A theoretical framework for analyzing investment portfolios based on their expected return and risk.

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Models crumbling down due to negative (nominal) interest rates

Dear Stackexchange users, given that the negative interest rates on a lot of sovereign bonds with maturity under 10 years are trading in the negative (nominal) interest rate territory (recently also ...
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1answer
153 views
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554 views

Formula for the efficient portfolios (mean-variance optimisation)?

Consider the setting of mean-variance portfolio optimisation: $n$ assets with expected returns $\overline{r}_1,...,\overline{r}_n$ and standard deviations $\sigma_1,...\sigma_n$. For a certain fixed ...
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47 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. ...
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313 views

Portfolio Optimization with Monte Carlo Simulation - How to do it with Excel?

If I have three asset classes and their historical weekly returns for five years, how can I construct a minimum variance portfolio and an efficient frontier plot with Excel? To do that do I have to ...
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48 views

Difference between Sharpe Ratio and Information Ratio

I am finding it difficult to understand the difference between the sharpe ratio and the information ratio and the relationship between the two, and cannot find a decent reference that breaks it down ...
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36 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 ...
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149 views

Portfolio optimization with absolute position constraints

I'm looking to optimize a portfolio maximizing expected return for a particular risk budget, but with absolute constraints on the individual instrument positions. I've been experimenting with QP, ...
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28 views

Hypothesis Testing for Portfolio Weights

Investigating international diversification is an ongoing topic in portfolio allocation literature. Britten-Jones and Kempf-Memmel , for example, use derived properties of the distribution of ...
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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 ...
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102 views

Tangent portfolio weights without short sales?

Consider a mean-variance investor in a world with a risk-free asset. Let $R_f>0$ be the return of the risk-free asset, $\mathbb{E}(R_i)>R_f$ the expected return of the risky asset $i$ and ...
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68 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 ...
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38 views

evaluating portfolio performance without knowing the amount held on cash accounts

I would like to evaluate the performance of a portfolio mananger. I know his trades, and the initial portfolio holdings. I do not know, however the amount held on his cash account. That is, I ...
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43 views

How do I determine what is a separate objective in a multi-objective portfolio optimization?

Is there a general rule to determining when to separate objectives when developing a multi-objective portfolio optimization? For example, one might start with a standard portfolio optimization of ...
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Interpretation of the CAPM model under Stochastic Portfolio Theory framework

The CAPM under the Modern Portfolio Theory approach is given as: $$ R_i = \beta_i R_\pi $$ Where $R_\pi$ the portfolios expected excess returns Under the stochastic portfolio theory approach: $$ r_i ...
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28 views

Definition of sharpe ratio maximising and variance minimising portfolios

In this paper, http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2226985, in the derivation of the mean variance efficient portfolio using lagrangians in the appendix, on page 29, the two portfolios ...
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72 views

How to use the asset covariance matrix for risk analysis in excess returns equation

New here and I have a question that may be very basic but despite my research I cannot connect the dots. I would like to know how to connect the nxn asset covariance matrix for an efficient tangency ...
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25 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 ...
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139 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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662 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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65 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 ...
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300 views

Easier references to understand “The Asset Pricing and Portfolio Choice Theory” of Back Kerry

I'm trying to read the excellent book "The Asset Pricing and Portfolio Choice Theory" of Back Kerry, but find it too much difficult. I really need to read it but before I assume that I may need to ...