I heard that this kind of questions appear a lot in the interviews. Here is one I saw from Galssdoor: Price a bond with coupon rate 3%, yield 9% and maturity 10 years. What is the typical way to do the approximation?
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$\begingroup$ It's a trick question, I'd like to believe. No compounding frequency is given for coupon rate and yield. $\endgroup$– BCLCCommented Oct 15, 2014 at 9:12
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$\begingroup$ yes you're right. but what if those information were provided. any typical method? $\endgroup$– user3337625Commented Oct 16, 2014 at 19:55
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$\begingroup$ Maybe set up the summation and then state the values? The bond price is the sum of coupons* e^(-yield*time). Coupon is 3 dollars a year except at the end where it is 103. Yield is constant 9% a year and so is t: t is 1 throughout. $\endgroup$– BCLCCommented Oct 16, 2014 at 20:09
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$\begingroup$ I would just write the formula. $\endgroup$– SmallChessCommented Aug 13, 2016 at 12:59
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4 Answers
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Back of envelope approach:
$dP \simeq \frac{\partial P}{\partial y} \times \Delta y$
You know that when $y=3\%$, $P=100$. So you can write
$P-100 \simeq \frac{\partial P}{\partial y} \times (c-y)$
and so
Price $\simeq$ 100 + Duration x (3%-9%).
Guess a duration of around 7.0 for a 10 year bond (they would assume that you would have a feel for this number).
So I get 100 - 7 x 6 = 100 - 42 = $58.
If I do this carefully assuming annual compounding then I get $61.5 which is in the same ball park. You can refine this using a second order correction but this would be an acceptable first guess that you can do without calculators.
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It might be more impressive to demonstrate that you have the tools and can use them. Go to the interview with a handheld calculator. The answer is a few keystrokes away.
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consider your bond initially was at par (cpn=3%~=yld_0) and now answer the question what is the price change given new yld_1=9%. for a very dirty estimate use relationship between price change vs yield change and duration (~=10).for a less dirty estimate you'll need some educated guess on the level of convexity. have a look at closed formula of convexity of par bond. hope this helps.
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$\begingroup$ thank you slava! i didn't think of using par bond before... $\endgroup$ Commented Oct 16, 2014 at 19:54
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Use Taylor Expansion to approx price changes for some variations in Yield. Guess the Duration to be less than Full maturity since its Paying coupons and go from there. First price it at Par.
