Essay on Bond Valuation

1583 Words Nov 19th, 2011 7 Pages
Assignment no. 1

Fixed Income Securities and Markets

Question A.1
Given the following bond:
|starting date |30/09/2011 |
|maturity date |30/09/2014 |
|coupon rate |4.00% |
|coupon frequency |annual |
|day count |act/act |
|nominal value |100 |

a) Calculate the price of the security on the 30/09/2011, if the yield to maturity is 5% (NB: Price=PV of future cash flows). b) Given the price and the yield to maturity of the bond, calculate the three components of the (expected) total return of this investment (if you invest 100
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PV of the 5 million that you will receive at maturity…) a) What is your profit/loss if you sell this security on the same day for a yield of 3%? Calculate also the duration of this security (NB: remember the definition of duration) b) What will be the price of the security on 30/04/2012 if you can see it for a yield of 2%? What is the profit/loss on your investment if you decide to sell it on 30/04/2011 at 2% yield? c) What is the duration of this security on 30/04/2012? (NB: you can calculate it changing the yield to maturity by 1% and ...)
Solution
a) if the security is sold at 3% yield to maturity, its PV is equal to:

[pic]

In this case the profit would be 4,854,369-4,901,961=-47,592. The duration will be equal to the maturity, given that it is a zero coupon bond, i.e equal to 1. The duration can be calculated also dividing the loss/profit from a 1% change in yield to maturity with the invested amount:

[pic]

b) What will be the price of the security on 30/04/2011 if you can see it for a yield of 2%? What is the profit/loss on your

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