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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345 views

MPT: Adding constraint on minimum asset weight

I'm new to finance in general, and recently read about Modern Portfolio Theory. Now I'm wondering how to add the following constraint on asset weights: Each asset weight $w_i$ should either be $w_i ...
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3answers
303 views

Determining optimal trading signals (buy/sell) from past data

Let's say we have a stock which our only actions are buy, sell and hold (with or without shorting). If we have sufficient past data of the stock, how can you determine the optimal trading action ...
4
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2answers
9k 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?
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2answers
836 views

Which objective function should I choose to minimize tracking error?

Let say I have $n$ assets and their returns over $m$ periods which are represented by a matrix $X \in \mathbb{R}^{m \times n}$, and I have some other asset with return over the same period which is ...
4
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1answer
130 views

Optimal Choice of exceeding time

Suppose you hold a share from company $Z$ whose vaue at time $t$ is $S_0+\sigma B_t$ where $B_t$ is Brownian Motion and $\sigma$ denotes some volatility. Now lets assume that company $Z$ may go ...
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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
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 ...
4
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1answer
179 views

Parameter estimation using martingale measures - include real world data?

Please note: I posted this in nuclearphynance first, but didn't get any replies. For desks which sell exotics it is common practice (as far as I know it) to calibrate the model (Stochastic ...
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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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218 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
97 views

Optimal mortgage rate strategy

When buying a mortgage, you can choose to "lock in" a rate at any point within 60 days of your closing date. Once locked in, you can't revert. This makes it a secretary problem - in the traditional ...
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459 views

Is there a standard method of scaling alpha forecasts to t-cost estimates?

Given a set of monthly alpha forecasts (i.e. standardized z-scores from a multi-factor return model) and a non-linear market impact model (or more specifically, its piecewise-linear approximation), is ...
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3answers
8k 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 $N$ ...
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4answers
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 ...
3
votes
1answer
256 views

How to apply Levenberg Marquardt to Max Likelihood Estimation

In this paper on p315: http://www.ssc.upenn.edu/~fdiebold/papers/paper55/DRAfinal.pdf They explain that they use Levenberg Marquardt (LM) (along with BHHH) to maximize the likelihood. However as I ...
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3answers
687 views

Optimizing a currency only portfolio with negative weights

I am testing various optimization methods for a currency-only portfolio. I have a vector of expected returns for the major developed currencies vs. the USD each week (based on a proprietary model). I ...
3
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3answers
755 views

Can I perform an asset allocation optimization if assets are perfectly uncorrelated?

(Here is a link to the original post) I received this interesting problem from a friend today: Assume that you are a portfolio manager with $10 million to allocate to hedge funds. The due diligence ...
3
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1answer
59 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 ...
3
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1answer
141 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
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 ...
3
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2answers
212 views

Is there any academic material regarding robust optimization with fixed transaction costs?

I'm looking to piece together a robust optimization model that handles robust optimization with fixed transaction costs and other combinatorial variables (e.g. asset count constraints). Here's what ...
3
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1answer
224 views

What is the difference between these two optimization procedures?

In this portfolio optimization utility (and others), mean return, standard deviation and correlation among assets are required inputs. http://finance.wharton.upenn.edu/~stambaugh/portopt.html At ...
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1answer
737 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 ...
3
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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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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 ...
3
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1answer
222 views

Is Optimization ignoring correlation valid?

I have a fairly pedestrian optimization problem: Max sharpe, subject to a x% vol target. I have a set of expected returns, asset vols and a correlation matrix. I am finding that when i set the ...
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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
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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 ...
3
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1answer
277 views

Which is the better risk sensitive measure?

Consider the two following optimization problem 1) $$ \min_{\theta} \ln E_{\theta}[ e^{X}]$$ 2) $$ \min_{\theta} E_{\theta}[ X]$$ with the constraint $$ Var_{\theta}[X] <c$$ Is it true that ...
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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 ...
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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 ...
3
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0answers
111 views

State Space models with Short Time Series

My problem is that I have a state space model that I estimate using the Berndt–Hall–Hall–Hausman (BHHH) algorithm. The state space model is relatively simple in that the hidden part follows a pure ...
3
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0answers
208 views

What R-packages for SOCP problems are there?

Currently, I am looking deeper into the topic of second-order cone programming. Could you suggest packages that solve SOCP-problems in R? With your answer, please provide a short description of ...
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118 views

A doubt about Evans and Jovanovic (1989) economic model for entrepreneurs with credit constraints

[I already posted this question on the math forum of stackexchange and I was advised that I should post this question here] In Evans and Jovanovic (1989) you will find a model for entrepreneurs with ...
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92 views

Optimizing stochastic functions numerically

Is there an efficient and commonly used optimization method for "more complex" investment strategies. For instance, say you have a function $f(X_1,...,X_n,c,v)$ where the $X_k$'s are your random ...
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155 views
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488 views

What is the use of the Euler equation in the Ramsey growth model?

I apologise for being brief, but I don't understand how is Euler equation used in the Ramsey growth model. I am reading a textbook "Dynamic General Equilibrium Modeling" and there is mentioned about ...
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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 ...
2
votes
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 ...
2
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1answer
76 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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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 ...
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vote
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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2answers
88 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 / ...
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2answers
427 views

Optimizing Principal Component factor weightings over time

I was given the returns of a cross-asset class portfolio of ETFs and I conducted PCA to obtain factors on dates from T-n, T-3, T-2,..., T. What I would like to do is decompose the market moves from ...
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1answer
188 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 ...
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vote
1answer
165 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. ...
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1answer
78 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 ...
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2answers
274 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, ...
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1answer
372 views

Blackbox Optimization + Bootstrapping = Parameter Selection?

Most automated trading systems have a number of embedded parameters such as the lookback periods, entry and exit thresholds, etc. This is like the moving average crossover system or any of the systems ...
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2answers
155 views

How can I estimate the parameters of an option value model of retirement?

I am modelling an option value model of retirement, see for instance Stock and Wise (1990). I am however not sure to which class of problems this model falls into and hence which optimization method I ...