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.

Filter by
Sorted by
Tagged with
4
votes
1answer
139 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}^...
2
votes
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 ...
0
votes
1answer
419 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 ...
1
vote
0answers
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 :...
1
vote
0answers
167 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 ...
2
votes
1answer
978 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:
1
vote
1answer
232 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 ...
2
votes
1answer
255 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
votes
1answer
742 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 ...
4
votes
0answers
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: ...
1
vote
0answers
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 $\{...
8
votes
1answer
772 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 ...
2
votes
0answers
604 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 ...
3
votes
1answer
103 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 ...
2
votes
1answer
275 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 ...
1
vote
0answers
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 ...
3
votes
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 ...
5
votes
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 ...
3
votes
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 ...
1
vote
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 ...
7
votes
2answers
529 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 ...
0
votes
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 ...
0
votes
1answer
181 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, ...
3
votes
1answer
253 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
votes
0answers
316 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)? ...
2
votes
2answers
5k 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 ...
0
votes
2answers
653 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 ...
0
votes
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 ...
2
votes
1answer
994 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 ...
0
votes
1answer
222 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 ...
14
votes
4answers
781 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-...
7
votes
3answers
9k 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 ...
1
vote
0answers
370 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. ...
2
votes
0answers
120 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 ...
1
vote
1answer
218 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^...
1
vote
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, ...
1
vote
1answer
522 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 ...
2
votes
2answers
705 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 $ ...
2
votes
1answer
251 views

Numerical Optimizer Matlab Calibration LMM

I am trying to mimimize the following function in order to calibrate the Libor Market Model $$\sum_{i=1}^{n} \left(\sigma_i^{market}-\sigma_i^{Reb}\left(a,b,c,d,\beta\right)/\sqrt{T_i}\right)^2,$$ ...
3
votes
1answer
345 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 ...
0
votes
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 $\{n_1,...,n_k\}$ ...
3
votes
1answer
338 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
votes
1answer
347 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 ...
2
votes
3answers
434 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 ...
0
votes
1answer
56 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 ...
2
votes
1answer
168 views

How to calculate a hypothetical minimum-variance point?

If we have $N$ assets which are uncorrelated, but have the same mean return of $\mu$ but the variances are different where $\sigma_i^2$ is the variance of each asset $i = 1, 2,...,N$ how can you write ...
1
vote
0answers
430 views

How to hedge an ETF position with a basket of its underlying components

In practice, when one takes on a large equity ETF position, I would imagine it's not necessarily "optimal" to hedge using a basket of all the constituents even though that should be a perfect hedge. ...
2
votes
0answers
58 views

Given (past) stock values for N assets, how to find the maximum - theoretical - profit?

In the past few days I have been thinking about a question which seems trivial, yet I can't think of any efficient way to find the optimal solution... Here is the problem: imagine you have a ...
14
votes
1answer
506 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{\...
1
vote
1answer
84 views

Segmented investment to yield same monthly return in each segment

Not an investment specialist, so please excuse the very basic math. Given a lump sum, I need to distribute this lump sum over (x) segments, each lasting (y) years (years can be different for each ...