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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1answer
107 views

How to find coefficient that will minimize the distance between few times series

I have 3 time series X1, X2, X3. I want to find the coefficient (c1, c2) that will minimize the distance between them as follow: $$MIN\sum\sqrt{(X1-(c1*X2+c2*X3))^2}$$ The constrains are: $$-1< ...
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1answer
233 views

Portfolio optimization in R with factor tilting while constraining volatility

what optimizer I can use in R to solve the following portfolio optimization problem: $min(f^Tx)$ st: 1. $ -a \le \sum_{i=1} ^{n} x(i) \le b$ 2. $ -c \le x(i) \le d$ 3. $ e \le \sum _{i=1} ^n |x(i)...
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4answers
2k 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 (...
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1answer
230 views

Optimisation with strong correlated Assets

I have the following settings: The allowed traded assets consists of 1 bank account, 1 non dividend paying stock and 19 call options whose maturity is in 30 days. I want to find an optimal static ...
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0answers
207 views

Optimisation problem with bid-ask spread

I want to optimise a static portfolio with a holding period of 90 days given 10 tradable assets. The assets are quoted in bid and ask prices. I want to minimise the risk measured by standard deviation ...
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1answer
152 views

Question on Rockafellar's Paper for optimisation of CVaR

In Rockafellar and Uryasev's Paper about CVaR Optimisation they showed in Equation (17) that using Monte-Carlo-Simulation one can use $$\tilde F_{\beta}(x,\alpha)=\alpha+\frac{1}{q(1-\beta)}\sum_{k=1}^...
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2answers
2k views

Variance Matrix with 'nan' values

I am trying to optimize a simple portfolio using several random weights and choosing the best. When the number of assets is large I get a covariance matrix with 'nan' values because some asset pairs ...
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1answer
444 views

Portfolio Optimization with maximum number of Trades constraint

i am currently running linear optimization and maximizing summation of (weight*score) for each assets. I am running it on assets that are difficult to trade and the universe is easily about 2000 of ...
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2k views

Improvement of Alpha Expression [closed]

I'm newbie user of Websim (websim), given Alpha Expression : (est_eps * (cashflow/sharesout) * (est_sales/sharesout))/est_dividend_ps Settings-Region:USA, Universe:TOP3000, delay:1,MAX stock weight :...
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172 views

Solution for Markowitz problem with Safety-First Ratio

What is the solution for the following markowitz unconstrained problem? The sum of the entries of the weights vector $w$ should always be requied to sum one? Or if we use the risk-free asset it can be ...
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1answer
1k views

Derivation of the efficient frontier set (markowitz problem)

I would like to find a Derivation of the efficient frontier set for the markowitz problem:
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1answer
238 views

Solving a Markowitz problem with restrictions (lower and upper bound) to the weights vector

I would like to find a step by step solutionfor the following Markowitx problem. It is a standard markowitz problem. The unique detail (wich is why I am posting this question here) is that there is a ...
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1answer
281 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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1answer
764 views

R optimization using OPTIM

I have a covariance matrix and vector of expected returns as my inputs. I have used optim to solve for the weights that maximize the portfolio's return/volatility. I like optim as you can create your ...
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3k views

Fitting GARCH(1,1) in Python for moderately large data sets

I am using the arch package in python to fit a GARCH(1,1) to fit daily S&P 500 returns from 1990 to 2017 (about 6800 data points). The code I am using is as follows: ...
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87 views

Confusion about Assumptions in Markowitz Optimization

Setup and Definition of Terms Supposed that we have a universe of possible securities $\mathcal{S}$. We wish to construct an "optimal" portfolio, which will be represented by proportional weights $\{...
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802 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 ...
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0answers
610 views

Optimal weights for portfolio optimisation (r)

The question is what R optimization could be applicable to find a vector of weights that when, multiplied by S matrix creates equal rows sums, and when set in the objective function returns the ...
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1answer
104 views

Proof that linear returns aggregate across securities

I keep reading that linear returns aggregate across securities, but I'm having trouble proving it. I suspect there's some mistake in my approach; I'd appreciate some help in seeing it. Suppose we ...
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1answer
288 views

Optimize portfolio of non-normal binary return assets

I am facing t = 1,..T investment periods where each period I have x$ to invest. Suppose each period I can build a portfolio from thousands of assets (some are uncorrelated whilst some are highly ...
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79 views

Maximum likelihood for lognormal mixture

I have a collection of historical data that I want to fit to the following model $$ y_{t+1} - y_t = \alpha + (\rho + \sigma_2 Z_{t+1} )y_t + \sigma_1 Z_{t+1} $$ where everything except the y's are ...
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2answers
2k views

Dmat argument in solve.QP R function: Cov or 2*Cov?

Background My final objective is to find a portfolio located on the efficient frontier from a choice of 100 stocks from a stock index (eg. S&P500). This efficient portfolio will be such that ...
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2answers
2k views

Black Scholes in Practice: Delta Hedging

From the Wikipedia page, we know call option as an example is price through delta hedging. $$\Pi=-V+V_SS$$ and over $[t,t+\triangle t]$ $$\triangle\Pi=-\triangle V+V_S\triangle S$$ My questions ...
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1answer
2k views

Portfolio optimization subject to transaction costs

Mean-Variance portfolio optimization attracted lots of attention in this forum so far. I am interested in the effect of incorporating transaction costs into the decision framework and I would like to ...
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2answers
2k views

How to build a market-neutral portfolio using CVXPY?

I am trying to implement a simple minimum variance portfolio optimisation with a few simple constraints: long-only portfolio fully invested (sums to one) market-neutrality, i.e sum(betas) = 0. I am ...
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2answers
545 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 ...
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1answer
56 views

DJIA Portoflio Optimization

I've been practicing R for about several months, and have begun transitioning from text book examples to what actually interests me. I'm currently participating in the CFA program, but my programming ...
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1answer
211 views

Translating matrix expression of Lagrangian into solve.qp() parameters (R)

I have no idea how to do this. I can set up the Lagrangian, but I don't know how to translate it into solve.qp() inputs. The inputs are Dmat, dvec, amat, bvec, ...
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1answer
296 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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0answers
333 views

Mean-Variance Optimization Techniques with Multiple Asset Classes

Why does it make sense to use single-period Markowitz mean-variance optimization techniques when we're trying to figure out asset allocation across multiple asset classes (bonds, stocks, REITs, etc)? ...
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2answers
6k views

Formula for Optimal Portfolio of 2 Assets when No Shorting Allowed?

I am looking for a formula to calculate the weights of two risky assets that produce the optimal portfolio (i.e highest Sharpe ratio). So far I have found the following formula from a website of ...
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2answers
667 views

Asset allocation problem using Hidden Markov Model

I am recently getting more interested in Hidden Markov Models (HMM) and its application on financial assets to understand their behavior. But what captured my attention the most is the use of asset ...
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1answer
182 views

EM for conditional Gaussian model

Let $$X_1\sim N(\mu_{X_1},\sigma_{X_2}^2)$$ $$X_2\sim N(\mu_{X_2}, \sigma_{X_2}^2)$$ where $\mu_{X_2}=c+aX_1$. Also, I have data $D$ (with missing values on $X_1,X_2$). How can I update/estimate the ...
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1answer
1k views

How to understand this Risk Parity Algorithm?

I am trying to understand an optimization algorithm to achieve risk parity in a portfolio. I need some help figuring out the notation in the following formula: I found this on THIS paper. I ...
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1answer
236 views

Portfolio with zero or negative initial cost

Let's say I have formulated an integer linear programming (ILP) problem with the objective function $$F(X)=V(T,X)-C(t,X),$$ where $V(T,X)$ is the payoff of portfolio, and $C(t,X)$ is the initial cost ...
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4answers
813 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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3answers
10k views

Why do we assume quadratic utility in portfolio theory?

In my text (Investments by BKM), the investor's mean-variance utility (given as $U = E[R] - \frac12A\sigma^2$) is stated to be the objective function we wish to maximize. Upon further digging, it ...
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0answers
372 views

Optimize a trading strategy created in excel with R

I have created quite a complex back test in excel spanning 15 years with 17 parameters. I would like to optimize the parameters which would give me maximum return given a maximum draw-down percentage. ...
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0answers
123 views

Using Market Prices of Bonds to Model the Discount Curve with a Polynomial (Math + R)

I have a small program I'm building to interpolate the discount curve from a portfolio of benchmark bonds. If anyone has any guesses as to whether it's my process, or my code that's messed up I would ...
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1answer
225 views

Portfolio optimization - maximize variance with exposure to risk factors equal to zero

Optimize a portfolio such that the exposure to risk factors is zero and the variance is maximized (instead of traditional minimization problem). so the optimization problem look like: $$maximize\;w^...
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0answers
45 views

Continous-time portfolio allocation optimization for a given consumption rate

I have the following PDE $0 = V_t - c(t)V_x - \lambda^2 V_x^2/V_{xx} + rxV_x + 1/2\lambda^2x^2V_{xx}$ where $t\mapsto c(t)$ is some given function and $r,\lambda$ are given constants. If necessary, ...
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1answer
527 views

Starting values for constrOptim() in R

I want to perform a constraint optimization for Maximum Likelihood Estimation in R to forecast volatility of returns. The probleme is that my initial values aren't in the permitted region. Is there ...
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2answers
733 views

Dealing with a constraint which is the square root of a quadratic form

I'm trying to maximize my portfolio, but don't know how to deal with the constraint which is on the form max $2u^Tx-x^T \Sigma x$ Subject to $e^Tx = 1$ $u^Tx - m (x^T \Sigma x)^{1/2} >= c $ ...
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1answer
253 views

Numerical Optimizer Matlab Calibration LMM

I am trying to mimimize the following function in order to calibrate the Libor Market Model $$\sum_{i=1}^{n} \left(\sigma_i^{market}-\sigma_i^{Reb}\left(a,b,c,d,\beta\right)/\sqrt{T_i}\right)^2,$$ ...
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1answer
356 views

dynamic Markowitz portfolio

Let's take 4 assets, whose values are known during a period of time of 2 years. Then I calculate the expected returns for each of these 4 assets thanks to these 2 years - historical data. I deduce the ...
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1answer
38 views

Equitable Allocation

This questions borders on the actuarial side of things but the general solution should have relevance in several situations. Suppose we have a set of $k$ people who will retire in $\{n_1,...,n_k\}$ ...
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1answer
353 views

Portfolio with lots of subportfolios

An account manager has $N$ distinct, equally-sized pots of money, which will be used to make $N$ distinct subportfolios, each of which is drawn from a slightly different (but potentially overlapping) ...
3
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1answer
358 views

Determining maximum strategy capacity and optimal order size for low frequency equity strategy

I have developed a low frequency equity trading strategy that seems to work well with stocks in the S&P 500. Someone asked me about the maximum capacity of the strategy (how much AUM I could ...
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3answers
468 views

What are the canonical books on optimization methods?

I am looking for some literature devoted to optimization methods in finance (portfolio optimization, asset pricing etc). Could you please recommend some books (perhaps, essentially non elementary: I ...
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1answer
58 views

Imposing MLE restrictions by logistic mapping

I am doing some Maximum Likelihood Estimation with a density that has time-varying parameters. I am using the fmincon function in Matlab, but I do not know how to ...