Risk Measures

Simulating Multiple Asset Paths in R

November 5, 2012 | systematicinvestor

I recently came across the Optimal Rebalancing Strategy Using Dynamic Programming for Institutional Portfolios by W. Sun, A. Fan, L. Chen, T. Schouwenaars, M. Albota paper that examines the cost of different rebablancing methods. For example, one might use calendar rebalancing: i.e. rebalance every month / quarter / year. Or one ... [Read more...]

Volatility Quantiles

June 4, 2012 | systematicinvestor

Today I want to examine the performance of stocks in the S&P 500 grouped into Quantiles based on one year historical Volatility. The idea is very simple: each week we will form Volatility Quantiles portfolios by grouping stocks in the S&P 500 into Quantiles using one year historical Volatility. Next ... [Read more...]

Gini Efficient Frontier

March 23, 2012 | systematicinvestor

David Varadi have recently wrote two posts about Gini Coefficient: I Dream of Gini, and Mean-Gini Optimization. I want to show how to use Gini risk measure to construct efficient frontier and compare it with alternative risk measures I discussed previously. I will use Gini mean difference risk measure – the ... [Read more...]

Backtesting Asset Allocation portfolios

March 18, 2012 | systematicinvestor

In the last post, Portfolio Optimization: Specify constraints with GNU MathProg language, Paolo and MC raised a question: “How would you construct an equal risk contribution portfolio?” Unfortunately, this problem cannot be expressed as a Linear or Quadratic Programming problem. The outline for this post: I will show how Equal ... [Read more...]

Multiple Factor Model – Building Risk Model

February 20, 2012 | systematicinvestor

This is the fourth post in the series about Multiple Factor Models. I will build on the code presented in the prior post, Multiple Factor Model – Building CSFB Factors, and I will show how to build a multiple factor risk model. For an example of the multiple factor risk models, ... [Read more...]

Backtesting Minimum Variance portfolios

December 12, 2011 | systematicinvestor

I want to show how to combine various risk measures I discussed while writing the series of posts about Asset Allocation with backtesting library in the Systematic Investor Toolbox. I will use Minimum Variance portfolio as an example for this post. I recommend reading a good discussion about Minimum Variance ... [Read more...]

Maximizing Omega Ratio

November 3, 2011 | systematicinvestor

The Omega Ratio was introduced by Keating and Shadwick in 2002. It measures the ratio of average portfolio wins over average portfolio losses for a given target return L. Let x.i, i= 1,…,n be weights of instruments in the portfolio. We suppose that j= 1,…,T scenarios of returns with equal ... [Read more...]

Minimizing Downside Risk

November 1, 2011 | systematicinvestor

In the Maximum Loss and Mean-Absolute Deviation risk measures, and Expected shortfall (CVaR) and Conditional Drawdown at Risk (CDaR) posts I started the discussion about alternative risk measures we can use to construct efficient frontier. Another alternative risk measure I want to discuss is Downside Risk. In the traditional mean-variance ... [Read more...]

Maximum Loss and Mean-Absolute Deviation risk measures

October 14, 2011 | systematicinvestor

During construction of typical efficient frontier, risk is usually measured by the standard deviation of the portfolio’s return. Maximum Loss and Mean-Absolute Deviation are alternative measures of risk that I will use to construct efficient frontier. I will use methods presented in Comparative Analysis of Linear Portfolio Rebalancing Strategies: ... [Read more...]

Introduction to Asset Allocation

October 12, 2011 | systematicinvestor

This is the first post in the series about Asset Allocation, Risk Measures, and Portfolio Construction. I will use simple and naive historical input assumptions for illustration purposes across all posts. In these series I plan to discuss: Maximum Loss, MAD, CVaR, CDaR, Omega Risk Measures 130:30 Long/Short portfolios and ... [Read more...]

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