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Hi, can you help me with this exercise ? I'm good in maths but don't understand these financial problems. I would be grateful for any help

One morning, Mr. Kowalski purchased a two-year bond with the face value of $1,000, the coupon rate qual to 10% (coupon payable at the end of each period of one year) and the average annual yield (YTM) being 12%.

Additionally he bought ten-year bond with the face value of $1,000, the coupon rate equal to 10% (coupon payable at the end of each period of one year) and the average annual yield (YTM) being 12%

It was unexpectedly announced in the afternoon that the central bank bad increased base inerest rates. Therefore, yields to maturity on the bond market increased; the average annual YTM on the bond purchased by Mr. Kowalski reached 14%. Calculate the price of the bond purchased by Kowalski and the price for which he could sell it in the afternoon (assume that transaction costs equal zero).

Michael
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1 Answers1

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Answer:

YTM $=12$% $= r$

Coupon $= 10$% of Facevalue $= 100 = C$

Annual payment of coupon in arrears

Maturity amount and the Face Value $= 1000 = M$

Time to Maturity $= T$

Give this,

Price of the Bond $P = \frac{C}{(1+r)^1} + \frac{C}{(1+r)^2}+\cdots + \frac{C+M}{(1+r)^T}$

Apply this formula for Bond 1 and Bond 2 with $T_1 = 2$ and $T_2 = 10$

Price of the Bond 1 $= 966.20$

Price of the Bond 2 $= 887.00$

In the afternoon after the there has been an interest rate hike, r becomes equal to $14$%

Remainder of the numbers remain the same and now compute the price and the results are

Price of the Bond 1 $= 934.13$

Price of the Bond 2 $= 791.36$

Portfolio value before the rate hike $= 1,853.19$

Portfolio value after the rate hike $= 1,725.49$

Intuitively it is correct because a rise in YTM reduces the price according to price yield relationship.

Goodluck

Satish Ramanathan
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