Context: I have bond A from say Apple, Apple also issued different types of bonds , namely B , C, D, E bonds. Bonds A B C D E are all same, except, they were issued at different times, have difference size and different maturity. I am trying to find: What is the yield difference between yield of A and yield curve of Apple comprised of bonds B C D E. Because Bonds B C D E and A were issued in different time, with different maturity and different sizes, i acknowledge that there is difference in liquidity between these bonds, and just comparing yield of A at time t to yield curve of firm at time t will be fallacious. I have bid ask spread of all bonds but no trade volume.
Question: How can I come up with a metric that gives me a liquidity of yield curve? that takes into account difference in issue size and maturity profile.
Prop1: I was thinking of finding distance of bonds B,C,D,E with bond A.
d(B)= bond A maturity - bond b maturity
d(C)= bond A maturity - bond C maturity etc...
Then Liquidity of synthetic bond ( yield curve) will be
= d(B) / (d(A)+d(B)+d(C)+d(D)) * Liq of bond B + d(C)/(d(A)+d(B)+d(C)+d(D)) * Liq of bond C +...etc for bond D and E.
So its weighted on how close this particular bond is to bond A, the closer this bond is in terms of maturity , the more weight does it have.
But this only accounts for maturity profile ( distance from bond A), How can I mathematically do this so that it also accounts for size of bonds ( more weight on liquidity of bond that is closest to size of bond A) and perhaps issuance date ( closest to issuance of bond A)
Thanks so much for reading and possibly answering :) Cheers!
PS: if you have a better way of finding weighted liquidity of portfolio(?), then by all means, i wanna hear it