# Questions tagged [modern-portfolio-theory]

A theoretical framework for analyzing investment portfolios based on their expected return and risk.

28 questions
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### Derivation of the tangency (maximum Sharpe Ratio) portfolio in Markowitz Portfolio Theory?

I have seen the following formula for the tangency portfolio in Markowitz portfolio theory but couldn't find a reference for derivation, and failed to derive myself. If expected excess returns of $N$ ...
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### How can I find the portfolio with maximum Sharpe Ratio - Using Lagrange Multipliers

In Markowitz' portfolio theory we can construct portfolios with the minimum variance for a given expected return (or vice versa). Across expected risks, this traces out the well-known efficient ...
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### Portfolio Optimization - Zero beta portfolio

I am trying to solve a optimization portfolio in R in which I do the following constraints: Set weight sum to within a boundary Set return to a certain value Set portfolio beta to 0 The purpose is ...
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### Maximum Certainty Equivalent Portfolio with Transaction Costs

Out of curiosity I tried to compute the portfolio weights of a maximum certainty equivalent allocation, however, by incorporating (quadratic) transaction costs. However, my result is not as intuitive ...
Suppose I have an amount $T$ to invest and $N$ available assets. The stochastic return per invested unit of asset $i$ is $R_i$. The variance and the expectation of $R_i$ are $\sigma^2_i$ and $\... 1answer 999 views ### How to implement Konno's Mean-Absolute Deviation Portfolio Optimization Model using LP methods in Excel Konno proposed a LP method for portfolio optimization using the Mean Absolute Deviation (MAD) 1answer 621 views ### Recommended Literature for creating Factor Mimicking Portfolios Is there a textbook that contains the basics for creating Factor Mimicking Portfolios? Although there is a lot of peer-reviewed literature on this, I cannot find textbooks on Asset Pricing that ... 4answers 346 views ### Portfolio Optimization using S&P Universes Assuming a set portfolio optimization problem, if all optimization inputs are kept constant, what would you expect, in terms of results, if you run the same optimization using the S&P500 as ... 1answer 141 views ### On a source for a mean-variance portfolio optimization result In the context of a mean_variance framework consider an optimizing investor who chooses at time$T$portfolio weights$w$so as to maximize the quadratic objective function:$$U(w) = E[R_p] - \frac{\... 2answers 2k views ### Risk contribution of part of a portfolio Is it quantitatively sound to say that if I have assets$x, y,$and$z$in a portfolio, and that the total variance of the portfolio is defined as$\sigma_p ^2 = w_x^2\sigma_x^2 + w_y^2\sigma_y^2 +...
It seems most Sharpe ratio derivations seem to be for portfolios but I am just tracking a single asset? $SR = (r_p - r_f) / \sigma_p$ but what would I derive with respect to for an optimization/ ...