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.
280
questions
2
votes
1answer
171 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
438 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
530 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:
$$L(K)=\frac{\...
1
vote
1answer
84 views
Segmented investment to yield same monthly return in each segment
Not an investment specialist, so please excuse the very basic math.
Given a lump sum, I need to distribute this lump sum over (x) segments, each lasting (y) years (years can be different for each ...
0
votes
0answers
260 views
Discrete Hedging of Options
Assume that a stock $S_t$ follows simple geometric Brownian motion. Let's say we sold option whose payoff is $f(S_T)$. Now, we are only allowed to trade 2 times in the interval [0,T]. What kind of ...
5
votes
1answer
294 views
Full Kelly portfolios having same weights as tangency portfolios
I'm currently comparing empirically the differences between Markowitz and Kelly portfolios. I calculated the Kelly weights for monthly return observations over 10 years for a sample of 50 stocks from ...
2
votes
3answers
2k views
Ledoit-Wolf Shrinkage estimator not giving positive definite covariance matrix
I used ten year daily data for 407 stocks and computed the daily and monthly covariance matrices. Since I have more variables than observations for the monthly matrix, I wasn't surprised to find the ...
1
vote
0answers
116 views
Smoothening yield curve by minimizing forward curve slope
I am using government bullet bond data and have bootstrapped a yield curve by solving the following optimization which minimizes unweighted price error:
$$\text{min}\sum_i\left(P_i-\sum_t\frac{F_{it}}...
1
vote
1answer
194 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 ...
4
votes
0answers
255 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 ...
3
votes
1answer
374 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.
$$
\text{Find } w^*=\underset{w}{\text{argmax}} \ \ r^Tw - \lambda w^{T} \Sigma w - tradingCost(|...
2
votes
3answers
659 views
What's the disadvantage of using linear programming for portfolio optimization?
I am a MFE student and we have project on the Markowitz portfolio optimization problem.
i am wondering how much impact there will be, if I use a simpler linear optimizater instead of a quadratic one.
...
4
votes
2answers
3k views
How to optimize return in a moving average crossover algorithm
Moving average crossover strategy is a widely used strategy in algo trading. Is there a way to optimize return in a moving average crossover stratergy. I have used this site to backtest MA crossover ...
3
votes
0answers
216 views
Fitting High Frequency Indicators
I have a high frequency time series of the bid and ask prices of a stock recorded on every tick. For each data point I also have a certain indicators that predict the future movement of the price. The ...
15
votes
1answer
496 views
Are there references about liquidation, transaction, market impact costs in portfolio optimization
I am looking for some references treating of what I would call
liquidation cost
market impact cost
transaction cost(*)
in the usual "portfolio optimization problem under linear constraints".
Let ...
7
votes
1answer
2k views
Sharpe Maximization under Quadratic Constraints
When doing Sharpe optimization
$$
\max_x \frac{\mu^T x}{\sqrt{x^T Q x}}
$$
there is a common trick (section 5.2) used to put the problem in convex form. You add a variable $\kappa$ such that $x = ...
3
votes
0answers
276 views
Residual Covariance Matrix, and MVO for Residual Variance and Alpha
My overall goal is to find an efficient frontier using QP in terms of $\alpha$ and residual variance ($\omega^2$) for a portfolio $P$ given a benchmark $B$.
We know the equation for residual variance ...
1
vote
0answers
23 views
Is there any theoretical work to find an optimum size for the size of horizon in finite-horizon optimization or control?
we learn a lot about finite and infinite horizon control in dynamic programming. but I was wondering if we want to minimize the cost per time(discrete time) is there any work to find the optimum size ...
6
votes
2answers
2k views
Beta Constrained Markowitz Minimum Variance Portfolio - Closed Form Solution
This question is related to recent rule changes in the Quantopian Open.
I am trying to figure out a closed form solution to a beta constrained minimum variance portfolio problem but it doesn't seem ...
10
votes
3answers
7k views
Application of Control Theory in Quantitative Finance
I have recently completed an MSc in Control Systems from a top university. It seems to me that control theory must have an application within quantitative finance. I would like to apply my degree ...
4
votes
2answers
162 views
When would dedicated portfolios do better than 'immunized' portfolios?
We just learned about cash-matching through dedicated portfolios (using risk free bonds) in my class that concerned mathematical programming. However, in an aside one of the notes said:
It should be ...
1
vote
0answers
381 views
Implementing Minimum Leverage in an SOCP Portfolio Optimization
I'm optimizing a portfolio of n assets and my optimization variable is of the form
$$x = [t,w,w_L,w_S]$$
where
$$t:= \text{slack variable for turning my QP objective into SOCP constraint}$$
$$w:=\...
12
votes
1answer
656 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 ...
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 ...
1
vote
1answer
1k views
How to implement Konno's Mean-Absolute Deviation Portfolio Optimization Model using LP methods in Excel
Konno proposed a LP method for portfolio optimization using the Mean Absolute Deviation (MAD)
7
votes
1answer
282 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.
...
4
votes
1answer
827 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 ...
5
votes
1answer
3k 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 ...
5
votes
3answers
2k views
How to apply the “Knapsack Problem” to minimise a portfolio's volatility?
Suppose I have a stock selection universe of 100 stocks.
I have estimated the covariance matrix of this 100 stocks.
I would like to create an equaly-weighted basket of 5 stocks which has the lowest ...
1
vote
1answer
621 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 ...
5
votes
1answer
724 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
612 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. ...
1
vote
0answers
87 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 ...
1
vote
1answer
192 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 ...
5
votes
2answers
404 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
138 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 $\tilde{E}\frac{...
0
votes
0answers
39 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
684 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 ...
1
vote
0answers
139 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 ...
1
vote
1answer
162 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:
...
3
votes
4answers
462 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 ...
2
votes
2answers
6k views
Calculating the efficient frontier from expected returns and SD
I'm trying to calculate the efficient frontier (and the optimal portfolio at the Sharpe ratio) given two vectors for a portfolio: (1) expected returns and (2) historical standard deviations. I would ...
1
vote
2answers
152 views
Weighting with restrictions, but no clear objective function?
I have 40 shares in an index and I want to weight them based on their market value, define the known value as $x_i$
In the traditional way, the weight of each share is calculated as:
$w_i = x_i / \...
1
vote
0answers
121 views
Transform MPT optimization problem
I am trying to teach myself about MPT and optimization.
I understand that MPT solutions can be found using three equivalent optimization problems:
Minimizing variance for given return limit
...
1
vote
0answers
331 views
What are the roles of “Game theory” and “optimisation (linear, integer, conic)” in Finance, Mathematical Finance? [closed]
Would you please give me some information about application of "Game theory" and "Optimisation" in Finance and Mathematical Finance? which is more important to know and learn?
How about "multi-...
1
vote
1answer
795 views
quadratic programming portfolio optimisation
I am using MATLAB to do an optimisation. The QP minimisation problem is set up in the standard form shown below. The optimisation is used to calculate the weights (x vector in the equation below) of a ...
2
votes
1answer
646 views
Efficient Frontier Derivation: why minimize half the portfolio variance instead of just the variance?
In Robert Merton's derivation of the efficient frontier of a portfolio, he minimizes
$\frac{1}{2}\sigma^2 $ over the investment weights in each asset, where $\sigma^2$ represents portfolio variance. ...
1
vote
1answer
120 views
optimisation problem with linear constraint
I have an optimisation problem.
I wish to maximise a function subject to a constraint. It is the constraint that is causing me problems. I am using an addin in Matlab which does the optimisation ...
1
vote
2answers
1k views
How to combine Gaussian marginals with Gaussian copula to obtain multivariate normals?
in the book "Numerical Methods and Optimization in Finance" I red the following:
"Combining the Gaussian copula with Gaussian marginal gives a fancy way of expressing multivariate normals. However, ...
