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 Feb 4 comment Covariance matrix and Cholesky decomposition @crunch Yes, definitely. Also, $LL^T$ does not have to be SPD for this definition. Thats probably a reason to define it this way: Its defines a broader class of distributions (because $\Sigma$ does NOT have to be SPD). Feb 4 comment Comparing cost of two alternative given their distribution @Mohsen There are many ways to formulate a utility function for a risk averse investor. In the general case you cant even be sure the distributions have fininte variance! You can look into the topics of first order and, probably more relevant, second order stochastic dominance. This would include a big class of utility functions. Another way would be too look at utlity functions that include a risk measure of your choice that does not explicitly use variance such as value at risk or interquartile range and rank the alternatives accordingly. Jan 29 comment VIX For Convertible Bonds Hi, I don't know of such an index but you could try to calculate an index yourself. In the VIX whitepaper, you can see the calculation methodology: cboe.com/micro/vix/vixwhite.pdf I think one of the problems is that the built-in options in convertible bonds all have different underlyings and are usually not of plain vanilla type. Just look at 3-5 random prospectus of convertible bonds - you will usually find lots of different trigger levels and optionalities. That makes it harder to compare the options in two different convertible bonds let alone a whole CB index. Jan 15 comment Law of large numbers necessary for APT derivation? To upvote and accept your answer I had to edit it first so I added the resource. Your explanation is not different from the paper but my question was aiming at something different. The shanken paper answered it though. What confused me was that the APT equation is only an approximate result! (which is unusual for an arbitrage argument and very seldomly stressed in the literature) Of course, $x^\prime \varepsilon=0$ can never hold for independent $\varepsilon_i$ and thus there will never be an arbitrage portfolio, even if arbitrage possibilities are present. Jan 14 comment Law of large numbers necessary for APT derivation? I am sorry I have to downvote this answer. To get the APT relation you could simply assume $x^\prime \varepsilon = 0$ for an arbitrage portfolio... If you think its about the assumptions, feel free to be more specific about "some extent making assumptions of linear regression". Please also explain in detail where these assumptions are needed and how they imply the need for the law of large numbers with respect to the no-arbitrage argument! Jan 8 comment Equall Risk Contribution and The Most Diversified Portfolio What is your question? Jan 7 comment Are there any tools or useful algos for identifying corner portfolios? Since its derivation is via the Lagrangian, I think it still holds... Jan 7 comment Are there any tools or useful algos for identifying corner portfolios? I think there are two different questions to be considered here: "How to calculate corner portfolios?" and "How to generate the efficent frontier?" The second question can be answered by the mutual fund separation theorem - at least if the asset weights should sum to one (or total wealth). If you impose weight constraints, I don't know. I think the other comments refer to the mutual fund separation theorem. Jan 7 comment Are there any tools or useful algos for identifying corner portfolios? @Bryce I downvoted this answer because I cannot find any reference to corner portfolios at all. It is just a basic introduction to some R functions. Dec 30 comment For the Dothan model $E^Q[B(t)]=\infty$? You can find the same argument in Brigo/Mercurio - Interest Rate Models - Chapter 3.2.2. Dec 30 comment For the Dothan model $E^Q[B(t)]=\infty$? @Roozbe Could you post your solution here for sake of completeness? Dec 9 comment Book recommendation on robust optimization Of course its a stretch as I dont know you nor your exact background so you might as well find it easy. You are more than welcome to try and see how you can handle the topics. The book is free for download. If you have a (very) solid background in optimization you schould be able to handle it. For an advanced finance course the books contents will be too much of a specialization I think. Dec 9 comment Book recommendation on robust optimization I am afraid for a bachelor in economics, the Ben Tal / Nemirovski book will be far too technical. Dec 4 comment How to extrapolate VaR? as @Richard pointed out, the scaling rule depends on the distribution. Value at Risk is a distribution quantile. The Quantile of a Normal Distribution with $\mu = 0$ scales with $\sqrt{T}$, in general it does not! Dec 2 comment How do I artificially generate intraday ticks data from a given input (Open,High,Low,Close,Volume) using Brownian Bridge method? @jaamor You could do that, but those times will not be independent I suppose. I think the result wouldnt look too good. I would take the high and low value and use it as a dispersion measure to improve my intraday volatility estimator and then create BB paths from it. They will, in general, not reach the high and low values but the question is: Does it make sense to enforce this? Dec 2 comment Is an arbitrary prior for Black-Litterman valid? Or do we need a market implied one? Hope it helps. Lets try to find a day - check your inbox in a few hours! Dec 2 comment Is an arbitrary prior for Black-Litterman valid? Or do we need a market implied one? @Richard I tried to clarify my answer a little and added an additional point. Dec 1 comment Is an arbitrary prior for Black-Litterman valid? Or do we need a market implied one? @Richard Hallo, I have to check the details about the risk parity portfolio agai and will catch up on that tomorrow. Oct 7 comment Determine $E[W_p W_q W_r]$ For a normal distributed rv $X ~ N(\mu,\sigma)$, $E[(X-\mu)^3] = \mu^3+3\mu\sigma^2$ (just search for moment normal). In our case, $\mu=0$ and $\sigma = p$. Alternatively, you can calculate it by hand (several times integration by parts) or via the moment-generating function. Oct 1 comment quadratic programming portfolio optimisation Hm, thats why I wasn't sure this is the right explanation because $x$ should be $x = [0.8,0,0.5,0,-0.3,0]$ in this case (splitting $x$ up in a positive and a negative part). Now, $x(1:3)+x(4:6)$ is the original portfolio and $x(1:3) - x(4:6)$ its component-wise absolute value.