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1

As regards the free sources, the best place where you can find material about credit risk management is defaultrisk.com; it is a website where are collected (almost) all academic (and not) articles and working paper, references and researchers. Moreover, as regards the forums, I think you should try visiting Credit Risk Group at Linkedin; it is a very ...


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Very few websites give Total Returns...Morningstar and mutual fund companies give performance numbers which include dividends... the ReturnFinder app and CorrectCharts app give this information in tabular and graphical form with the plots showing both price and total returns.


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It's supposedly more robust. But they all fail as do any plugin estimator version of things. The estimators are typically optimized and unbiased, but the optimized portfolio weights are absolutely biased. Bayesian methods have gone much further. It's better to smear out your estimators before you optimize.


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Reviewing the available literature and doing my own initial tests seems to confirm that the results of the MAD method versus those of the classical MVO are a statistical dead heat with MVO perhaps having a slight return edge - possibly due to MAD, which is more sensitive to fat tails, producing slightly more conservative portfolios*. However for moderate to ...


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Think of mean-variance as using a quadratic risk function. MAD uses a linear one.


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This spreadsheet shows how to implement Konno's Mean Absolute Deviation (MAD) Portfolio Optimization in Excel using LP Simplex methods. For strictly multivariate normal underlyings, the method can be shown to be equivalent to the standard Mean Variance Optimization method of Markowitz et al. The method is based on the paper Further Reduction of the ...


4

If you could hedge continuously with zero transaction costs, the gamma would be irrelevant: you would perfectly replicate with delta hedging and be done. In practice, hedging is discrete and there is a certain amount of slippage giving a random outcome with mean zero. The larger the gamma, the bigger the variance of slippage. Trading more frequently ...


1

since you've assumed that all returns are independent, the covariance matrix, $C,$ is diagonal. In the comments, you are assuming that the investor is a mean-variance investor. It's a general result that every portfolio that maximizes return for a given variance is a tangent portfolio for some risk-free rate, $R.$ Let $e=(1,1,...,1).$ and let $\mu$ be the ...


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I don't have 50 reputation, so cannot comment. But Richard's answer is a high-level answer toward approaches used by practitioners in quantitative portfolio management. I have worked with firms that sourced data on the components from multiple providers who charge tens of thousands per user to pre-calculate the components periodically and give you a ...


6

If you measure risk by the standard deviation of the portfolio return $$ \sigma = \sqrt{w^T \Sigma w}, $$ then it is usual to define risk contributions for each asset by $$ \sigma_i = w_i (\Sigma w)_i/\sigma, $$ then diversified could mean that these $\sigma_i$ are evenly spread over the assets in the portfolio. You find this approach and more in this paper ...


2

This paper, Equity Portfolio Diversification by W. Goetzmann and A. Kumar, uses the following diversification measures to measure the diversification of retail investors: Normalized portfolio variance: $$ NV = \frac{\sigma_p ^2}{\bar{\sigma} ^2} $$ Sum of Squared Portfolio Weights (SSPW). Since the weight in the market portfolio is very small ...


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Your question accurately addresses of the practical problems of applying Modern Portfolio Theory (i.e. mean-variance optimization) in practice. Generally the correlations are considered much more difficult to accurately estimate in this context. I am not sure I understand the question. Isn't $E(r)$ is an unbiased estimator of $r$? You may want to look ...


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In their paper on their S&P 500 Implied Correlation Index the CBOE has defined a measure for the market-capitalization weighted average correlation of the S&P 500 index which could be applied to portfolios in general. The equation $$ \rho_{av} = \frac{\sigma^2 - \sum_{i=1}^N w_i^2\sigma_i^2}{2 \sum_{i=1}^N \sum_{j>i}^N w_i w_j \sigma_i ...



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