1+1.0%/2)*(1+1.5%/2)] = \$104.710.
The carry-roll-down is the price change due to the passage of time = 104.710 - \$107.44 = -
\$2.730; or with exact pricing: -\$2.73140.

Doubt- \$103/[(1+1.0%/2)*(1+1.5%/2)- why they are dividing with two rates- can you give me an explaination
Source- web

vighnesh.mehta
Good Student
Posts: 16
Joined: Tue Sep 03, 2013 1:16 pm

### FRM- Realised Forward rates

The present value of a bond is derived by discounting it with the yield(spot rates) associated with the cash flow of the bond.
As we have the six month spot rate, we have to derive the 1 year spot rate when the bond matures.
This can be derived with the formula of (1+S2)^2= (1+S1)*(1+1F1).