# Questions tagged [modern-portfolio-theory]

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

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### Variance of returns on a portfolio

This must be very basic, but I don't seem to be able to express the variance of returns on a portfolio in terms of variances-covariance sum of returns of its constituents, which seems to be what is ...
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### Process for a portfolio of stocks where each share follows a log-normal process

Given a portfolio of shares $I = \sum{w_iS_i}$ for some fixed weights $w_i$ where each stok $S_i$ has a log-normal distribution, what is the process / distribution followed by the portfolio? That is, ...
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### Covariance Matrix: Calculating Error [duplicate]

I have a sample covariance matrix that is non positive-semi definite (due to missing data points). I am looking at a number of techniques to 'fix' my covariance matrix and make it positive semi-...
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### What CAPM/Financial ratios involve kurtosis?

Simple question, what universally accepted financial ratios involve kurtosis? I'm not looking for a made up one. I want something that academics may have discussed.
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### Optimisation with strong correlated Assets

I have the following settings: The allowed traded assets consists of 1 bank account, 1 non dividend paying stock and 19 call options whose maturity is in 30 days. I want to find an optimal static ...
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### MPT Tangent Portfolio: Buck for the Bang Ratio

The $R_{TP}$ is the tangent portfolio return, but I don't understand the step regarding $\frac{dV(R)}{dw_n}$, you apply this, and how come it get rids of the summation?
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### Mean-variance portfolio returns illogical weights

I have a dataset with 5 assets. I apply mean-variance portfolio: ...
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### How to prove that every point on the capital market line corresponds to a unique portfolio

Prove that every point on the capital market line corresponds to a unique portfolio. Attempted proof I know that each point on the capital market line represents a linear combination of the risk ...
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### Annualization of coskewness and cokurtosis

I am constructing a mean-variance-skewness-kurtosis portfolio based on monthly data with a holding period of one year. Meucci describes how to annualize higher order moments in general, but not how to ...
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### Portfolio optimization subject to transaction costs

Mean-Variance portfolio optimization attracted lots of attention in this forum so far. I am interested in the effect of incorporating transaction costs into the decision framework and I would like to ...
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### What does an optimized portfolio really tell us?

I am very new to this field, and have very recently started doing some self study on this topic. After reading some papers and reproducing some of the results in them, I am not very clear about what ...
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### Two fund separation when there's a risky asset?

I am currently reading a book which begins its portfolio theory section with the case with $n$ risky assets where it proves that 2-fund separation applies (any minimum variance portfolio is a linear ...
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### What does each bar in the empirical average eigenvalues spectrum of the correlation matrix of log-returns of stocks represent?

An example diagram, taken from this paper, looks like follows: What is its physical interpretation? The highest eigenvalue, the paper says, represents market mode. So, what does the difference in ...