# Questions tagged [modern-portfolio-theory]

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

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### Covariance Matrix by Multi-Factor Model

I have been trying to find literature for the derivation of the covariance matrix, following a multi-factor model. I have had no luck at all, every single article I have found on the web already ...
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### Are there optimal portfolio theories than instead of the expected value they were based on the Mode of distributions

Are there optimal portfolio theories than instead of the expected value they were based on the Mode of distributions? During my engineer student days I saw the Markowitz theory for portfolio selection ...
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### Tangency portfolio negative maximum Sharpe ratio

Suppose I have three assets: the market, factor A and factor B. The market is in excess returns of the risk free rate. The other two factors are long-short portfolios. I have net returns for these ...
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### N asset covariance matrix vs N-1 asset covariance matrix

so I have been using a M-V framework to form M-V efficient portfolios. I have noticed that every time I make my investment universe smaller the minimum variance frontier moves to the right. This ...
64 views

### Why do we use half of the risk in objective function of markowitz portfolio theory

In some documents I have seen objective function of markowitz portfolio theory is as follows. minimize 1/2 * w'Σw where w is weights Σ is covariance matrix I could ...
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### Risk Factors, Portfolio Optimization

I really need help with a project that I am working on, for my university.I study in Ecuador and the research material here is very limited. Nonetheless I have tried my best to start with the basics ...
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### Unexpected Inflation and Asset Allocation

If asset allocation decisions were made prior to the news of unanticipated inflation, how should asset allocators incorporate the fact the inflation is now 5% higher than the 2% inflation target? It ...
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### Correlation Matrix to Variance Covariance Matrix Portfolio STDEV

I have a correlation matrix that I wanted to convert into a variance covariance matrix. I also have the weights in a column in excel along with each assets standard deviation. What excel function can ...
56 views

### Mean-variance optimization and hedging

I've read--and have been able to replicate empirically--that mean-variance optimization will trade two positions against each other if assets are highly correlated. For example, if stocks $A$ and $B$ ...
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### Maximum expected return portfolio: Lagrangean derivation of closed-form analytical solution

\begin{align} \arg \min_w \enspace & -w^\top \mu \\ \mathrm{s.t.} \enspace & 1_N^\top w = 1 \\ & w_i \geq 0 \enspace \forall i=1,\dots, N \end{align} is the optimization problem for ...
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### Mathematical proof that the covariance between two portfolios is $w_A^\top\Sigma w_B$
How to prove in a line-by-line derivation that the covariance between two mean-variance efficient portfolios is equal to $$w_A^\top\Sigma w_B$$ where $w_i$ is a unique portfolio weight vector, and \$\...