Optimum bond portfolio selection

[kbharadwaj]

Hi,

I am looking at various bonds (20 bonds) and I would like to find an optimum bond portfolio consisting of 2 bonds that would result in allocating my $300 million portfolio thus matching my liabilities. Could any one come up with an algo that would help me in coming up with the optimum bond portfolio.

FYI>> The bonds are of different credit ratings.
Mean = 6.5%
Standard deviation = 4%

 

[Joy Pathak]

lol You want us to do your homework?

This is an asset allocation problem. The two common ones are equally weighted, and risk weighted. Look into Black-Litterman Asset Allocation model also.

What is optimum? You will have to try several variations before finding an optimum portfolio based on historical data but you run into the issues of over-fitting then. Run some loops and see which ratios give you the highest return and lowest variance, and this is your "optimum" portfolio.

Edit:

For liabilities you will have to add that in as a variable too for optimality, but it will be hard to quantify unless you're given specifications.

 

[bob]

Hi,

I am looking at various bonds (20 bonds) and I would like to find an optimum bond portfolio consisting of 2 bonds that would result in allocating my $300 million portfolio thus matching my liabilities. Could any one come up with an algo that would help me in coming up with the optimum bond portfolio.

FYI>> The bonds are of different credit ratings.
Mean = 6.5%
Standard deviation = 4%

This is actually quite a difficult problem; how you approach it depends upon the type of liabilities you have and what you construe "optimal" to mean--i.e., what the goals are.

In real life, Asset Liability management (ALM) is a big deal for both operating entities and money managers, pension funds, etc. with assets and liabilities that are to some degree both random. The standard methods of approaching these problems involve Monte Carlo simulation to try to get a sense of where the funding gaps are, under what circumstances they arise, and (to whatever degree this is possible) how likely they are to occur.

Hedge funds in particular face these issues due to the fact that their liabilities are putable with some notice period and the secondary market is limited / nonexistent, meaning that you care a great deal about your mark-to-market and must find some way to model the fact that you're naturally strongly long liquidity due to effects from both sides of your balance sheet.

So I guess my short answer to your question is that it is inadequately specified.

 

[kbharadwaj]

Joy - Not my homework, and nothing related to what my stat arb homework is too.

Bob - I used to montecarlo to come up with the amount of pay off, and then determined the number of bonds from that. Then randomly selected combinations of AAA and AA bonds because their default rate is 0, thus coming up with a probability of match. I am assuming this would be enough to prove that they match. Am I doing it right?

 

[Joy Pathak]

Bob - I used to montecarlo to come up with the amount of pay off, and then determined the number of bonds from that. Then randomly selected combinations of AAA and AA bonds because their default rate is 0.

They are not exactly 0 although really close. I think only munies are 0 with Aaa.