# Tagged Questions

The professional management of an investment portfolio of various securities (shares, bonds and other securities) in order to meet specified investment goals. The process includes the specification of investment objectives and constraints, choice of asset mix, formulation of portfolio strategy, ...

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### 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 ...
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### Making portfolios better than others for a 16 week portfolio game? [closed]

I'm going to participate in a game of making portfolios. The objective of the game is to make the portfolio with the bigger ROI over 16 weeks. Over each week every player can see the ROI of each ...
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### Calculate correlation between two sub portfolios and the combined portfolio

I have two sub portfolios (lets call them portfolio a & portfolio b - a portfolio is just a vector of weights that sum to 1) that combine to create a total portfolio. I also have a 2 x 2 ...
280 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?
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### How to reason about leverage in terms of elasticity

Return of an investment for a given period is by definition: $$r = \frac{P}{W_0} - 1$$ where $P$ is the price of the investment at the end of the period, and $W_0$ is the initial investment. I want ...
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### 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 $N$ ...
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### Capital Allocation for Portfolio of Multi-Strategy and Multi-Instrument

I would like to know if there is a way (or theory) to manage a multi-strategy, multi-instruments portfolio that would calculate the optimal weight to allocate capital for each combination of strategy ...
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### Budget Constraint in Sharpe Ratio Optimization

I am a math student and I am trying to understand the budget constraint in Sharpe Ratio optimization for portfolio design. Recall the budget constraint requires that the sum of the portfolio weights ...
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### Value at Risk from Delta of a single asset portfolio

I am trying to figure out the following, for me unfamiliar type of question: Given is a single asset portfolio: the Delta of the portfolio is 15, the value of the asset is 10 and the daily volatility ...
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### On the interface between Quant finance and actuarial-science/insurance-math

Actuaries (at least in Europe) are frequently severily lacking in quant finance topics. At best they are familiar with B&S model. People going into quant finane or striving to become a quant on ...
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### 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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### Why does it “say” portfolio diversification not suitable during market turmoil?

Currently I am trying to get a hold of MPT, asset allocation and related applications. While reading a particular resource, it says diversification works best for "normal" financial markets and ...
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### How do I simulate stock prices for a 10 asset portfolio, over a period of 10 years in MATLAB? [closed]

If I have given vectors for return and volatility (i.e. I have two 1x10 vectors), and I assume at first that their correlation is 0 (meaning my covariance-variance matrix is just diagonal), how do I ...
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### Why does my posterior mean differs from Idzorek's results?

I have implemented two different expressions (Idzorek p.6, Walters p.51) of a posterior mean return calculation within a Black-Litterman framework. My results are the same, irrespective of the ...
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### How to score a portfolio's diversity based on security returns?

What is the best way to score a portfolio's diversity based on it's returns covariance matrix? I know that if my portfolio has two securities and their returns' correlation coefficient is -1 that is ...
336 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 ...
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### I want to optimize an equity portfolio for the four central moments can anyone help me with the problem formulation

Basically i am confused as to which formula to use for portfolio skew and kurtosis and how to use the same in the optimization problem. I would also like to know the options available regarding the ...
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### tail correlation during crisis

I am seeking a recommendation for an empirical paper on increased correlations of returns during the 2008 financial crisis, or 'tail correlation' during the crisis, if that is different, or whatever ...
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### What is the correct Stutzer index and Sharpe ratio relation, assuming a normal returns distribution?

Assuming the returns distribution is normal, then there is a relation between Stutzer index and Sharpe ratio. However, I found in the following paper 2 different equation: Paper I (page 10-11)‎ ...
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### In Mean-Variance Analysis, why not the efficient frontier being pushed to the left near the axis?

I took some classes in portfolio theory, and learnt the Markowitz Mean-Variance Analysis. If only two risky assets, the efficient frontier would be a hyperbola passing through the two points; now if ...
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### 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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### How to compute a sector's volatility within a portfolio?

Assume I have a large portfolio of equities spread across three sectors. I am attempting to compute the volatility of these sectors within the portfolio considering the cross correlations among the ...
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### Testing Valuation, Size and Momentum (proprietary factors) from 1988-2013: No evidence of driving cross-sectional returns

I am currently testing whether three proprietary factors - Valuation, Size and Momentum - explain cross-sectional returns. A sample of 3000 securities was tested using Fama-MacBeth two-pass ...
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### R: Fast and efficient way of running a multivariate regression across a (really) large panel (First pass of Fama MacBeth)

I am attempting to run a rolling multivariate regression (14 explanatory variables) across a panel of 5000 stocks: For each of the 5000 stocks, I run 284 regressions (by rolling over my sample ...
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### Portfolio software that shows 'total return' for each investment

I'm a high school technology teacher and sponsor for the Charity Student Investment Project. Currently our students track our investment portfolio via a google spreadsheet (http://...
1k views

### Risk Budgets with Target Portfolio Volatility

I'm working through the implementation of a risk budgeting approach as described in the recent Roncalli paper. The idea is that the portfolio manager sets a contribution of total portfolio volatility ...
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### Robust Bayesian portfolio optimization in matlab?

I am working through this paper. I want to implement the robust Bayesian optimization (see pages 6 onward) in Matlab using fmincon. Here is a brief overview of my problem: Let $\alpha$ be the ...
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### What do the terms in-sample and out-of-sample estimates mean in MVO?

How do the in-sample estimates and out-of-sample estimates I so often hear authors refer to in emperical analysis of MVO differ?
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### Analyzing the angle between vector of weights and vector of returns in mean-variance optimization

I am using the paper "A Sharper Angle on Optimization" by Golts and Jones (2009) as a basis for my (minor) masters thesis in mathematical finance. The paper focuses on the mean-variance analysis of ...
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### Optimizing a currency only portfolio with negative weights

I am testing various optimization methods for a currency-only portfolio. I have a vector of expected returns for the major developed currencies vs. the USD each week (based on a proprietary model). I ...
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### Determining portfolio risk return in R given historical data for individual holdings?

Currently we compute portfolio risk and return via our own C# program. Historical data is stored in a SQL database. We want to compute the risk and return parameters - given a portfolio (i.e. not ...
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### How to build an electricity portfolio for an electricity production company?

I am referring to an electricity production company. Company is located in AsiaPac. The power is generated using Natural Gas fired combined-cycle power plants. Then this electricity is distributed to ...
237 views

### Does entropy pooling apply to distributions with time-varying drift?

I have a returns process that is drawn from a normal distribution with a nonlinear time-varying drift, so I was wondering if the entropy pooling method still applies or if I need an invariant ?
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### Expected length and depth of drawdown

Does anyone know of any model to estimate the distribution of drawdown length and depth assuming a certain portfolio dynamics? The arcsine law seems to suggest that a portfolio can spend a large ...
760 views

### Why do low standard deviation stocks tend to have superior future returns?

I've recently stumbled on something that really surprised me. These papers (1, 2) find that past standard deviation of returns is inversely related to future returns. That is, portfolio of low ...
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### Using alpha to evaluate trading strategy

I have a trading strategy that generates returns $R_{t}$. I want to test the strategy by looking at the alpha: $R_t - R_{f,t} = \alpha + \beta (R_{m,t} - R_{f,t}) + e_t$ I compare my alpha against ...