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6
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3answers
134 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
43 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
98 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
90 views
0
votes
1answer
41 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 ...
2
votes
0answers
50 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
29 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
67 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?
0
votes
1answer
211 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
42 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
21 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
99 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
98 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
126 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
38 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] - ...
2
votes
1answer
78 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
138 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
votes
0answers
115 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
86 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
187 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 ...
0
votes
1answer
59 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
votes
0answers
25 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
35 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
78 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
244 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
202 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
487 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
60 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
232 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
131 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
143 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
39 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
68 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
210 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
63 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
166 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
222 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
803 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
132 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
121 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
676 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
556 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 ...
3
votes
1answer
136 views

Create optimal portfolio by Treynor and Jensens Alpha

I would like to know which formula to use in order to optimize a portfolio based on highest Treynor and Jensens Alpha. I am aware that usually one optimize a portfolio by highest Sharpe ratio (the ...
2
votes
1answer
137 views

What are the assumptions of portfolio optimisation with higher moments?

I was wondering whether there are a set of assumptions for portfolio optimisation with higher moments (including kurtosis and skewness) as there are for regular mean-variance optimisation?
2
votes
1answer
100 views

Partition assets into minimally correlated portfolios

My question covers a more or less classical portfolio optimization situation with a twist: How to partition assets into minimally correlated portfolios, with and without asset overlap. I have $N$ ...
2
votes
0answers
139 views

What happened to Mountain View Analytics?

I stumbled over Thomas Cover's work on algorithmic portfolio selection; apparently, an outfit called "Mountain View Analytics" attempted to implement the suggestions from Cover's research. ...
4
votes
1answer
222 views

Portfolio optimization with Portfolio CVaR Constraint

I wanted to optimize a portfolio based on a portfolio-wide CVaR constraint (i.e. $CVaR_p \leq 0.08$). Unfortunately, I only find solution that minimizes the entire CVaR of the Portfolio. Do you mind ...
4
votes
3answers
463 views

Sampling problem in portfolio optimization

In a summary I am trying to do the following Bond Subset 1 : Get list of USD Bonds --> Filter out Bonds which have YTM > y% DUR > 10 Y etc. .. This gives us Bonds which we are interested in. So ...
5
votes
1answer
138 views

Overview of robust/regularized portfolio selection

I am looking for either a review paper or individual papers on portfolio selection using robust statistics or regularization (e.g. LASSO, Ridge, etc.) I.e. a review on methods along the lines of: M ...