So, with my mid semester coming up this Saturday, I’ve begun heavy revision on FINS3630 — Bank Financial Management.

One problem which I’ve been really struggling with has been the from the Week 2 homework. “There are two different bonds, Bond A and Bond B, which a customer can purchase. Bond A is a 2 year, $1,000 bond which provides an annual coupon worth 10%. Bond B is also a 2 year bond, with a face value of $1000 however with 0 coupons paid out.

Does the Yield to Maturitity affect Bond A or Bond B more?”

Originally when attempting the question earlier in the semester, I neglected it and skipped over it. I usually just ask a friend for help, but today I decided to knuckle down and give this a crack myself.

That said, today I spent a good hour at my desk trying to tackle and solve the problem. To do this, I began to break the problem into parts.

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  • First, I needed to calculate my initial duration of the bond A at a default rate (say 10%).
10% Yield to Maturity, 10% Coupon

From the above result, the calculated duration is 1.91.

  • The duration provided above really didn’t mean anything to me as a number. I wanted to know how it changed with different YTM’s, so I decided to test different stages of duration, to see how the duration might change. I gave it two test percentages (8% & 10%).
8% Yield to Maturity, 10% Coupon Rate
12% Yield to Maturity, 10% Coupon Rate

From these two results, it was clear to see that the higher the Yield to Maturity for a coupon bond, the lower the duration, and vice versa. This is a great thing to note when matching different liabilities/assets.

  • I then decided to test the duration of a non-coupon bond (bond B) at a default rate (10%), the same as a coupon bond
10% Yield to Maturity, No Coupon

At such a glaringly clean number (2.000), it would seem that there was a reason for this.

  • I decided to test two more YTM’s, again 8% and 10% for a non coupon bond. My findings were as below:
8% Yield to Maturity, No Coupon
12% Yield to Maturity, No Coupon

As expected, there was a reason for such a glaringly clean number. It appears that any changes in duration do NOT change the duration for a bond. Which in theory makes sense, as the main thing that affects duration would be the changing return.

  • From my findings, I was then able to answer the key question.

Bond A has a greater variance from the changes in Yield to Maturity, and thus is impacted more from Yield to Maturity. A zero coupon bond on the other hand, would not be impacted at all, a finding which I learnt through working through the exercise.

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The exercise itself here is irrelevant, however what was pertinent from this case study is how I was able to break problems down into parts, and then test things out myself to figure out the answer. This is something which Richard has always emphasised in lectures, and has finally started being drilled into me!

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