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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48
votes
8answers
51k views

What are some useful approximations to the Black-Scholes formula?

Let the Black-Scholes formula be defined as the function $f(S, X, T, r, v)$. I'm curious about functions that are computationally simpler than the Black-Scholes that yields results that approximate $...
40
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12answers
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 ...
28
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12answers
18k 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 ...
24
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1answer
6k views

Algorithm to fit AR(1)/GARCH(1,1) model of log-returns

I am fitting numerically an AR(1)/GARCH(1,1) process to index and stock log-returns, $r_t=\log(P_t/P_{t-1})$, where $P_t$ is the price at time $t$, and thus far am not clear on where the observed log ...
23
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4answers
8k views

Techniques to optimize the placement of orders in market making strategy?

Market making often requires placing and canceling a lot of orders. You have to buy and sell nearly simultaneously, so you need to move orders pretty often to beat other traders. But I would like to ...
22
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4answers
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. ...
20
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5answers
12k views

portfolio optimisation with VaR (or CVaR) constraints

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 ...
20
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1answer
2k views

Portfolio optimization with monte carlo sampling from predictive distribution

Let's say we have a predictive distribution of expected returns for N assets. The distribution is not normal. We can interpret the dispersion in the distribution as reflection of our uncertainty (or ...
16
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5answers
6k views

Why is the Drawdown measure not used for portfolio optimization?

I was asked yesterday by a colleague why we are doing asset allocation using optimizers which target, for a minimum expected return: the portfolio with the minimum variance or the portfolio with ...
16
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3answers
3k views

Role of skewness in portfolio optimization?

What is the role of skewness in portfolio optimization?
15
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3answers
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 $N$ ...
15
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1answer
401 views

Are there references about liquidation, transaction, market impact costs in portfolio optimization

I am looking for some references treating of what I would call liquidation cost market impact cost transaction cost(*) in the usual "portfolio optimization problem under linear constraints". Let ...
14
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5answers
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 ...
14
votes
1answer
410 views

Max option leverage strike

Since options represent leveraged stock investments, at which strike $K$ does a European option provide maximum leverage? Hereby define leverage $L$ as ratio of Delta/Optionprice: $$L(K)=\frac{\...
13
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4answers
1k views

Why is Markowitz portfolio optimisation so popular considering it is worse than an equal weighted portfolio?

The original paper by Markowitz from the '60s has ~20,000 citations (definitely popular). However several papers I came across show that a $\frac{1}{n}$ asset allocation gives higher Sharpe ratios (...
13
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1answer
811 views

Portfolios from Sorts

Some time ago Almgren and Chriss proposed a method for portfolio optimization based on sorting criteria such as $r_1 > r_2 >... > r_N$ instead of explicit expected returns: see portfolios ...
12
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4answers
3k views

What .NET library can I use to solve optimization problems?

I'm working with C# and I start being bored writing optimization algorithm. Do you know any free library containing this sort of algorithms? In particular I'm currently working with Semidefit ...
12
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2answers
3k views

robust portfolio optimization re-balancing with transaction costs

The optimal re-balancing strategy takes account of factors including i) objective function, ii) current portfolio weights, iii) expected return vector containing updated views/alpha forecasts, iv) ...
12
votes
3answers
1k views

What is the expected return I should use for the momentum strategy in MV optimization framework?

As all research on the momentum strategies are focused on the indicator, i.e. the entry point, there seems not much discussion on its expected return? Though there are some discussions on the exit ...
12
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1answer
621 views

The danger of using Principal Component Analysis (PCA) in Robust Optimization problems

I have received a reviewer's comment on a paper which applies PCA to reduce the size of a problem and the application is in the robust optimization field. The reviewer implies that "In robust ...
12
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2answers
534 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-...
11
votes
1answer
650 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 ...
10
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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 ...
10
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1answer
1k views

Min VaR and Min TE 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 ...
10
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2answers
2k views

How to apply risk-parity portfolio construction to a dollar-neutral portfolio?

Long-only risk-parity portfolios have proliferated in recent years. An optimized long-only risk-parity portfolio requires that the asset weight * marginal contribution to risk of the asset is ...
10
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0answers
1k views

Formula for the efficient portfolios (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 $...
9
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3answers
5k views

Application of Control Theory in Quantitative Finance

I have recently completed an MSc in Control Systems from a top university. It seems to me that control theory must have an application within quantitative finance. I would like to apply my degree ...
9
votes
1answer
2k views

Optimizing a portfolio of ETFs

I am aware of how to do mean-variance or minimum-variance portfolio optimization with constraints like weights must add to 1.0 no short sells max weight in any ticker using basic quadratic ...
8
votes
2answers
301 views

How to represent constraints for optimization problems in a data model?

I am at the moment writing a program focusing on asset allocation and I am thinking about how I should represent my constraints in the data model. The first approach that came to mind was to define ...
8
votes
1answer
557 views

What's the importance of duality theory in portfolio optimization?

I'm interested in portfolio optimization and there's a lot of modelizations out there using duality theory. Since I didn't study that yet, I searched around the net to understand what it means and ...
8
votes
1answer
3k views

How can I use Entropy-pooling of Atillio Meucci to constuct a portfolio?

I am trying to get my hands on Entropy Pooling which was introduced by Meucci in this paper. As an example, assume I want to construct a portfolio with five stocks and I have my view on CVaR. How ...
8
votes
1answer
803 views

Optimal trading strategy in toy world of simple Hidden Markov model with Gaussians

I want to solve the following optimization problem: What is the optimal general trading strategy (in the sense of the highest Sharpe ratio) on a time series which is the result of a Hidden Markov ...
8
votes
2answers
2k views

optimal re-balancing strategy with asynchronous alpha signal

You want to construct an optimal portfolio. Let's say you have an alpha signal that arrives with some period (say quarterly). The alpha signal predicts arithmetic returns one-year ahead. You have ...
8
votes
4answers
1k views

How to optimize a portfolio under *both* maximum diversity ratio and minimum variance

I have a follow-on question to questions that appeared here and was not sure if the right way was to ask in the comments or post a new question. My question is: how can I optimize a portfolio to suit ...
7
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5answers
2k views

portfolio optimization from empirical return distributions

I'd like to do a portfolio optimization of a set of ETF's but want to avoid traditional problems with normality assumptions in returns etc. Are there techniques that let me sample 'draws' from the ...
7
votes
2answers
3k views

Comparing MVO with Resampled Efficient Frontier

My question: How can I compare the Resampled Frontier (REF) to the standard MVO frontier when I have been provided with $\mu$, $\Omega$, and don't have access to true future data to test real out of ...
7
votes
4answers
5k views

Markowitz mean-variance optimization as “error maximization”

I hear it said a lot that standard MV optimization "maximizes errors". But I can't find a good explanation for what exactly they mean by this "maximization" of estimation error. I understand that if ...
7
votes
4answers
1k views

How to cluster ETFs to reduce cardinality for portfolio selection

I'm looking to run portfolio optimizations using various optimization goals - e.g. minimum variance, max diversification etc. My challenge is if I want to do this on ETF's which ones do I pick to run ...
7
votes
3answers
19k views

What do the terms in-sample and out-of-sample estimates mean in MVO?

How do the in-sample estimates and out-of-sample estimates I so often hear authors refer to in emperical analysis of MVO differ?
7
votes
2answers
9k views

Typical risk aversion parameter value for mean-variance optimization?

What are typical values for risk aversion parameters $\lambda$ used in mean-variance optimization? Please provide references. Just to be clear, I'm talking about the $\lambda$ in $U(w) = w'\mu - \...
7
votes
1answer
175 views

Question about quadratic form of f* in the Continuous Kelly Criterion

I am trying to follow the Optimal Kelly derivation on Wikipedia for two continuous assets: one risky and one risk-free. The derivation begins by assuming that the risky assets follows a GBM (a ...
7
votes
3answers
449 views

What is the canonical reference for Minimum Variance Portfolio's uniqueness?

I am writing a white paper in which I am trying to compare a strategy to different well-known - and classic - asset allocation optimization approaches. One of the methods I chose is the minimum ...
7
votes
1answer
236 views

Stochastic control (HJB) for wealth process involving stopping times

Given a wealth process that evolves as $$d w_t = r w_t dt + \theta_t ( \sigma dW_t + (\mu-r) dt) - c_t dt.$$ where $\theta_t$ is the worth of holding at time $t$ and $c_t$ is the consumption stream. ...
6
votes
3answers
827 views

Maximum Sharpe portfolio (no short selling restrictions)

Suppose we have $n$ assets whose expected return vector is $r$ and is positive, and whose covariance matrix is $\Sigma$. Is there a closed form or quasi closed form (like the eigenvector of a matrix ...
6
votes
2answers
5k views

How to define the objective function for a custom optimization problem?

I would like to find the allocations that would minimize some user-defined metric (Sortino, minimum drawdown, etc) for a portfolio of assets. How would one go about formulating the objective ...
6
votes
3answers
3k views

Do hedge fund trading desks use portfolio optimization?

I tend to think that hedge funds that actively trade (and most of the ones I have seen trade very actively), don't use optimization methods like MVO or ...
6
votes
2answers
4k views

How to implement Maximum Diversification in R?

I am trying to code up the optimization problem for Max Diversification Portfolios. The main problem I am having is properly translating the objective function in to code and port it in to the ...
6
votes
1answer
2k views

cvxpy portfolio optimization with risk budgeting

I'm trying to do some portfolio construction in cvxpy in Python: ...
6
votes
2answers
382 views

Maximum Certainty Equivalent Portfolio with Transaction Costs

Out of curiosity I tried to compute the portfolio weights of a maximum certainty equivalent allocation, however, by incorporating (quadratic) transaction costs. However, my result is not as intuitive ...
6
votes
2answers
546 views

Choice of prior as a shrinkage target in portfolio construction?

There's various research showing how priors such as the minimum variance portfolio turn out to be a surprisingly effective shrinkage target in portfolio construction. The sell point of these priors ...