Bond Valuation
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 Euro). c) What will be the price of this bond after one year (on 30/09/2012) if its yield to maturity is 3%? d) If on 30/09/2012 you decide to sell the bond at the price calculated in the previous question, what will be the return of your investment? How this differs from the expected return calculated in (b)? Comment.
Solution
a) Using the pricing formula for bonds:
[pic]
b) The three different components are: a. Coupon: holding the bond until maturity, the investor will receive three coupons of size 4 Euro, therefore the coupon component will be nC=12 b. Capital gain: it is the difference between the price at maturity and the price at purchase, equal to 100-97.26= 2.74 c. The interest on interest is 0.61, from the following formula:
[pic]
The total expected return from this investment is therefore equal to 12+2.74+0.61=15.35. In percentage terms, the return is equal to 15.35 divided by the invested amount (97.26), minus 1, or 15.78%. In annual term the percentage return will be one third of the period return, i.e. 5.12%.
c) Applying again the formula used in (a):
[pic]
d) If the bond is sold on 30.09.2012 at 3% yield to maturity, the
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 Euro). c) What will be the price of this bond after one year (on 30/09/2012) if its yield to maturity is 3%? d) If on 30/09/2012 you decide to sell the bond at the price calculated in the previous question, what will be the return of your investment? How this differs from the expected return calculated in (b)? Comment.
Solution
a) Using the pricing formula for bonds:
[pic]
b) The three different components are: a. Coupon: holding the bond until maturity, the investor will receive three coupons of size 4 Euro, therefore the coupon component will be nC=12 b. Capital gain: it is the difference between the price at maturity and the price at purchase, equal to 100-97.26= 2.74 c. The interest on interest is 0.61, from the following formula:
[pic]
The total expected return from this investment is therefore equal to 12+2.74+0.61=15.35. In percentage terms, the return is equal to 15.35 divided by the invested amount (97.26), minus 1, or 15.78%. In annual term the percentage return will be one third of the period return, i.e. 5.12%.
c) Applying again the formula used in (a):
[pic]
d) If the bond is sold on 30.09.2012 at 3% yield to maturity, the