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4

If I understand you correctly, then you have a filter defined for your portfolio that is defined by "1.". A) So you either filter out these bonds before you start anything that has to do with the optimization. This should be the way to go if you are interested in speeding up your program. B) If you want to do everything in the optimization, then you need ...

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I would use a Metropolis Monte Carlo / simulated annealing approach to solve your problem. Start with an arbitrary fully invested portfolio which satisfies constraints (2), (3) and the cardinality constraint $N \le K$. Then choose one of the following trial moves: Select two bonds $i,j$ at random and perform a random weight shift $w_i \rightarrow w_i + ... 2 The Lyxor white paper Regularization of Portfolio Allocation contains a lot on this topic. The head of quant research there, Thierry Roncalli, also held a talk about this recently. 1 In many cases, clients want to be fully invested and don't want their assets lying around in cash. Hence the budget constraint$\sum_i w_i = 1$is fairly common in practice. By the way, there are also cases where the constraint$\sum_i w_i = 0\$ is applied: the result is a dollar neutral portfolio with long and short positions, but no net investment (short ...

1

I see your argument with the math. "1" is an arbitrary choice of positive numbers, and you could choose anything. In the end, you're going to scale the whole thing to fit your capital anyway. If you are using a numerical optimizer, it will be happier with something noticeably away from 0 and away from infinity, so I recommend choosing a specific positive ...

1

Portfolio management is about solving problems in the real world. In the real world, it is highly unlikely that EVERY asset has a negative expected return. If all the assets in your universe have negative returns, expand your universe to include a short-term fixed income security that is bound to produce a return greater than (or at a minimum equal to) ...

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Assume that instead of a possible portfolio of 1000 bonds, the portfolio may only contain M bonds. The input vector then needs to contain both the weightings and the choice of bonds, but how can you present the choice of bonds as an input vector? Consider sorting the candidate bonds by Macaulay duration. Given a single Macaulay duration value, then, you ...

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