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You seem to have two distinct problems: How to generate random portfolios How optimal portfolios are structured Ad 1) A straightforward way to simulate the weights of random portfolios is to use the Dirichlet distribution $Dir(\alpha_1,\ldots,\alpha_n)$. This is a distribution on the Simplex (i.e. on $S=\{x\in\mathbb{R}^n | \sum x_i =1, x_i\geq 0\}$, ...

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The problem is how to generate random weights subject to a constraint that the sum of the weights has to be equal to 1. The following pseudo-code illustrate one method: Let free_weight := 1 For i=1 to N Select an asset j **at random** among the assets not yet given a weight If i < N then Let w(j) := free_weight * rand1() /* rand1() ...

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Carry is most often defined as the effect on the bond if the yield curve does not change. Roll down is seen as a component of carry that results from changes on the position of the yield curve. See this reference on the topic.

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You do it the same way as with long only as weighted sum of the durations of each position. You have two possibilities for calculating the weights: long/short with respect to a benchmark: then take as basis the dollar value of your portfolio P USD, set the benchmark to the same dollar value and calculate each weight as fraction of the position $w_i = P_i/... 1 One way might be to calculate a proxy yield based on peer group metrics such as credit rating and currency. This won't however make any allowance for the liquidity premium, but nonetheless, it might still be a useful approximation. If the credit rating history is not available, then you might have to use something like the KMV model (part of Moody's ... 1 Assume that there are two zero coupon bond with maturities$N_1$and$N_2$with prices$P_1 = \frac{CF_1}{(1+y)^{N_1}}$and$P_2 = \frac{CF_2}{(1+y)^{N_2}}$respectively. If we construct a bond portfolio by purchaing one each of the two ZCB, the price of the portfolio is$P=P_1+P_2$. Now, the convexity of the portfolio is$\begin{align} {Convexity}_p &= ...

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Ok, so I think you are just asking what is the dv01 of the bond. So if the yield goes up one bp what's the new price? And if it goes down, what's the new price? That's the simple way that people look at it. For a bond that can't be called or converted in any way it's pretty easy. Let's assume that's what you have. Here's the process: So first you need ...

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Your question depends on the discount factor you wish to use for pricing. If u use the risk-free rate (from the bond), it wouldn't be in line with the no-abitrage condition to assume an risk neutral agent can't/wouldn't invest in bonds to carry money into next period. To understand this: just assume a 1 period model with two outcomes for S, where both ...

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This question complicates a simple issue. Model e.g. Italian sovereign as a credit, and then treat the spread either against Germany or IRS curve, and stress as you would any financial/non-financial credit risk. The underlying benchmark curve would naturally fall onto the interest rate risk.

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