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

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Finding Expression for Optimal Markowitz Weights

So there are two assets with return rates $r_1$ and $r_2$ which have identical variances and a correlation coefficient $p$. The risk free rate is $r_f$. I need to find an expression for the optimal ...
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201 views

Portfolios from Sorts

Some time ago Almgren and Chriss proposed a method for portfolio optimization based on sorting criteria such as $r_1 > r_2 >... > r_N$ instead of explicit expected returns: see portfolios ...
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391 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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133 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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37 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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37 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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40 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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103 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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47 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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44 views

Compute the average efficient frontiers with estimated parameters from generated time series

My overall objective is to analyse the impact of error in mean-variance analysis from historical data. I am given the returns and standard deviation for the five assets under consideration, as well as ...
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204 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 ...
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how to obtain optimal portfolio with different borrowing and lending rates?

I have some risky assets and risk free assets and I am trying to find out optimal portfolio with constraints like following. Suppose I wish to obtain an expected return of 12%, what portfolio will ...