Questions tagged [optimization]

The selection of a best element from some set of available alternatives. Typically consists of maximizing or minimizing a real function by systematically choosing input values from within an allowed set and computing the value of the function.

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4
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1answer
379 views

How to (efficiently) calculate the maximum possible return of a perfect "crystal ball" investment strategy?

I am new to the world of investing, so please excuse the clumsy wording of the question... there is probably a better term for what I am looking for or maybe this is even a known/classic problem. If ...
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27 views

Multivariable objective function optimization similar to optimx in R

I have an optimization model in R that utilizes a single variable in my objective function. See below: ...
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1answer
350 views

PortfolioAnalytics [R] - optimize.portfolio.rebalancing / rebalancing period

I am having difficulties trying to set up the rebalancing period to semi-annual or every 9 months in the optimize.portfolio.rebalancing function in the package ...
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34 views

Efficient frontier plot including Mean-Variance and Mean-CVaR frontiers

I am trying to compare the outcomes of a Mean-Variance and Mean-CVaR Optimization approach. I succeeded in plotting the efficient frontiers + tangency portfolios for both cases. Does anyone know how ...
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1answer
132 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 ...
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3answers
1k views

Optimization of Take-Profit and Stop-Loss

Three questions: What branch of mathematics would help me optimize profit if I have a trading strategy that on an individual trade basis (Trade 1, Trade 2, ..., Trade N) has a draw down of (X1,X2,......
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1answer
1k views

Market Making Strategies Found by Hamilton-Jacobi-Bellman Equation

Im working my way through the book "Algorithmic and High-Frequency Trading" (AHFT) by Cartea, Jaimungal and Penalva and i'm curious to see how the market making model with an exponential utility ...
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29 views

Optimisation Multiple Constraints - Using CVXOPT

I am trying to solve a linear algebra problem: an optimisation problem and I am using CVXOPT. I've split the problem into 3 components In its simplest form, The general formulation for CVXOPT is ...
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28 views

How to assign stock sales to purchases in order to minimize capital gains tax?

Imagine you have the following transactions: fiscal year day type amount price 2020 1st of October Buy 10 000 stocks of XY corporation 14 000 € 2020 1st of November Buy 10 000 stocks of XY ...
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1answer
80 views

Multiple tracking error constraints - is this problem convex?

Let's say I have a return forecast for each stock in the DAX index. I also have a covariance matrix for these 30 stocks. I want to solve for the 30 weights by maximising the forecast portfolio ...
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55 views

establishing an optimal take profit

Please let me know what you thoughts are on this. Say for example that you have a perpetuity, which guarantees you indefinite payments of a certain amount. Say then that you also have the opportunity ...
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1answer
106 views

Mixed-integer programming approach for index tracking

Suppose you currently own a portfolio of eight stocks. Using the Markowitz model, you computed the optimal mean/variance portfolio. The weights of these two portfolios are shown in the following table:...
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6answers
2k views

Does mean-variance portfolio optimization provide a real edge to those who use it?

Mean-variance optimization (MVO) is a 50+ year concept, and perhaps the first seminal idea of quantitative finance. Still, as far as I know, less than 25% of AUM in the US is quantitatively managed. ...
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118 views

Convex optimization of ex-ante information ratio

I am trying to optimize an ex-ante information ratio using a convex optimizer. I have started with the Sharpe ratio and have managed to reform it into a conic problem as such: https://people.stat.sc....
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45 views

Mean variance portfolio optimization with long short positions

Sorry if this has been asked before. Can someone point me to some places explaining how to set up the mean variance optimization on long short portfolios? Classical formulation has long only. Is it as ...
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0answers
29 views

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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2answers
649 views

When looking for arbitrage among a LARGE amount of assets, is there an optimal way?

Looking for arbitrage opportunities when looking at 3 pairs of related currencies is easy. However if we assume that we have a large amount of currencies, is there an optimal way to swipe through them ...
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1answer
112 views

Is optimising for the Final Wealth is the same as optimising log of growth rate in Kelly Criterion?

A direct, brute force approach could be used to find the Optimal Portfolio. Consider simple play. There's a biased coin with 55% probability of win. The simulator play as a single person with 100$ ...
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1answer
90 views

Curve fitting under different regions and stitching

Is there a way to fit a 2D curve under the following conditions: The curve is defined by 2 functions for x>a, and x<a Prefer a fit that is continuous and differentiable at x=a
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68 views

Python: Parametric Portfolio optimization with data from Kenneth French

I am fairly new to Python and struggling right now. I am trying to build the parametric portfolio policies by Brandt (2009) with the data of the Fama French Factors by Kenneth French, which is taken ...
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1answer
175 views

Optimize Bollinger Bands Strategy

I was proving a very simple strategy with Bollinger Bands for a intraday timeframe (1 minute) that buy on lower band and sell in a higher band (Very common strategy), but in backtesting in E-Mini SP ...
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4answers
162 views

Cant replicate minimum variance portfolio variance by simulating many random portfolios in R

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{\...
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0answers
67 views

MatLab code does not work for Heston model calibration

I am trying to calibrate Heston model on some data and I have the following code. Code is supposed, after it reads the data, to give back 5 parameters. However, I get an empty answer from MatLab. Does ...
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1answer
3k views

Optimal execution and reinforcement learning

Suppose a fairly simple problem: You have to buy (resp sell) a given number of shares V in a fixed time horizon H with the aim to minimize your capital spent (resp maximize your revenue). There are ...
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1answer
213 views

Optimal Strategy in 3 Dice Game

In a recent interview I received the following question (an optimisation/strategy game)...which left me a bit stumped. The rules of play, you start with 0 points, then: Roll three fair six-sided dice;...
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101 views

Vasicek Model With Jumps

I'm trying to calibrate a mean-reverting, jump diffusion model using the outline provided on page 11 here: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.40.3489&rep=rep1&type=pdf ...
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62 views

Optimal withdrawal rate based on alpha and drawdown

My trading returns is about 50% monthly(alpha) and maximum drawdown is about 20%. Is there a mathematical way to define the optimal withdrawal rate X%(say when profit level reach y%) to avoid risk of ...
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0answers
77 views

An example that mixes the stock market, game theory and linear programing

First of all i am not entirely sure if this is the correct place to discuss this problem but i shall give it a try. I'm currently doing an assignment for a degree in Linear Programing. My objective ...
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0answers
18 views

Interest Expense Optimization

So I have a problem I need to solve and no idea how to approach it. Its a verbal problem without any specific numbers given except for those below. So it is up to me to determine how to structure the ...
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0answers
66 views

Optimising returns weighted by Sharpe ratio in the context of Supervised Learning

In the Kaggle Jane Street market prediction competition we are put in a Supervised Learning Framework to deal with 'trade opportunities'. That is, we are given instances of previous trade ...
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0answers
57 views

$\epsilon$-arbitrage model

In the model here described, Bertsimas says that we can use the Robust Optimization to find the replicating portfolio the value of which is such that minimize the difference $|P(\widetilde{S},K)-W_T|=\...
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0answers
68 views

There are several ways optimize portfolio, why use Black Litterman rather than Mean variance

I know there are two ways to optimize portfolio. What are the limitations and advantages by using Black Litterman over Mean variance.
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1answer
1k views

Minimum Variance and Minimum Tracking Error portfolio as second order cone program

The quadratic optimization (min variance) $$ w^{T} \Sigma w \rightarrow \text{min}, $$ where $w$ is the vector of portfolio weights and $\Sigma$ is the covariance matrix of asset returns, is a well ...
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71 views

Conic optimization in finance

Linear programming and quadratic programming are types of convex optimization that are often used. Does conic optimization or programming have any applications in finance? Or for where the previous ...
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0answers
20 views

Is the feasible set of portfolios an epigraph?

In mathematics, the epigraph of a function is the set of points lying on or above its graph, in this case a convex function: The efficient frontier from mean-variance portfolio analysis encloses an ...
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0answers
290 views

Maximizing sharpe ratio using cvxpy or cvxopt

I have a dataframe $n$ by $m$ representing $m$ timeseries of returns (each column is a different time series) with total $n$ number of observations, I want to find weight vector of length $m$ such ...
3
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1answer
296 views

Derivation of mean-variance portfolio weights as closed-form analytical solution from Lagrangean equations

I am trying to find a closed form solution for the constrained MVO problem below. $\max_w w'\mu - \frac{\lambda}{2}w'\Sigma w $ s.t. $w'$1 = 1 The Lagrange for the objective is $L(w, \gamma) = w'\mu ...
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0answers
170 views

Can genetic algorithm help in portfolio optimisation when convexity is not verifiable

I have the following portfolio cost function to maximise: $$ w^T\mu-\frac{1}{2}\gamma w^T\Sigma w+\frac{1}{6}\gamma^2 w^TM_3(w\otimes w), $$ which considers the co-skewness ($M_3$ tensor), $γ$ is the ...
2
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1answer
138 views

Is quadratic programming used to maximize portfolio skewness and kurtosis?

Quadratic programming, a type of convex optimization, is used to solve the minimum variance portfolio weights $$w = \arg \min_w \sigma_P^2 = w^\top \Sigma w$$ because the objective function coincides ...
4
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1answer
130 views

Tangency portfolio with two additional constraints so that portfolio weights are unconstrained

I know that the formula for determining the weights of the Tangency portfolio is given as $w_{tan}$ = $\frac{\Sigma \mu}{\iota^{\prime}\Sigma\mu }$, but I was wondering how to derive the weights in ...
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0answers
2k views

Formula for the efficient portfolios in mean-variance optimisation?

Consider the setting of mean-variance portfolio optimisation: $n$ assets with expected returns $\overline{r}_1,...,\overline{r}_n$ and standard deviations $\sigma_1,...\sigma_n$. For a certain fixed $\...
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5answers
15k views

Portfolio optimisation with VaR or CVaR constraints using linear programming

I would like to optimize a portfolio allocation (maximizing the exposure or the expected return), but with VaR or CVaR contraints. (some parts of my portfolio cannot exceed a certain VaR) How can I ...
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3answers
717 views

What's the disadvantage of using linear programming for portfolio optimization?

I am a MFE student and we have project on the Markowitz portfolio optimization problem. i am wondering how much impact there will be, if I use a simpler linear optimizater instead of a quadratic one. ...
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0answers
118 views

Linear programming optimization problems in finance

I'd like to know what are, if any, the applications of linear/non linear programming optimization techniques for financial markets. I'm a business major, and I want to find an argument for my thesis ...
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1answer
154 views

Maximize account equity over a historic time series

Inputs: array of OHLC forex bars of size N, max leverage L, e.g. 200:1, a fixed bid ask spread S, a fixed lookahead whipsaw window W (e.g. 3 bars long, see below). Desired output: a list of tuples {...
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0answers
1k views

Is there a standard method of scaling alpha forecasts to t-cost estimates?

Given a set of monthly alpha forecasts (i.e. standardized z-scores from a multi-factor return model) and a non-linear market impact model (or more specifically, its piecewise-linear approximation), is ...
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1answer
97 views

Double objective in portfolio optimization

Is there anything infeasible or ethically wrong about optimizing portfolios like this? $$\min_w \enspace w' \Sigma w + w' C w$$ where $\Sigma$ is the asset return covariance matrix, and $C$ is the ...
4
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1answer
180 views

Optimization problem with a constraint

Consider the following maximization problem $$\max_{\{\tau(\cdot),q(\cdot)\}}\int_{\underline{\theta}}^{\bar{\theta}}\left(\theta q(\theta)-\dfrac{\gamma\sigma^{2}}{2}q^2(\theta)-\tau(\theta)\right)f(\...
4
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1answer
330 views

stochastic programming book recommendations

Hi: Can anyone recommend an introductory book on stochastic programming ? There are obviously so many books on Amazon but I can't tell easily which ones could be useful. It would be good if it had ...
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0answers
39 views

Configuration of control parameters tol and delta in the rsolnp package

I am working with the rugarch package which includes a solver.control argument. I am using the solnp solver. I can pass values for tol and delta. In the rsolnp the authors suggest that the control ...

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