HI, I wish to pick 100 bonds from a universe of around 240 bonds with a specified mean and sd. Trying all combinations of portfolios takes too long. sampling at random, finding means and sd seems to take too long. I need something quick that will provide an optimal (or very close answer) does anyone have a solution??? Would be very much appreciated...

c(240,100) is a huge number and portfolio optimization would require you to vary weights so that makes achieving optimilaity impossible.example: if you want best risk-return then have a cut-off based on sharpe ratio or something like that. for every criterion like credit quality or something like that one can have a well-known measure to pick securities. after picking 100 best, have positions so that risk-return is optimized.

Maybe you could filter the suboptimal ones to reduce the number of the bonds to choose from?

Hi, just to make the problem clearer, I am not worried about correlation, diverisfication etc. The problem is simply pick one hundred numbers from three hundred with a specific mean and sd. Find the optimal answer, or close. Very interesting problem, deceptively simple, I think you'll agree. David.

some sort of optimization routine perhaps ?take some initial portfolio and use a matrix newton's method ?I'm not an expert, but you should be able to use a package

Hi, could you please elaborate? Thanks, David.

Sounds difficult to solve exactly in general, for instance, just finding a subset of the numbers that match a desired mean is NP-complete I believe. If I really had to solve it, I'd set it up as an integer program: For instance, let x_i be 0 or 1 depending on whether it's in the selection or not. Then if your numbers are K_i and you want to select N of them with a mean M and stdev S then you need: sum_i x_i K_i=MN and sum_i x_i (K_i-M)^2=(N-1)SD^2. You can rewrite this as: sum_i x_i a_i=1 and sum_i x_i b_i =1 for suitable a and b vectors. Still hard to solve even after you've fixed N. If you were willing to allow a tolerance in your mean and/or stdev you could make this into a quadratic program with integer variables and throw it into a optimization solver (see e.g., axioma, cplex, etc.).

The last reply sounds good, i will try this and get back to you. Might take some time as I dont have access to an optimizer right now... Thanks, David.