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This paper 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 diversification could be approximated by the sum of squared portfolio ...


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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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I think you might be looking for the portfolio return variance: $$\sigma_p^2 = \sum_i \sum_j w_i w_j \sigma_i \sigma_j \rho_{ij},$$ where $\rho_{ij}$ is the Pearson product-moment correlation coefficient between the returns on assets $i$ and $j$ and $\rho_{ij} = 1$ for $i=j$. In your case you could either weigh the assets equally or according to the real ...


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Assume the weights of the two assets are $w$,$1-w$ respectively;the expected returns and standard deviations are denoted by $\mu$,$\sigma$ with subscripts 1,2,p(for portfolio),i.e,we have $\mu_1$,$\mu_2$,$\mu_p$,$\sigma_1$,$\sigma_2$,$\sigma_p$.The correlation coefficent is $\rho$ Then $$\sigma_p^2=w^2\sigma_1^2+(1-w)^2\sigma_2^2+2w(1-w)\sigma_1\sigma_2\rho ...


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The clearest and most intuitive article I have seen so far is Kritzman et al., Regime Shifts: Implications for Dynamic Strategies in FAJ (May / June 2012) It not only shows how you can use HMM for financial modelling but it also goes through the actual estimation algorithm (Baum-Welch) step-by-step and even gives full Matlab-code. From the abstract: ...


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most models in financial maths are linear so prices and Greeks just add. This is in particular true of Black--Scholes so Yes. However, once one starts taking into account value adjustments non-linearities appear and it is a lot more complicated.


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7 years ago I had to solve the problem of a efficiency frontier under linear constraints on the asset weights and also stumbled upon Markowitz Critial Line Algorithm. I still have a directory with some resources in it. Since Bryce already gave a practical implementation with R code by Eric Zivot, I will concentrate on some papers which might help. I ...


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If you give a covariance matrix an inverse Wishart prior, then it simplifies a lot of math in the calculations. This is called a conjugate prior. If you don't understand conjugate priors, you might want to work through the math on the univariate normal case with an inverse gamma or chi square prior for the variance. The Wishart distribution is just a ...



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