# Questions tagged [modern-portfolio-theory]

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

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### Many quants optimize sharpe ratios, sortino ratios, or anything of the form A/B. What about maximizing something of the form (AB)/(CD)?

The Sharpe ratio is defined as return/risk, generally as mean(ret)/sd(ret), where ret represents the data set of returns of an investment. However, I have seen other ratios that I also like. What I ...
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### How to choose a tangency portfolio without a risk-free rate

How do you choose an optimal portfolio from the efficient frontier if no risk-free rate is given? I know that if there exists risk-free asset, then you would combine a portfolio from the efficient ...
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### Generalized Mean Variance Portfolio

Utility based portfolio optimization deals with the problem of finding the optimal portfolio $x_T$ by maximizing the utility/objective function $O(x_T,x_0)$ where $x_0$ is the current portfolio. In ...
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### Trouble computing the VaR for Student's t-distribution for a minimum-variance portfolio composed of four cryptocurrencies (BTC, ETH, LTC, and XMR)

I have modelled the time-series of daily log-returns from August 2015 to October 2017 of a minimum-variance portfolio composed of four cryptocurrencies (BTC, ETH, LTC, XMR) by fitting the data to four ...
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### Derivation of arithmetic variation of a portfolio over multiple periods [closed]

I am very confused on how to derive the attached equation (15). Would someone be kind enough to walk me through the proof?
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### How to calculate the contribution (%) of an asset to the global correlation of the portfolio?

I have a portfolio X with weights $w_i$. I am trying to find the contribution $\xi_i$ of asset $i$ to the total correlation $\rho_{XM}$ of the portfolio X to an index M. I can't find these ...
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### Private Equity: Direct Alpha vs Excess IRR

I'm trying to understand the advantages and disadvantages of using Direct Alpha versus Excess IRR for computing excess returns over a market index for private assets. Wikipedia references a highly ...
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### Why do anomalies disappear after they get detected?

In financial markets, anomalies refer to situations when a security or group of securities performs contrary to the notion of efficient markets, where security prices are said to reflect all available ...
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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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### 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 +...
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### Fama French & Solving for Alpha

This is a question about comparing results from the Fama french 3 factor model. I have not physically done this, but let's assume a Fama French 3 factor regression was performed for Coca-Cola (KO) ...