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For more than 2 correlated assets, you should use the cholesky decomposition of the correlation matrix. Please read this article for further information: https://myfinancialmarkets.club/2018/01/06/how-to-generate-correlated-assets-and-why/ As for testing, you can try to price basket options with your generated paths and compare them with values in the ...


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To preserve the dependence structure of market returns the easiest way is to do a resampling (bootstrap): Take your returns and normalize each asset by its daily standard deviation. Then at each step draw a uniformly chosen random date in your sample and use the vector of normalized returns from that date as your IID noise. This procedure preserves the ...


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Portfolio beta is a function of market vol, portfolio vol and correlation between market and portfolio; so correlation is indeed the only free variable. (But if you have complete control over the portfolio-construction process, you might as well target beta and then scale the weights so that you meet your volatility target.) To control correlation, you'll ...


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This is a case of bivariate normal as there are two normal variables (as opposed to two variables driven by the same common random factor). The answer to your question is the conditional distribution of one of the variables given the other variable: $Y|X \sim N\left(\mu_y+\rho \sigma_y \frac{x-\mu_x}{\sigma_x}, \sigma_y^2 \left(1-\rho^2\right) \right)$ For ...


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I would turn the stock level matrix (which I assume would be a dataframe) into a tall table that would have rows that look something like this: etc... Now, having this dataframe, called corr_df, for example I would use this code: corr_df_avg = corr_df.groupby(['date','ind1','ind2'])['correlation'].mean() to get the average correlation between ind1 and ...


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Gold's "safe haven" credentials and its correlation to equities are not necessarily quite the same thing. Gold is a safe haven, in the sense that whatever happens in the economy, an ounce will always remain an ounce. It remains gloriously unchanged, whatever else happens around it. Which is why asset allocators often think about it as akin to a perpetual ...


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I do not think that you were terribly wrong thinking that gold and SPX (or equity market in general) are negatively correlated. The reason behind this is that gold and stocks are in fact negatively correlated in stress periods. Here are some stress periods and the correlations for SPX and gold (and silver): However, if you include normal periods, then the ...


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