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20 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
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1answer
55 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
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1answer
45 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
39 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" ...
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0answers
11 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
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1answer
51 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
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0answers
65 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
107 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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0answers
34 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
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1answer
56 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 ...
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3answers
85 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
95 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 ...
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1answer
54 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
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1answer
113 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
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1answer
39 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 ...
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0answers
23 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 ...
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0answers
34 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
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1answer
67 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
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2answers
182 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
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4answers
197 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 ...
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0answers
209 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 ...
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0answers
56 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
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2answers
167 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
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1answer
115 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
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1answer
137 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 ...
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1answer
36 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 ...
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0answers
59 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
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1answer
158 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
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0answers
57 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, ...
3
votes
1answer
130 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
169 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
1answer
517 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
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2answers
108 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
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1answer
104 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
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4answers
610 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
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1answer
414 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
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1answer
117 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
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1answer
109 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
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1answer
94 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
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0answers
129 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
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1answer
196 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
421 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
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1answer
133 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 ...
3
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2answers
657 views

Portfolio Optimization : Shrinkage of Covariance Matrix when data is available

It seems that shrinking the covariance matrix is especially useful if the number of individual stocks is greater than the number of data points. However is there any special gain if you're not ...
2
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0answers
125 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 ...
6
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2answers
278 views

how to choose top n assets?

I have m assets, and have estimated their future returns and covariance matrix. I would like to invest in an evenly weighted n product basket from this universe, where 0<n<m. How do i find the ...
4
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0answers
240 views

Optimization: Factor model versus asset-by-asset model

In portfolio management one often has to solve problems of the quadratic form $$ w^T \Sigma w + w^T c \rightarrow Min $$ with portfolio weights $w \in \mathbb{R}^N$ a constant $c \in \mathbb{R}^N$ and ...
5
votes
1answer
333 views

Min VaR and Min TE as second order cone program

The quadratic optimization (min variance) $$ w^{T} \Sigma w \rightarrow \text{min}, $$ where $w$ is the vector of portfolio weights and $\Sigma$ is the covariance matrix of asset returns, is a well ...