a.  The matrix pricing strategy is adopted for the fixed-rate bonds without an active market or those bonds that are not yet issued. Since there is no active market, therefore there is no market price to calculate the YTM.

b.  Therefore in these cases, we use the liquid comparables to find the YTM and then calculate the price of the bond.

c.  Thus the steps of calculating the price of the bonds, as per the matrix pricing method are:

     i.  Step 1: Find the comparable credit quality corporate.

    ii.  Step 2: Calculate the YTM for each bond.

   iii.  Step 3: Find average YTM per bond.

   iv.  Step 4: Interpolate the results to find the YTM of the required bond.

d.  For example, we have to find the YTM for the 3-year, 4% semi-annual corporate bond. And, we have the data available for 2, 3, 4, and 5-year bonds with the coupons of 2%, 3%, 4%, and 5%.

We would take the data of a 2-year bond with a coupon of 3% and 5%, and a 5-year bond with a coupon of 2% and 4%. The prices of these bonds are:

Since, we are given the information regarding the price, coupon rates, and term to maturities, we can calculate the YTM of each bond, using the financial calculators.

The YTM of each of the required bond is:

Now, we calculate the average YTM of the bonds with 2 and 5 years to maturity.

The average YTM of the bonds with 2 years to maturity is (3.786 +3.281) / 2 = 3.8035%

And, the average YTM of the bonds with 5 years to maturity is (4.181 +4.196) / 2 = 4.1885%

Now, we interpolate these averages to calculate the YTM of the required bond as follows:

YTM = 3.8085 + [(4.1885 – 3.8085) / (5-2)] = 3.93183

Using this YTM we can calculate the price of the bond as $ 100.191.

e.  For the bonds not yet issued, we need the required yield spread over the benchmark rate. This is mainly because; most of the corporate bonds trade at a spread above the government rates.
The benchmark rate here is the comparable ‘term-to-maturity’ on government bonds.

f.  For example, suppose a company proposes to issue a new 5-year bond and we have to find the spread that would be required for the desired YTM, given the following information:

     #.  The company has the previous issue of 4-year, 3%, and semi-annual bond trading at $ 102.40.

     #.  The information for any 4-year government bond is not available, but a 3-year government bond is giving a YTM of 0.75% and a 5-year bond is giving a YTM of 1.45%.

     #.  The term structure of the credit spread is such that a 5-year bond should yield 25 bps more than a 4-year bond.

Now we can calculate the required spread as follows:

     #.  First, we calculate the YTM of the 4-year, 3%, and semi-annual bond trading at $ 102.40 on our financial calculator; which comes out to be 36%.

     #.  This 2.36% equals the return on a 4-year government bond plus a spread (for the risk on the corporate bond).

     #.  For the return on 4-year government, we take the average of the returns on 3-year and 5-year bonds, which is 1%.

     #.  Therefore, the spread on the 4-year company’s bond is 126 bps (i.e. 2.36% – 1.1%).

     #.  Thus the required YTM on the bond would be a sum of yield on a 5-year government bond plus a spread on a 4-year bond plus term spread. Thus, the YTM would be: