# Questions tagged [portfolio-optimization]

Questions related to mathematical methods used for searching of optimal portfolio structures. Also related to questions on optimal structure of portfolios from both strategic and tactical point of view

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### Optimal active risk

Can someone help me prove the statement or share a link of the proof - "The optimal amount of active risk is the level of active risk that maximizes the portfolio’s Sharpe ratio. This optimal ...
310 views

### How to set a fixed return for mean-CVaR portfolio optimization?

I'm using the timeSeries and fportfolio package in R to minimize the CVaR with different constraints for a given portfolio. Everything is working out so far. However, I can't manage to set a fixed ...
1 vote
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### Maximum Sharpe ratio and mean-variance optimization

I want to understand why this holds: $argmax_w ( \frac{\mu^T w}{\sqrt{w^T\Sigma w}})=\Sigma^{-1}\mu$ I just found this post: Derivation of the tangency (maximum Sharpe Ratio) portfolio in Markowitz ...
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### Which Times Series Database framework for Python is best for portfolio optimization project?

I am starting to build a portfolio optimization algorithm in Python and want to structure a database to manipulate financial data. Although I have Python experience, I have never used SQL or such ...
1 vote
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### factor hedging erodes portfolio alpha

I am hedging a long-short equity portfolio for statistical factors, and finding an improvement in sharpe but not surprisingly an erosion of portfolio alpha (ex ante and ex post). No one factor is ...
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### Is this an Example where Maximum Adverse Excursion (MAE) is not useful for a Stop-Loss?

Below is an attached screenshot of a scatter plot of a long position Percentage Return of a Asset Security on the Y-axis, and the Maximum Adverse Excursion (MAE) Percentage on the X-axis. Green dots ...
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### Weight of asset has to be smaller than b% in the portfolio(Portfolio Optimization)

Given a certain portfolio with y assets, calculate the weight of each asset in the portfolio based on the asset position. The weight for each asset is calculated by (yn is the position of a certain ...
62 views

### zero-beta portfolio $z$ solves optimization problem

Consider a market with $p$ risky assets with expected return $\mu \neq k 1$ and positive definite covariance matrix $C$. Let $z$ be a zero-beta portfolio w.r.t the market portfolio $x_M$. Show that z ...
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### Black-Litterman model with only positive weights

I'm trying to realize Black-Litterman Model for my stocks portfolio, but under optimization, I get a subset of weights with negative values. I want to get only positive weights. IS it possible to add ...
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### How to evaluate Asset Allocation skill?

There have been studies that show that Asset Allocation can explain 90% of the variance of returns on a portfolio. If true and Asset Allocation is the primary driver of return risk, how can you ...
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### Minimize Composite Dispersion

Let's say that we have a composite of 10 fixed income portfolios, each with the same benchmark, the US Aggregate. Additionally, let's say that each portfolio has a position in Corporation ABC. The ...
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1 vote
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### Value of continuously rebalanced stock portfolio

I'm thinking about what a theoretical continuously re-balanced stock portfolio could look like, in which the portfolio is uniformly distributed over a selection of stocks at all times. For example, if ...
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### Strange efficient frontier, when I try to calculate BTC & ETH ratios using MPT(Modern Portfolio Theory) [closed]

The 10k Monte-carlo simulations all fall on the same line, instead of a proper scatter plot.. Not sure what I'm doing incorrect. It all works fine, if I include Monero in the mix. Any pointers ? I'm ...
1 vote
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### Change weights of the portfolio [closed]

I have spent a lot of time finding some trading alphas. Now, I have about 10 alphas to trade Future, I also optimized the portfolio by using Markowitz's Modern Portfolio Theory (MPT) to get weights. ...
55 views

### Multiple Indices for CAPM model [closed]

I am new to quantitative finance so, please excuse me if the terms are not correct. I am trying to apply CAPM on a portfolio which has multiple indices (S&P 500, Russel 1000 and S&P Financials)...
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### 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. ...
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### global minimum variance portfolio vs all-bond portfolio

I'm leaning portfilio theory and have got some questions. global minimum variance portfolio is defined as the leftmost point on the efficient frontier which suggest it is a all-bond portfolio if risk ...
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### Portfolio allocation question: is it not circular reasoning?

Is portfolio allocation not circular reasoning? Say we have a portfolio manager, Michael, and a risk manager, Vito. Michael has a portfolio and would like to determine the optimal allocation of his ...
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### Misconception about replicating portfolio [closed]

I am solving a problem in which following payoff is provided: With $S_0=100$ and $T=8$. Looking at the payoff it seems obvious that it is replicated with two european put options ($K=100$ and $K=150$)...
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I have computed the theoretical minimum variance portfolio using the 30 stocks in the Dow. The formula used is: \underset{N\times 1}{\omega_{mvp}}=\frac{\lambda}{2}\cdot \Sigma^{-1}\iota=\frac{\...