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2
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0answers
20 views

Matlab Portfolio Optimization with bid ask spread

I'm trying to find the optimal portfolio of options and stock which minimizes the standard deviation of the portfolio returns but also taking into consideration the bid and ask prices of the assets. ...
6
votes
0answers
36 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 ...
4
votes
1answer
58 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
39 views

Reference Request: Horse Race for Portfolio Allocation

Probably the most popular horse race study for portfolio strategies is Optimal versus Naive Diversification: How Inefficient Is the 1/N Portfolio Strategy?, with DeMiguel, L. Garlappi and R. ...
2
votes
0answers
29 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 ...
2
votes
2answers
66 views

When to adjust portfolio weights?

In portfolio allocation literature there is lot of effort made in obtaining 'better' portfolio weights, for example via improving parameter estimates, introducing Bayesian approaches, incorporating ...
2
votes
1answer
45 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 ...
7
votes
3answers
224 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 ...
0
votes
1answer
36 views

Portfolio of Assets

The following represents a model for an economy. At time $t=0$, four assets have the value $X_1= £5$, $X_2=£5$, $X_3=£10$ and $X_4=£4$. Three possible states of the world exist ($\alpha_1$, ...
1
vote
0answers
46 views

Investing in all assets with positive expected return and allowing for positive correlation

How does the answer to this question Risk minimization by investing in all assets with positive expected return change if assets can be positively correlated (but not perfectly) and short sales are ...
1
vote
3answers
120 views

What are pros and cons of mean absolute deviation portfolio optimization?

In this question a paper about mean absolute deviation portfolio optimization is mentioned and in the answer a spreadsheet with an implementation is attached. What is the use of this procedure? Does ...
0
votes
1answer
110 views
1
vote
1answer
44 views

portfolio optimization with uncertain returns

What is the usual method of dealing with many uncertain mean returns in portfolio optimization? For example say you have a 3 asset portfolio with assets A, B and C. All the correlations and variances ...
3
votes
0answers
66 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. ...
0
votes
0answers
37 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 ...
0
votes
1answer
69 views

Computing the minimum variance portfolio

Given two risky assets and their corresponding covariance matrix, how do I compute the global minimum variance portfolio, its standard deviation and its expected return?
2
votes
1answer
286 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 ...
1
vote
1answer
49 views

The importance of good optimizers in Portfolio Optimization

I work as a Quant for an Asset Management and Insurance company and have recently enrolled for Masters degree in Computer Science. I am thinking about investigating how important having a "good" ...
0
votes
0answers
24 views

What is the difference between generating portfolios on the efficient frontiers and generating different efficient frontiers

This question is bothering me for a while. We suppose a very simple and basic set up. Given are a certain amount of assets from which we want to build an portfolio in an "optimal sense". MPT gives us ...
1
vote
1answer
119 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 ...
2
votes
1answer
103 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 ...
2
votes
1answer
131 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
1answer
65 views

On a source for a mean-variance portfolio optimization result

In the context of a mean_variance framework consider an optimizing investor who chooses at time $T$ portfolio weights $w$ so as to maximize the quadratic objective function: $$U(w) = E[R_p] - ...
4
votes
3answers
131 views

On learning the bayesian approach to portfolio optimization

I am required by my course to write a small paper on the Bayesian approach to portfolio optimization, I am following Applied statistical decision theory [by] Raiffa, Howard. Which can be consulted ...
0
votes
3answers
155 views

Portfolio Optimization - Zero beta portfolio

I am trying to solve a optimization portfolio in R in which I do the following constraints: Set weight sum to within a boundary Set return to a certain value Set portfolio beta to 0 The purpose ...
0
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0answers
126 views

Black-Litterman with simple portfolio

In an attempt to learn Black-Litterman I have come across this "simple" example. Suppose that you analyze market data using CAPM $$r_i-r_f=\beta_i(r_m-r_f)+\epsilon_i$$ Suppose there are 2 assets in ...
-1
votes
1answer
102 views

Equall Risk Contribution and The Most Diversified Portfolio [closed]

I am a master degree student on applied economics at Brazil and my thesis will be about smart beta strategies. I pretend to apply Equal Weigth, Mininum Variance, Most Diversified Portfolio and Equal ...
1
vote
1answer
210 views

short-sale constraint with nonpositive-definite matrix in portfolio optimization

I need help about portfolio optimization in R. I have inverted matrix and I want to use it as an input in portfolio optimization. It was non-positive definite before I have handled it. In portfolio ...
1
vote
1answer
67 views

Critical Appraisal of Approaches countering Parameter Uncertainty in Portfolio Optimization

It is very hard to come up with legit and solid advantages and drawbacks of the various approaches wich are trying to counteract parameter uncertainty in portfolio optimization procedures. In my ...
2
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0answers
30 views

Sharpe Ratio for loans

I am trying to calculate the sharpe ratio for a set of loans. These loans have already matured and I know if they were good or not: grades are the different grades of the loans. interest rate is the ...
0
votes
0answers
36 views

volatility grouping

I was working on risk levels of a combined portolfio (includes options,futures as well as stock). While using greeks we can asses some value of a portolio, but when one needs to assess some kind of ...
1
vote
1answer
81 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: ...
4
votes
2answers
260 views

Factor Model - Minimum Variance Portfolio [Complete Proof]

Can someone check my proof? I think there is something not quite right. I have found limited resources online for this as well so I think it might benefit others to get this on the internet. Assume ...
2
votes
4answers
207 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 ...
0
votes
0answers
566 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 ...
0
votes
0answers
64 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 ...
2
votes
2answers
261 views

Portfolio Turnover Constraint

I have a few bonds and OAS and Duration for each. I had a Linear programming type of problem where I had to maximize OAS and keep duration <= constraint. There are few other constraints. I could ...
1
vote
1answer
137 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 ...
3
votes
1answer
146 views

Different ways of portfolio optimization

There are different ways to optimize portfolios: $$ \max R^Tw\tag{1}$$ or $$ \min w^T \Sigma w\tag{2}$$ and finally using a risk tolerance $\lambda$: $$ \min{(w^T\Sigma w-\lambda R^T ...
1
vote
1answer
41 views

MPT and the connection to asset prices / initial capital

I have some question about MPT. Suppose we want to build a portfolio given $N$ assets: $A_1,\dots,A_N$. At time $t$ we build the portfolio using MPT, which yields some weight vector ...
0
votes
0answers
74 views

Fixed volatility portfolio with max returns creates skewed results

I am trying to create a portfolio of only four components using the mean-variance optimization (MVO). I am setting up my problem such that I want to maximize the expected returns with a fixed vol ...
3
votes
1answer
221 views

Portfolio Optimization - n risky assets

I'm currently implementing a CAPM model in Excel: A portfolio of n risky assets when n=6 (in this case) A riskless borrowing rate of 8% and riskless lending rate of 3% I'm given the expected return ...
0
votes
0answers
66 views

multi factor equity model exposures not as expected

I'm researching an equity multi factor model. It contains three factors, say A, B & C. The factors are weighted as such, ...
4
votes
1answer
182 views

factor models and using cross section regression

I have been doing some reading on factor models. In the literature it mentions that when creating a portfolio that maximises particular attributes it may lead to unwanted bias to other factors. I ...
3
votes
1answer
227 views

Why maximize expected growth rate?

It seems to me that the optimality of the Kelly Criterion relies on the assumption that it is in an investor's best interest to maximize his portfolio's expected growth rate. Why would he care what ...
2
votes
2answers
887 views

Bond Portfolio Immunization - Duration Matching

**Question is at the bottom** Suppose you have a portfolio of bonds A, B, and C with the following characteristics: (the "Frequency" column is the # of coupon pmts per year and also the # of ...
2
votes
2answers
142 views

Finding a basket of stocks that tracks an index

Given an index, let's say S&P500, I am trying to find a list of maximum n underlyings, which altogether track the index quite well. I am thinking of running a portfolio optimization algorithm, ...
1
vote
1answer
130 views

reference question about portfolio optimization

I know the "classical" modern portfolio theory. However I have quite a lot of different sources. It seems that there is not a book which cover this topic in a rigorous way: theory application ...
8
votes
4answers
707 views

Why shrink the covariance matrix?

I'm trying to understand why it's useful to shrink the covariance matrix for portfolio construction or in fact general. Think I missing something. I know if you have 5,000 stocks it's a lot of ...
0
votes
1answer
601 views

How do I do a mean variance optimization with constraints?

I am using python and the cvxopt library to calculate an efficient frontier, per the docs: http://cvxopt.org/examples/book/portfolio.html However, I cannot figure out how to add a constraint so that ...