I first read about the Couch Potato strategy in the MoneySense magazine. I liked this simple strategy because it was easy to understand and easy to manage. The Couch Potato strategy is similar to the Permanent Portfolio strategy that I have analyzed previously. The Couch Potato strategy invests money in ... [Read more...]

First, just a quick update: I’m moving the release date of the SIT package a few months down the road, probably in November. Now back to the post. Recently I came across a series of interesting posts about the Permanent Portfolio at the GestaltU blog. Today I want to ... [Read more...]

Today I want to continue with Adaptive Asset Allocation theme and examine how the strategy results are sensitive to look-back parameters used for momentum and volatility computations. I will follow the sample steps that were outlined by David Varadi on the robustness of parameters of the Adaptive Asset Allocation algorithm ... [Read more...]

Today I want to highlight a whitepaper about Adaptive Asset Allocation by Butler, Philbrick and Gordillo and the discussion by David Varadi on the robustness of parameters of the Adaptive Asset Allocation algorithm. In this post I will follow the steps of the Adaptive Asset Allocation paper, and in the ... [Read more...]

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...]

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...]

Nico brought to my attention the 130/30: The New Long-Only (2008) by A. Lo, P. Patel paper in his comment to the Multiple Factor Model – Building CSFB Factors post. This paper presents a very detailed step by step guide to building 130/30 Index using average CSFB Factors as the alpha model and MSCI ... [Read more...]

I wrote about Rebalancing in the Asset Allocation Process Summary post. Deciding how and when to rebalance (update the portfolio to the target mix) is one of the critical steps in the Asset Allocation Process. I want to study the portfolio performance and turnover for the following Rebalancing methods: Periodic ... [Read more...]

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...]

During the final stage of asset allocation process we have to decide how to implement our desired allocation. In many cases we will allocate capital to the mutual fund managers who will invest money according to their fund’s mandate. Usually there is no perfect relationship between asset classes and ... [Read more...]

The Black-Litterman Model was created by Fisher Black and Robert Litterman in 1992 to resolve shortcomings of traditional Markovitz mean-variance asset allocation model. It addresses following two items: Lack of diversification of portfolios on the mean-variance efficient frontier. Instability of portfolios on the mean-variance efficient frontier: small changes in the input ... [Read more...]

Small changes in the input assumptions often lead to very different efficient portfolios constructed with mean-variance optimization. I will discuss Resampling and Covariance Shrinkage Estimator – two common techniques to make portfolios in the mean-variance efficient frontier more diversified and immune to small changes in the input assumptions. Resampling was introduced ... [Read more...]

What is important for an investor? The rate of return is at the top of the list. Does the expected rate of return shown on the mean-variance efficient frontier paints the full picture? If investor’s investment horizon is longer than one period, for example 5 years, than the true measure ... [Read more...]

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...]

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...]

The “Minimum Correlation Algorithm” is a term I stumbled at the CSS Analytics blog. This is an Interesting Risk Measure that in my interpretation means: minimizing Average Portfolio Correlation with each Asset Class for a given level of return. One might try to use Correlation instead of Covariance matrix in ... [Read more...]

In the last few posts I introduced Maximum Loss, Mean-Absolute Deviation, and Expected shortfall (CVaR) and Conditional Drawdown at Risk (CDaR) risk measures. These risk measures can be formulated as linear constraints and thus can be combined with each other to control multiple risk measures during construction of efficient frontier. ... [Read more...]

In the Maximum Loss and Mean-Absolute Deviation risk measures post I started the discussion about alternative risk measures we can use to construct efficient frontier. Another alternative risk measures I want to discuss are Expected shortfall (CVaR) and Conditional Drawdown at Risk (CDaR). I will use methods presented in Comparative ... [Read more...]

The Minimum Investment and Number of Assets Portfolio Cardinality Constraints are practical constraints that are not easily incorporated in the standard mean-variance optimization framework. To help us impose these real life constraints, I will introduce extra binary variables and will use mixed binary linear and quadratic programming solvers. Let’s ... [Read more...]

The 130/30 funds were getting lots of attention a few years ago. The 130/30 fund is a long/short portfolio that for each $100 dollars invested allocates $130 dollars to longs and $30 dollars to shorts. From portfolio construction perspective this simple idea is no so simple to implement. Let’s continue with our discussion ... [Read more...]