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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57 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
30 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
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1answer
140 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) ...
2
votes
1answer
75 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
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3answers
110 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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15 views

Question in the proof of “Optimization of conditional value-at-risk”

I'm reading the paper "Optimization of conditional value-at-risk" by Rockafellar and Uryasev. The state two theorems within the paper which are proven in the appendix. Let me introduce some notation ...
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1answer
32 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
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1answer
47 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 ...
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65 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
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0answers
43 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 ...
7
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189 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: ...
0
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1answer
76 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 ...
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72 views

Discrete Hedging of Options

Assume that a stock $S_t$ follows simple geometric Brownian motion. Let's say we sold option whose payoff is $f(S_T)$. Now, we are only allowed to trade 2 times in the interval [0,T]. What kind of ...
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1answer
68 views

Full Kelly portfolios having same weights as tangency portfolios

I'm currently comparing empirically the differences between Markowitz and Kelly portfolios. I calculated the Kelly weights for monthly return observations over 10 years for a sample of 50 stocks from ...
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2answers
74 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 ...
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0answers
42 views

Smoothening yield curve by minimizing forward curve slope

I am using government bullet bond data and have bootstrapped a yield curve by solving the following optimization which minimizes unweighted price error: ...
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1answer
50 views

optimization with absolute constraints

Suppose I have an optimization where I need to impose ADV-like constraint (for a case where Shorting is allowed): $\max \mu'w - \lambda w'\Sigma w$ $ |w| \le V $ $ Aw = 0$ and I want to use a ...
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0answers
100 views

How would it be possible to use Dynamic Programming to search a space of investment strategies to find an optimum?

As my question states, the problem I am having is finding a sensible way to search a large space. Any help or insight that could be provided would be hugely appreciated. Currently I am trying to ...
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vote
1answer
105 views

How to scale $\alpha$, trading costs in a standard portfolio optimization problem

In the usual "portfolio optimization problem under linear constraints". Let me define the terms here. $$ \text{Find } w^*=\underset{w}{\text{argmax}} \ \ r^Tw - \lambda w^{T} \Sigma w - ...
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217 views

How to optimize return in a moving average crossover algorithm

Moving average crossover strategy is a widely used strategy in algo trading. Is there a way to optimize return in a moving average crossover stratergy. I have used this site to backtest MA crossover ...
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0answers
102 views

Fitting High Frequency Indicators

I have a high frequency time series of the bid and ask prices of a stock recorded on every tick. For each data point I also have a certain indicators that predict the future movement of the price. The ...
8
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1answer
114 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 ...
5
votes
1answer
105 views

Sharpe Maximization under Quadratic Constraints

When doing Sharpe optimization $$ \max_x \frac{\mu^T x}{\sqrt{x^T Q x}} $$ there is a common trick (section 5.2) used to put the problem in convex form. You add a variable $\kappa$ such that $x = ...
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0answers
57 views

Residual Covariance Matrix, and MVO for Residual Variance and Alpha

My overall goal is to find an efficient frontier using QP in terms of $\alpha$ and residual variance ($\omega^2$) for a portfolio $P$ given a benchmark $B$. We know the equation for residual variance ...
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0answers
11 views

Is there any theoretical work to find an optimum size for the size of horizon in finite-horizon optimization or control?

we learn a lot about finite and infinite horizon control in dynamic programming. but I was wondering if we want to minimize the cost per time(discrete time) is there any work to find the optimum size ...
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2answers
160 views

Beta Constrained Markowitz Minimum Variance Portfolio - Closed Form Solution

This question is related to recent rule changes in the Quantopian Open. I am trying to figure out a closed form solution to a beta constrained minimum variance portfolio problem but it doesn't seem ...
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3answers
676 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 ...
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2answers
89 views

When would dedicated portfolios do better than 'immunized' portfolios?

We just learned about cash-matching through dedicated portfolios (using risk free bonds) in my class that concerned mathematical programming. However, in an aside one of the notes said: It should be ...
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66 views

Implementing Minimum Leverage in an SOCP Portfolio Optimization

I'm optimizing a portfolio of n assets and my optimization variable is of the form $$x = [t,w,w_L,w_S]$$ where $$t:= \text{slack variable for turning my QP objective into SOCP constraint}$$ ...
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91 views

How to compute the Coskewness Matrix in excel?

I'm triyng to compare two portfolio based on same sample of equities returns. And i want to know how to compute the coskewness matrix without using VBA, only in excel. Even a simple example with three ...
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0answers
33 views

scale alpha forecasts to align with covariance matrix

I have a set of monthly alpha forecasts and my covariance matrix has been annualized. I would like to do a mean variance optimization with a linear tcost penalty term. How do I rescale my alpha ...
8
votes
1answer
150 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 ...
0
votes
1answer
400 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 ...
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1answer
320 views
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83 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. ...
3
votes
1answer
134 views

Markowitz Mean-Variance Implied Returns

What is the closed form solution for the following inverse Markowitz problem? Given a mean-variance optimized fully invested portfolio $X$, a risk aversion parameter $\lambda$ and a var-covar ...
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votes
0answers
57 views

Calculating the optimal portfolio for an investor with quadratic utility

The problem is from Asset Pricing and Portfolio Theory by Back and can be found here. The relevant info from section 2.5 can be found here. Given that we have the Expected value and the variance of ...
3
votes
1answer
732 views

constrained portfolio optimization by fmincon

I am working through this paper, http://www.nber.org/papers/w8922.pdf I want to implement the portfolio weight constraints see page 6-7. Here is the brief overview of my problem: Let ...
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1answer
187 views

constrained portfolio optimization in matlab

I am working through this paper, http://www.nber.org/papers/w8922.pdf I want to implement the portfolio weight constraints see page 6-7. Here is the brief overview of my problem: Let ...
3
votes
1answer
240 views

Portfolio choice problem of a CARA investor with n risky assets

Ok, I am working on a problem that consists of the following: I am looking to solve the portfolio choice optimization problem (maximizing utility with a known utility function) in the case where all ...
3
votes
1answer
231 views

Constant Relative Risk Aversion

The question: Consider a person with constant relative risk aversion p. (a) Suppose the person has wealth of 100,000 and faces a gamble in which he wins or loses x with equal probabilities. ...
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38 views

Multi-objective optimization: Where to find qualified examples for portfolio management?

I am looking for qualified examples of multi-objective optimization applied to a portfolio management situation in non-normal markets. Where can I find one or more examples of such a multi-objective ...
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1answer
111 views

Asset Liability Management Test Topic Interpretation

I will write a test based on Excel and one of the topics is "The Asset Liability related analysis: including the input assumptions generation, constraints, portfolio optimization analysis and results ...
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2answers
176 views

Portfolio Optimization to include ALL Securities?

I'm currently optimizing portfolio weights for an investment team with N stocks. We buy stocks with a conviction it will generate a return and it is up to me to determine weighting. However, with ...
3
votes
1answer
104 views

Maximizing utility subject to a wealth constraint

Let $\tilde{E}$ be the risk neutral expectation, and $X_t$ the wealth that time t and $R$ the return of a risk-free investment. Consider maximizing the function $EU(X_N)$ subject to ...
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17 views

dynamic programming with serially independent returns

Book suggests that "asset returns are assumed to be serially independent, so wealth is a single state connecting one period to the next". I understand path dependency is lost in case of serial ...
3
votes
1answer
152 views

formulating MVO with costs

I am trying to formulate this simple MVO utility function with a linear transaction cost penalty added using Quadprog in MATLAB tcost = 0.001; lambda = 4; mu = vector of expected returns (say 4x1) S ...
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0answers
77 views

Model-independent dynamic portfolio optimization techniques

For a problem where we need to optimize the portfolio based on the data, going for Markowitz MPT has the following advantage: we only have to estimate mean and covariance to find optimal weights. I'd ...
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1answer
102 views

Optimization metric that takes into account number of trades vs expectancy

In optimizing my automated trading system I find that certain combinations while increasing the expectancy: ...
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225 views

Portfolio Optimization using S&P Universes

Assuming a set portfolio optimization problem, if all optimization inputs are kept constant, what would you expect, in terms of results, if you run the same optimization using the S&P500 as ...