The Matrix Pricing Method of Fixed Income Valuation
So you pull market pricing data on four comparable bonds and create the following matrix:
| Years to Maturity | 3% Coupon | 4% Coupon | 5% Coupon | 6% Coupon |
|-----------------|-----------|-----------|------------|------------|
| 4 | $97.33 3.97% | | $101.23 4.66% | |
| 5 | | | Target Bond | |
| 6 | | $98.65 4.26% | | $103.77 5.25% |
What do you think would be the next step in estimating the target bond’s price?
Great job!
You would want to incorporate price and yield data from each comparable bond:
Four years to maturity:
$$\displaystyle 0.04315 = \frac{0.0397 + 0.0466}{2}$$.
Six years to maturity:
$$\displaystyle 0.04755 = \frac{0.0426 + 0.0525}{2}$$.
Incorrect.
To have a more accurate estimate, you would want to incorporate price and yield data from each comparable bond:
Four years to maturity:
$$\displaystyle 0.04315 = \frac{0.0397 + 0.0466}{2}$$.
Six years to maturity:
$$\displaystyle 0.04755 = \frac{0.0426 + 0.0525}{2}$$.
Now that you have the average yields, you can use linear interpolation to find the interpolated yield of the target bond:
$$\displaystyle 0.04535 = 0.04315+\left(\frac{5-4}{6-4}\right)\times \left(0.04755-0.04315\right)$$
Luckily for you, the curriculum does not require you to calculate an estimated yield using linear interpolation based off matrix pricing. It only requires you to be able to describe the process. That being said, you should still be able to value a bond given a yield.
What is the estimated price of the target bond?
Incorrect.
Try using your financial calculator to solve for the bond’s price.
Incorrect.
Try solving for the present value, instead of the future value of the bond.
Correct! So:
$$\displaystyle 102.04 = \frac{5}{(1 +.04535)^1} + \frac{5}{(1 + .04535)^2} $$
$$\displaystyle+ \frac{5}{(1 + .04535)^3} +\frac{5}{(1 + .04535)^4} + \frac{5 + 100}{(1 + .04535)^5}$$
You can also solve for the bond’s price by using your financial calculator. Set $$FV = 100$$, $$N = 5$$, $$PMT = 5$$, and $$I = 4.535$$. Press "CPT," then $$PV$$ should show as $$= -102.04$$.
In summary:
[[summary]]
Assume you are considering buying a bond from a cloud storage company, but the bond is not priced in the market. The bond pays a 5% annual coupon and matures in five years. You decide to estimate the bond’s price and yield using __matrix pricing__, which is used to value a bond that rarely trades and doesn't have a market price or yield.
Calculate the average yield for four years to maturity and six years to maturity
Interpolate the target price from the known bond price of the 5% and 6% coupon bonds
$97.45
$102.04
$102.50
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