Skip to main content

# Questions tagged [mean-variance]

Mean-variance is the starting point of most portfolio optimisation techniques.

182 questions
Filter by
Sorted by
Tagged with
0 votes
1 answer
54 views

### Mean variance optimisation as error-maximisation: why would negative correlation increase standard error of estimates?

"The unintuitive character of many optimized portfolios can be traced to the fact that MV optimizers are, in a fundamental sense, estimation error maximizers. Risk and return estimates are ...
2 votes
2 answers
188 views

### What is the proper way to derive risk definitions from utility functions?

In typical mean-variance analysis, the risk-adjusted relative value of an individual asset takes the general form $\frac{\mu}{\sigma^2}$, with further weighting and normalization depending on the ...
• 73
0 votes
1 answer
153 views

### How to construct a delta-neutral portfolio containing stocks using correlations?

I’m aware of the mean-variance framework where we construct a portfolio such that we attempt to minimise the variance and maximise returns. What if instead we’re in a scenario where the main goal is ...
• 99
0 votes
0 answers
35 views

### How to prove that the feasible set of a two-asset portfolio is a hyperbola?

The question comes from ‘Mathematics for Finance: An Introduction to Financial Engineering’ by Marek Capiński (Author), Tomasz Zastawniak. The book does not give a complete proof, and I did not find a ...
0 votes
1 answer
172 views

### Portfolio optimization with Scipy in Python

I performed Scipy portfolio optimization in two scenarios: 1) when I cannot lend or borrow at the risk-free rate; 2) when I can lend and borrow at rf=1.5%. Now, optimal risky portfolio weights anyway ...
0 votes
1 answer
67 views

### How to prove the inequality for the standard deviation of a linear combination of two random variables

The variance of the linear combination V of random variables X₁ and X₂ is given by the following formula: $$\sigma_{V}^{2} = s^{2} \sigma_{1}^{2}+(1-s)^2 \sigma_{2}^{2}+2 s(1-s) c_{12}$$ where s and ...
1 vote
1 answer
129 views

### Calculating marginal risk contribution of FX for foreign asset portfolio

I am a European investor investing in US equities. My US equities portfolio returns in EUR can be broken down into (1) equities returns in USD terms, and (2) USDEUR spot currency returns. Using the ...
• 25
0 votes
0 answers
40 views

• 359
2 votes
1 answer
100 views

### Optimal Portfolio Formulation

I'm currently studying Luenberg's Article "Projection Pricing" (Jrl of Optimization Theory and Applications, Vol. 109, No. 1, pp. 1–25, April 2001) and there is a claim that I can't prove. ...
-1 votes
1 answer
154 views

### Covariance Matrix for asset returns [closed]

Hey guys I'm pretty new here, not sure how to code my question so I'll include a picture reference instead. I'm a bit confused on how the standard deviation of F (commodity price) would affect the ...
0 votes
1 answer
1k views

### Corner portfolios

This is more a theoretical problem rather than a technical one. I am looking for a clear and rigorous definition of corner portfolios and I like to understand more precisely their relation with the ...
• 359
0 votes
1 answer
263 views

### Should a stock with high return autocorrelation be weighted more heavily in a portfolio?

Some say the presence of autocorrelation (aka serial correlation) in a stock's financial return time series helps with forecasting its next-day movements, unlike a stock that has low serial ...
• 3,080
0 votes
1 answer
426 views

### Calculate weight of an asset

Suppose there are three assets, and the first asset has volatility 18%, the second asset has volatility 16%, and the third asset has volatility 16%. Suppose also that the first two assets' returns ...