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I would suggest you to add spreads to the implied hazard rates, spreads that you regress on the macroeconomic factors. Then you stress by calculating the spreads corresponding to the stressed factors.

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Speaking from equity quant factor building experience, it is a common practice to build multi-factor models by regressing one component against other(s) and using the residual scores. This is done to avoid bias as you mentioned - these biases could be from the factor itself (in different regimes, Quality / Momentum influencing each other - or earnings, value ...

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I would suggest Time Series Analysis by James Douglas Hamilton

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For your first question, your derivative is incorrect. It instead is $\frac{\partial C^2}{\partial x \partial y} = 1+\theta(1-2x-2y+4xy)$. Note also that $x+y-2xy \geq x^2 + y^2 -2xy = (x-y)^2 \geq 0$. That is, $1-2x-2y+4xy \leq 1$. On the other hand, $1-2x-2y+4xy = 2(1-x)(1-y)+2xy - 1 \geq -1$. Then, $\frac{\partial C^2}{\partial x \partial y} \geq 0$, for ...

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got an answer from one of my pals, thought it might be interesting to share it here. The reason why we often use the normal distribution is because the distribution will be stable regardless of the number of samples (central limit theorem). Imagine you had a normal distribution after transforming x amount of samples, and across time, u get more variables ...

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Short answer: It offers some degree -- and in many cases, a greater degree -- of comparability between two types of data (different assets, returns, etc.) Long answer: You may already know this, but keep in mind that "normalization" can mean different things (see this question). There are various methods and purposes for normalizing data (financial or ...

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To take into account lag-like discrepancies between two time series, DTW(Dynamic Time Warping) algorithm is generally used. Quoting from wiki - "In general, DTW is a method that calculates an optimal match between two given sequences (e.g. time series) with certain restrictions. The sequences are "warped" non-linearly in the time dimension to determine a ...

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It is not uncommon to find significant differences in historical price data from different sources & data vendors. For example, if you look at ETF ticker symbol "EEM" for the period from 2001 until now using free Yahoo data and free Google data from the Internet, you will see that for some of this period they agree and for some of the time they are quite ...

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You need the weights for each index to compute the portfolio return time series. The portfolio return would be the weighted average of the returns at each time step. Once you have a single time series of portfolio returns you can compute the the statistics. Averaging the returns without any weights would be a purely mathematical exercise at this point. By ...

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