When fixedrate bonds are not actively traded or there is no market price to calculate the rate of return required by investors, it is common to estimate the market discount rate and price based on quoted or flat prices of more frequently traded comparable bonds with similar credit quality, maturity, and coupon rates. This estimation process is called matrix pricing.
Illustrative Example
Assume that an analyst needs to value a 4year, 5% annual coupon payment bond, BondK, which is not actively traded. The analyst could find some other bonds, however, with a comparable credit quality:
 BondL: 3year, 5.5% annual coupon payment bond at a price of 108; and
 BondM: 5year, 4.5% annual coupon payment bond at a price of 105.
Therefore, we start off with the following matrix:
4.5%coupon Bond 
5%coupon Bond 
5.5%coupon Bond 

3year Bond 
Price = 108 YTM = ? 

4year Bond 
Price = ? YTM = ? 

5year Bond 
Price = 105 YTM = ? 
Step 1: Find the Yieldtomaturity of Observed Bonds
Using the financial calculator for BondL: N=3; PV=108; PMT=5.5; FV=100; CPT => I/Y = 2.6887. The required yield on BondL is 2.69%.
For BondM: N=5; PV=105; PMT=4.5; FV=100; CPT => I/Y = 3.3959. The required yield on BondM is 3.40%:
We now have two more data points in our matrix:

4.5%coupon Bond  5%coupon Bond  5.5%coupon Bond 
3year Bond 
Price = 108 YTM = 2.69% 

4year Bond 
Price = ? YTM = ? 

5year Bond  Price = 105
YTM = 3.4% 

Step 2: Find the Yieldtomaturity of the Nonactively Traded Bond
The estimated market discount rate for a 4year bond having the same credit quality is the average of two required yields:
$$ YTM_{BondK} = \frac{2.69\% + 3.40\%}{2} = 3.045\% $$
We now have the following matrix:
4.5%coupon Bond  5%coupon Bond  5.5%coupon Bond  
3year Bond  Price = 108
YTM = 2.69% 

4year Bond  Price = ?
YTM = 3.045% 

5year Bond  Price = 105
YTM = 3.4% 
Step 3: Find the Price of the Nonactively Traded Bond
Given an estimated yieldtomaturity of 3.045%, the estimated price of the 4year 5% illiquid bond is 107.26 per 100 of each par value. To find this value, we need to plug in the following variables into the financial calculator: N=4; I/Y=3.045; PMT=5; FV=100; CPT => PV = 107.26
Alternatively, we could use a timeline to find the same value:
Time period  1  2  3  4  
Calculation  \(\frac{$5}{(1+3.045\%)^1}\)  \(\frac{$5}{(1+3.045\%)^2}\)  \(\frac{$5}{(1+3.045\%)^3}\)  \(\frac{$105}{(1+3.045\%)^4}\)  
Cash flow  $4.85  + $4.70  + $4.56  + $92.92  = $107.03 
Benefits of Matrix Pricing
Matrix pricing is also used during the underwriting process to get an estimate of the required yieldspread over the benchmark rate, where the benchmark rate is generally the yieldtomaturity of a similar government bond. Yield spreads are often stated in terms of basis points (bps). For example, if we have a yieldtomaturity of 3.75% and the comparable government bond yield (or benchmark rate) is 2.5%, the yieldspread will be 1.25% or 125 bps.
Question
Matrix pricing allows investors to estimate:
A. The required yield spread as well as prices for bonds that become substantially risky after bond’s initial issuance
B. The bond coupon rates for bonds that are comparable to government bonds
C. The market discount rates as well as the prices for bonds that are not actively traded
Solution
The correct answer is C.
Matrix pricing is a price estimation process that uses market discount rates based on the quoted prices of similar bonds (similar maturity, coupon rates, and credit quality) when a fixedrate bond is not actively traded or there is no market price.
Reading 52 LOS 52e:
Describe matrix pricing