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# Questions tagged [modern-portfolio-theory]

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

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### CAPM (SML) Problem

I got 1.3636 for beta for the problem below(165/121). But I became so unsure about the answer when I solved (c) because then the market risk becomes larger than the variance of Stock A. Beta^2*σ(M)^2=...
495 views

### Efficient Frontier Derivation: why minimize half the portfolio variance instead of just the variance?

In Robert Merton's derivation of the efficient frontier of a portfolio, he minimizes $\frac{1}{2}\sigma^2$ over the investment weights in each asset, where $\sigma^2$ represents portfolio variance. ...
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188 views

### What's wrong with this asset growth simulation?

Sorry if this is too basic, but I have this spreadsheet that simulates asset growth of a portfolio under a given return and risk using MPT. Here is a plot of probability distribution of asset ...
532 views

### In Mean-Variance Analysis, why not the efficient frontier being pushed to the left near the axis?

I took some classes in portfolio theory, and learnt the Markowitz Mean-Variance Analysis. If only two risky assets, the efficient frontier would be a hyperbola passing through the two points; now if ...
271 views

### Portfolio optimization with absolute position constraints

I'm looking to optimize a portfolio maximizing expected return for a particular risk budget, but with absolute constraints on the individual instrument positions. I've been experimenting with QP, ...
884 views

### VaR Calculation - Covariance matrix is not positive semidefinite

This is a basic question. I have three assets, equally weighted, and all the mutual covariances are -1. Then, the covariance matrix looks like - ...
21k views

### 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 $N$ ...
10k views

227 views

### Is there an optimal covariance one would want forecasts to have?

Often in a quant process, one will generate a time series of return forecasts and use them in some sort of optimization to generate a portfolio. Generally, there will be a covariance matrix of market ...
353 views

### Do weights from portfolio theory contain bias?

I want to experiment with some portfolio modelling and I was wondering if you guys could help me with something. If I try to estimate and implement the traditional two-fund portfolio consisting of one ...
27k views

### Why does the minimum variance portfolio provide good returns?

I've been a researching minimum variance portfolios (from this link) and find that by building MVPs adding constraints on portfolio weights and a few other tweaks to the methods outlined I get ...
2k views

### How can higher co-moments be applied to portfolio optimization in an asset allocation context?

Traditional portfolio optimization involves mean variance optimization, where only the mean and covariance matrix of returns are estimated. What asset allocation and portfolio optimization techniques ...