The fact that mean-variance optimizers are highly sensitive to changes in expected returns […] is well known in investment practice1, with a couple of practi...
Introduction It is common knowledge that returns to hedge funds and other alternative investments [like private equity or real estate] are often highly seri...
The equal risk contribution (ERC) portfolio, introduced in Maillard et al.1, is a portfolio aiming to equalize the risk contributions from [its] different co...
In the previous post, I introduced the index tracking problem1, which consists in finding a portfolio that tracks as closely as possible2 a given financial ...
In a previous post, I described a parametric approach to computing Value-at-Risk (VaR) - called modified VaR12 - that adjusts Gaussian VaR for asymmetry and...
An index tracking portfolio1 is a portfolio designed to track as closely2 as possible a financial market index when its exact replication3 is either impracti...
In a multi-asset portfolio, it is usual that some assets have shorter return histories than others1. Problem is, the presence of assets whose return histori...
The turbulence index, introduced in the previous blog post, is a measure of statistical unusualness of asset returns popularized by Kritzman and Li1. It pro...
Continuing the series of blog posts on diversification indicators, I describe in this post a correlation-based measure of portfolio diversification called th...
In a previous post, I introduced near efficient portfolios, which are portfolios equivalent to mean-variance efficient portfolios in terms of risk-return bu...
One well-known stylized fact of the Markowitz’s mean-variance framework is that, irrespective of the quality of the estimates of asset returns and (co)varian...
The Ulcer Performance Index1 (UPI) is a portfolio reward-risk measure introduced by G. Martin2 similar in spirit to the Sharpe Ratio, but using the Ulcer In...
In a previous post, I introduced the Hierarchical Risk Parity portfolio optimization algorithm1. In this post, I will present one of its variations, called ...
In this short post, I will introduce the Hierarchical Risk Parity portfolio optimization algorithm, initially described by Marcos Lopez de Prado1, and recen...
In 2018, guys at ReSolve Asset Management published the paper Portfolio Optimization: A General Framework for Portfolio Choice in which they describe a s...
The previous post of this series on mathematical problems related to correlation matrices introduced the nearest correlation matrix problem1, which consists...
Clustering consists in trying to identify groups of “similar behavior”1 - called clusters - from a dataset, according to some chosen characteristics. An exa...
In the previous post of this series on covariance matrix forecasting, I reviewed both the simple and the exponentially weighted moving average covariance mat...
In the initial post of the series on volatility forecasting, I described the simple and the exponentially weighted moving average forecasting models, that a...
Bootstrapping is a statistical method which consists in sampling with replacement from an original data set to compute the distribution of a desired statist...
In the previous posts of this series, I detailed a methodology to perform stress tests on a correlation matrix by linearly shrinking a baseline correlation m...
The Gerber statistic is a measure of co-movement similar in spirit to the Kendall’s Tau coefficient that has been introduced in Gerber et al.1 to estimate c...
In this post, I will describe a measure of the homogeneity of a universe of assets, called the informativeness, introduced by Brockmeier et al.1 in their pap...
The estimation of empirical correlation matrices in finance is known to be affected by noise, in the form of measurement error, due in part to the short leng...
In this short post, I will provide an overview of the TIC algorithm1 introduced by Marcos Lopez de Prado in his paper Estimation of Theory-Implied Correlatio...
Many different measures of portfolio diversification have been developed in the financial literature, from asset weights-based diversification measures like ...
I previously described on this blog an intuitive way of performing stress tests on a correlation matrix, which consists in shrinking a baseline correlation ...
Quantifying how diversified is a universe of assets is an open problem in quantitative finance, partly because there is no definite formula for diversificati...
Financial research has consistently shown that correlations between assets tend to increase during crises and tend to decrease during recoveries1. The recen...
Estimating how individual assets are moving together is an important part of many financial applications1 and the most commonly used measure for this is the ...
In the previous post of this series on measuring financial risk, I described the absorption ratio, a measure of financial market fragility based on principa...
Continuing this series on covariance matrix forecasting (c.f. here and there for the previous posts), I will now describe a relatively recent1 data-driven, ...
In the previous post of this series on covariance matrix forecasting, I reviewed both the simple and the exponentially weighted moving average covariance mat...
In the initial post of the series on volatility forecasting, I described the simple and the exponentially weighted moving average forecasting models, that a...
Introduction It is common knowledge that returns to hedge funds and other alternative investments [like private equity or real estate] are often highly seri...
Bootstrapping is a statistical method which consists in sampling with replacement from an original data set to compute the distribution of a desired statist...
The Gerber statistic is a measure of co-movement similar in spirit to the Kendall’s Tau coefficient that has been introduced in Gerber et al.1 to estimate c...
The turbulence index, introduced in the previous blog post, is a measure of statistical unusualness of asset returns popularized by Kritzman and Li1. It pro...
Continuing the series of blog posts on diversification indicators, I describe in this post a correlation-based measure of portfolio diversification called th...
Many different measures of portfolio diversification have been developed in the financial literature, from asset weights-based diversification measures like ...
In the previous post, I reviewed the turbulence index, an indicator of financial market stress periods based on the Mahalanobis distance, introduced by Chow...
One of the challenges in portfolio management is the timely detection of financial market stress periods, typically characterized by an increase in volatilit...
Quantifying how diversified is a universe of assets is an open problem in quantitative finance, partly because there is no definite formula for diversificati...
In the previous post of this series on measuring financial risk, I described the absorption ratio, a measure of financial market fragility based on principa...
The turbulence index, introduced in the previous blog post, is a measure of statistical unusualness of asset returns popularized by Kritzman and Li1. It pro...
In this post, I will describe a measure of the homogeneity of a universe of assets, called the informativeness, introduced by Brockmeier et al.1 in their pap...
In the previous post, I reviewed the turbulence index, an indicator of financial market stress periods based on the Mahalanobis distance, introduced by Chow...
One of the challenges in portfolio management is the timely detection of financial market stress periods, typically characterized by an increase in volatilit...
Quantifying how diversified is a universe of assets is an open problem in quantitative finance, partly because there is no definite formula for diversificati...
In this series on volatility forecasting, I previously detailed the Heterogeneous AutoRegressive (HAR) volatility forecasting model that has become the workh...
In the initial post of the series on volatility forecasting, I described the simple and the exponentially weighted moving average forecasting models, that a...
Among the different members of the family of volatility forecasting models by weighted moving average1 like the simple and the exponentially weighted moving...
In the previous post of this series on volatility forecasting, I described the simple and the exponentially weighted moving average volatility forecasting m...
One of the simplest and most pragmatic approach to volatility forecasting is to model the volatility of an asset as a weighted moving average of its past sq...
Volatility estimation and forecasting plays a crucial role in many areas of finance. For example, standard risk-based portfolio allocation methods (minimum ...
The fact that mean-variance optimizers are highly sensitive to changes in expected returns […] is well known in investment practice1, with a couple of practi...
Introduction It is common knowledge that returns to hedge funds and other alternative investments [like private equity or real estate] are often highly seri...
An index tracking portfolio1 is a portfolio designed to track as closely2 as possible a financial market index when its exact replication3 is either impracti...
In a previous post, I introduced near efficient portfolios, which are portfolios equivalent to mean-variance efficient portfolios in terms of risk-return bu...
One well-known stylized fact of the Markowitz’s mean-variance framework is that, irrespective of the quality of the estimates of asset returns and (co)varian...
The most common approach to measuring portfolio (risk) factor exposures is linear regression analysis, which describes the relationship between a dependent ...
The J.P. Morgan Efficiente 5 Index is a tactical asset allocation strategy designed by J.P. Morgan based on a broad universe of 13 ETFs. This post will illu...
Crypto-assets (Bitcoin, Ethereum…) have recently been attracting the attention of more and more investors, with for example JPMorgan Chase & Co. suggesti...
In this post, I will show you how to integrate the Portfolio Optimizer Web API in Google Sheets. As a working example, I will display the mean-variance mini...
In the previous post of this series on measuring financial risk, I described the absorption ratio, a measure of financial market fragility based on principa...
Many different measures of portfolio diversification have been developed in the financial literature, from asset weights-based diversification measures like ...
In the previous post, I reviewed the turbulence index, an indicator of financial market stress periods based on the Mahalanobis distance, introduced by Chow...
Quantifying how diversified is a universe of assets is an open problem in quantitative finance, partly because there is no definite formula for diversificati...
In this short post, I will provide an overview of the TIC algorithm1 introduced by Marcos Lopez de Prado in his paper Estimation of Theory-Implied Correlatio...
In a previous post, I introduced the Hierarchical Risk Parity portfolio optimization algorithm1. In this post, I will present one of its variations, called ...
In this short post, I will introduce the Hierarchical Risk Parity portfolio optimization algorithm, initially described by Marcos Lopez de Prado1, and recen...
In a previous post, I described a parametric approach to computing Value-at-Risk (VaR) - called modified VaR12 - that adjusts Gaussian VaR for asymmetry and...
The turbulence index, introduced in the previous blog post, is a measure of statistical unusualness of asset returns popularized by Kritzman and Li1. It pro...
One of the challenges in portfolio management is the timely detection of financial market stress periods, typically characterized by an increase in volatilit...
In a previous article, I described several classical bootstrap techniques — i.i.d. bootstrap, circular block bootstrap, and stationary block bootstrap — and ...
Bootstrapping is a statistical method which consists in sampling with replacement from an original data set to compute the distribution of a desired statist...
In statistics, a bootstrap method, also called bootstrapping, is a compute-intensive procedure that allows to estimate the distribution of a statistic throu...
In a previous article, I described several classical bootstrap techniques — i.i.d. bootstrap, circular block bootstrap, and stationary block bootstrap — and ...
Bootstrapping is a statistical method which consists in sampling with replacement from an original data set to compute the distribution of a desired statist...
In statistics, a bootstrap method, also called bootstrapping, is a compute-intensive procedure that allows to estimate the distribution of a statistic throu...
As noted in Surz1, the question “Is [a mutual fund’s]2 performance good?” can only be answered relative to something1, typically by comparing that fund to a ...
In the research report Random rotations and multivariate normal simulation1, Robert Wedderburn introduced an algorithm to simulate i.i.d. samples from a mu...
The turbulence index, introduced in the previous blog post, is a measure of statistical unusualness of asset returns popularized by Kritzman and Li1. It pro...
Value-at-Risk (VaR) is one of the most commonly used risk measures in the financial industry1 in part thanks to its simplicity - because VaR reduces the mark...
In a previous post, I described a parametric approach to computing Value-at-Risk (VaR) - called modified VaR12 - that adjusts Gaussian VaR for asymmetry and...
Modified Value-at-Risk (mVaR) is a parametric approach to computing Value-at-Risk introduced by Zangari1 that adjusts Gaussian Value-at-Risk for asymmetry a...
As noted in Surz1, the question “Is [a mutual fund’s]2 performance good?” can only be answered relative to something1, typically by comparing that fund to a ...
In the previous post, I introduced the index tracking problem1, which consists in finding a portfolio that tracks as closely as possible2 a given financial ...
An index tracking portfolio1 is a portfolio designed to track as closely2 as possible a financial market index when its exact replication3 is either impracti...
As noted in Surz1, the question “Is [a mutual fund’s]2 performance good?” can only be answered relative to something1, typically by comparing that fund to a ...
The J.P. Morgan Efficiente 5 Index is a tactical asset allocation strategy designed by J.P. Morgan based on a broad universe of 13 ETFs. This post will illu...
In the previous post of this series on measuring financial risk, I described the absorption ratio, a measure of financial market fragility based on principa...
In the previous post, I reviewed the turbulence index, an indicator of financial market stress periods based on the Mahalanobis distance, introduced by Chow...
When backtesting an investment strategy, that is, when simulating an investment strategy using historical prices to test how this strategy would have behaved...
I am sometimes asked if I recommend any stock market data (web) API for a personal use, especially because I mention Alpha Vantage and Tiingo in a couple of ...
In the first post of this series about the Sharpe ratio considered as a statistical estimator, I introduced a probabilistic framework to answer the question...
The Sharpe ratio1 is one of the most commonly used measure of financial portfolio performance, but because it is deeply rooted in mean-variance theory, its ...
In a multi-asset portfolio, it is usual that some assets have shorter return histories than others1. Problem is, the presence of assets whose return histori...
Continuing the series of blog posts on diversification indicators, I describe in this post a correlation-based measure of portfolio diversification called th...
In a previous post, I described a parametric approach to computing Value-at-Risk (VaR) - called modified VaR12 - that adjusts Gaussian VaR for asymmetry and...
The turbulence index, introduced in the previous blog post, is a measure of statistical unusualness of asset returns popularized by Kritzman and Li1. It pro...
In the previous post, I introduced the index tracking problem1, which consists in finding a portfolio that tracks as closely as possible2 a given financial ...
An index tracking portfolio1 is a portfolio designed to track as closely2 as possible a financial market index when its exact replication3 is either impracti...
Clustering consists in trying to identify groups of “similar behavior”1 - called clusters - from a dataset, according to some chosen characteristics. An exa...
The equal risk contribution (ERC) portfolio, introduced in Maillard et al.1, is a portfolio aiming to equalize the risk contributions from [its] different co...
In this post, I will show how to integrate the Portfolio Optimizer Web API in a web page. As a working example, I will display the mean-variance minimum var...
As an investor, have you ever wondered how to convert an optimal portfolio1, possibly made of real-valued weights with dozens of decimals (e.g., 12.3456789%)...
In this post, I will show you how to integrate the Portfolio Optimizer Web API in Excel. As a working example, I will display the assets weights $(w_1, w_2)...
Crypto-assets (Bitcoin, Ethereum…) have recently been attracting the attention of more and more investors, with for example JPMorgan Chase & Co. suggesti...
The most common approach to measuring portfolio (risk) factor exposures is linear regression analysis, which describes the relationship between a dependent ...
I am sometimes asked if I recommend any stock market data (web) API for a personal use, especially because I mention Alpha Vantage and Tiingo in a couple of ...
Systematic trading strategies have the unfortunate habit of exhibiting worse performances in real-life than in backtests, partially due to backtest overfitti...
Systematic trading strategies have the unfortunate habit of exhibiting worse performances in real-life than in backtests, partially due to backtest overfitti...
In this post, I will describe a measure of the homogeneity of a universe of assets, called the informativeness, introduced by Brockmeier et al.1 in their pap...
Continuing the series of blog posts on diversification indicators, I describe in this post a correlation-based measure of portfolio diversification called th...
Continuing the series of blog posts on diversification indicators, I describe in this post a correlation-based measure of portfolio diversification called th...
With more than $1.2 trillion under management in the U.S. as of mid-July 20221, investors are more and more using bond ETFs as building blocks in their asset...
With more than $1.2 trillion under management in the U.S. as of mid-July 20221, investors are more and more using bond ETFs as building blocks in their asset...
Modified Value-at-Risk (mVaR) is a parametric approach to computing Value-at-Risk introduced by Zangari1 that adjusts Gaussian Value-at-Risk for asymmetry a...
Modified Value-at-Risk (mVaR) is a parametric approach to computing Value-at-Risk introduced by Zangari1 that adjusts Gaussian Value-at-Risk for asymmetry a...
Modified Value-at-Risk (mVaR) is a parametric approach to computing Value-at-Risk introduced by Zangari1 that adjusts Gaussian Value-at-Risk for asymmetry a...
The Gerber statistic is a measure of co-movement similar in spirit to the Kendall’s Tau coefficient that has been introduced in Gerber et al.1 to estimate c...
In the research report Random rotations and multivariate normal simulation1, Robert Wedderburn introduced an algorithm to simulate i.i.d. samples from a mu...
In the research report Random rotations and multivariate normal simulation1, Robert Wedderburn introduced an algorithm to simulate i.i.d. samples from a mu...
In a multi-asset portfolio, it is usual that some assets have shorter return histories than others1. Problem is, the presence of assets whose return histori...
As noted in Surz1, the question “Is [a mutual fund’s]2 performance good?” can only be answered relative to something1, typically by comparing that fund to a ...
As noted in Surz1, the question “Is [a mutual fund’s]2 performance good?” can only be answered relative to something1, typically by comparing that fund to a ...
The equal risk contribution (ERC) portfolio, introduced in Maillard et al.1, is a portfolio aiming to equalize the risk contributions from [its] different co...
Bootstrapping is a statistical method which consists in sampling with replacement from an original data set to compute the distribution of a desired statist...
Capital market assumptions1 (CMAs) are forecasts of future risk/return characteristics for broad asset classes over the next 5 to 20 years produced by leadi...
Whether we manage our own investment assets or choose to hire others to manage the assets on our behalf we are keen to know how well our […] portfolio of ass...
Standard portfolio allocation algorithms like Markowitz mean-variance optimization or Choueffati diversification ratio optimization usually take in input as...
Standard portfolio allocation algorithms like Markowitz mean-variance optimization or Choueffati diversification ratio optimization usually take in input as...
Value-at-Risk (VaR) is one of the most commonly used risk measures in the financial industry1 in part thanks to its simplicity - because VaR reduces the mark...
Value-at-Risk (VaR) is one of the most commonly used risk measures in the financial industry1 in part thanks to its simplicity - because VaR reduces the mark...
In the previous post of this series on measuring financial risk, I described the absorption ratio, a measure of financial market fragility based on principa...
The fact that mean-variance optimizers are highly sensitive to changes in expected returns […] is well known in investment practice1, with a couple of practi...
The fact that mean-variance optimizers are highly sensitive to changes in expected returns […] is well known in investment practice1, with a couple of practi...