Estimating a Bond’s Price from Yield Using Duration
Summary
The document presents a mental-math estimate for a bond priced away from par after its yield changes. It starts from the par case, where coupon rate and yield match, then uses the first-order relationship between price change and yield change. For the example of a bond with a 3% coupon, 9% yield, and 10-year maturity, one answer estimates duration at about 7 and applies it to the six-percentage-point yield increase, arriving at an approximate price of 58. The document reports a more careful annual-compounding calculation of 61.5 for comparison.
Other responses recommend using a calculator, guessing a duration closer to full maturity, or adding a convexity adjustment through a Taylor expansion. These alternatives show the estimate’s limits: duration is only guessed, and a linear approximation omits convexity, so the result is a rough interview estimate rather than a precise valuation. The example does not specify other bond conventions or market details.
Key ideas
- A quick estimate can start from the bond’s par value when its coupon rate initially matches its yield.
- Duration gives a first-order estimate of how price changes when yield moves.
- The example uses an estimated duration to approximate the effect of a six-percentage-point yield rise.
- Convexity can refine the estimate because the linear duration approximation is rough for larger yield changes.
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Full text
# How to price a bond without paper during interview?
# How to price a bond without paper during interview?
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?
## Answer by Dom (score 3)
https://quant.stackexchange.com/a/29609
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.
## Answer by tavmem (score 2)
https://quant.stackexchange.com/a/15030
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.
## Answer by slava (score 1)
https://quant.stackexchange.com/a/15044
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.
## Answer by SohoNYC75 (score 0)
https://quant.stackexchange.com/a/29604
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.Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.