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
75 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
1k 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 $\...
2
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1answer
86 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 ...
21
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5answers
13k 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 ...
2
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3answers
559 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. ...
3
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0answers
83 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 ...
0
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1answer
36 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 ...
1
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1answer
148 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 ...
1
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1answer
226 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 ...
0
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1answer
89 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
164 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
188 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
15 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 ...
0
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0answers
37 views

Optimizing Portfolio Return by Targeting Variance

I understand Markowitz and targeting returns to minimize our variance. I know this optimization problem well and its constraints. However when the reverse scenario is to be considered I get very ...
3
votes
1answer
167 views

Which Maximum Diversification Approach in MATLAB is correct?

I am currently trying to find the portfolio weights of the Maximum Diversification Portfolio and found two approaches which result in different outcomes. The first one is based on this paper:https://...
0
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0answers
31 views

Extreme and rare events affecting the market

There are extreme events affecting the high-probability [short-term] market such as lowering interest rates that rocket stock prices, even though such events are rare and the market's response can be ...
8
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1answer
3k views

cvxpy portfolio optimization with risk budgeting

I'm trying to do some portfolio construction in cvxpy in Python: ...
1
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1answer
360 views

Create a hedging portfolio

If, given a return stream of unknown composition, what is the best find a portfolio of assets that replicates that return stream from a universe of assets? In other words, what is the best ...
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2answers
472 views

Fixed Income Portfolio Optimization

I'm trying to solve for a maximum sharpe ratio portfolio in the fixed income space. To do so, i use CVXPY in python. I use this Paper as reference. This is my "setup": ...
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2answers
3k views

portfolio optimization with weights constraint in python

I'm trying to optimize a portfolio using cvxpy. My original construction is the following: ...
28
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13answers
19k views

What is the reference python library for portfolio optimization?

Does anyone know of a python library/source that is able to calculate the traditional mean-variance portfolio? To press my luck, any resources where the library/source also contains functions such as ...
1
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0answers
60 views

How to optimize a non-linear least squares problem with cvxpy/cvxopt

I know how to minimize a linear function $f : \mathbb{R}^{n} \rightarrow \mathbb{R}$ with CVXPY but in my problem the function $f$ is quadratic and hence the problem is now in the form : $$\lVert AW-...
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1answer
41 views

How to build a portfolio following the Smart beta process by dividend? [closed]

I'm having trouble finding the method to track smart beta dividend management. I have an Excel file which contains the prices and the dividends of certain companies, and I want to build a portfolio ...
5
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2answers
375 views

Estimation of Risk-Neutral Densities Using Positive Convolution Approximation - Python

I'm trying to estimate the risk-neutral density through positive convolution approximation (introduced by Bondarenko 2002: https://papers.ssrn.com/sol3/papers.cfm?abstract_id=375781). I'm currently ...
2
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0answers
108 views

Transform this non-linear portfolio optimization problem into a quadratic optimization problem

I have a portfolio optimization problem similar to this question here, with a V-shape transaction costs such that we pay a fee proportionally to the sum of absolute rebalancing: $$TC(\omega) = \frac{1}...
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0answers
114 views

Dynamic programming and Bellman equation to obtain the maximum

This is the problem of Marhsall (1992) "Inflation and Asset Returns in a Monetary Economy" and Balvers and Huang (2009) "Money and the C-CAPM" Suppose an endowment economy where the representative ...
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0answers
46 views

Martingale optimal transport

I'm a student and currently studying martingale optimal transport for deriving upper and lower contract bounds but i happen struggling on the fact that in most papers , interest rates are not taken in ...
2
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2answers
421 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,......
2
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2answers
2k views

maximize Sharpe ratio in portfolio optimization

I am trying to understand how to maximize Sharpe ratio in portfolio optimization. $\boxed{\begin{align}\max\>&\frac{r^Tx-r_f}{\sqrt{x^TQx}}\\ & \sum_i x_i = 1\\ & x_i\ge 0\end{align}}$ ...
0
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0answers
15 views

Monte carlo error and minimum variance hedge ratio

So I was running a monte carlo simulation for two assets and a portfolio consisting of 1 quantity of the first asset and short a fraction x of the second asset to hedge, where the fraction is ...
2
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1answer
66 views

Backtesting with a walkforward approach

I am setting up a backtesting using a walkforward optimization model to find out if a trading strategy performs well or not and I would like to clarify some doubts: First of all what is the correct ...
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0answers
67 views

CVaR portfolio optimization with risk aversion parameter

I'm trying to implement the Rockafellar's function described in this paper http://past.rinfinance.com/agenda/2009/yollin_slides.pdf with a risk aversion parameter for my thesis. The function to ...
3
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1answer
217 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 ...
0
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1answer
22 views

Suggestions for choosing an optimization algorithm for fitting custom GARCH models by QMLE in R?

I am trying to fit a custom GARCH model by QMLE in R. I have written out the log likelihood function and am now working on optimizing it. However, choosing an optimization algorithm has proven to be ...
4
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2answers
2k views

How can I find the portfolio with maximum Sharpe Ratio - Using Lagrange Multipliers

In Markowitz' portfolio theory we can construct portfolios with the minimum variance for a given expected return (or vice versa). Across expected risks, this traces out the well-known efficient ...
2
votes
2answers
137 views

Problem with the maximum likelihood for a GARCH-type of model

I'm currently working with the following GARCH process from Heston and Nandi (2000): \begin{align*} r_{t+1} - r_f &= \lambda h_{t+1} - \frac{h_{t+1}}{2} + \sqrt{h_{t+1}}z_{t+1} \\ h_{t+1} ...
14
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4answers
756 views

Quantum Computing for Quantitative Finance

It's been a while that quantum computing is looked as the next step in computational science. I somewhat always tought we were decade aways from it's happening but it appears I was wrong: ibm-quantum-...
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0answers
50 views

Optimized search for yield-to-worst of a callable bond

Suppose that I need to find the yield-to-worst of a callable bond, and that the option is American (call any time). The bond may have step-up coupons and/or non-constant call price (oprion strike). ...
0
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1answer
28 views

Weighting function for parametric estimation of the Risk-neutral density function

I would like to estimate the Risk-neutral density function (RND) implicit in financial Call option prices by a parametric approach where the parameters of the RND (for instance mean and variance for a ...
0
votes
0answers
31 views

setting up a inequality constraint that is dynamic

I have the following problem: typical mean variance minimize w_long(S)w_long.T + w_shortSw_short.T - lambda*mu I am having issue formulating this constraint in cvxopt lets say we have 10 securities ...
0
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0answers
71 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$ ...
0
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1answer
202 views

Optimization with turnover constraint

I am optimizing using scipy.optimize using SLSQP. I am looking to minimize the variance with some upper bounds and lower bounds on each stock. I am also looking to constraint the weight so that the ...
1
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0answers
85 views

Error in optimize.portfolio with transaction costs constraint

I am experimenting with the PortfolioAnalytics package to optimize portfolio with dollar neutral and transaction costs as constraints to the quadratic utility objective function. A sample R snippet is ...
0
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1answer
431 views

solve.QP error: constraints are inconsistent, no solution!

I am trying to solve a constrained optimization with the following statement and struggling with the error constraints are inconsistent, no solution!: ...
2
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3answers
1k views

Ledoit-Wolf Shrinkage estimator not giving positive definite covariance matrix

I used ten year daily data for 407 stocks and computed the daily and monthly covariance matrices. Since I have more variables than observations for the monthly matrix, I wasn't surprised to find the ...
1
vote
1answer
2k views

Portfolio optimzation : efficient frontier with respect to risk aversion parameter with R

I am currently trying to write a little script in R to determine the optimal weights given a fixed risk aversion parameter. The problem I have is that by increasing the risk aversion parameter I think ...
6
votes
2answers
1k views

Random Portfolios vs Efficient Frontier

I understand the concept of the efficient frontier and am able to calculate it in Python. But even when generating 50'000 random 10 asset portfolios, the single portfolios are not even close to the ...
2
votes
1answer
97 views

Choosing best expressions from all possible combinations on variables, unary operators and binary operators along with hyper parameters

I have a few financial variables of a stock universe like OHLC prices, volume, and other fundamentals with varying time-frequency. Using this set I'm creating an expression that gives the weights to ...
2
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0answers
70 views

Interchange Expectation and Supremum in Snell Envelope/American Options

I had a question about the properties of a snell envelope, $\sup_{t\le\tau\le T} \Bbb E\left(Z_\tau\mid \mathcal F_t\right)$, which came to me while studying American options. I know that in general,...

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