The capital asset pricing model (CAPM) is a widely adopted model in asset pricing theory and portfolio construction because of its intuitive nature. One of its main conclusions is that there exists a global market portfolio that each rational investor should hold in proportion with the risk-free...

This note demonstrates how a covariance matrix estimated using log-returns of multiple assets in their respective base currencies can be converted directly into a covariance matrix in a single common currency using basic matrix multiplication. This approach eliminates the need to compute returns...

In this note we prove a simple formula to compute the Incremental Volatility, i.e. the change in the portfolio volatility due to the removal of one asset from the portfolio. The common practice adopted in the literature and in the industry is to avoid the full recalculation of the portfolio...

The aim of this paper is to shed new light on the concept of diversification showing that it is not necessarily related to the reduction of the volatility of a portfolio, as it is commonly perceived. We introduce a diversification index that exploits the decomposition of portfolio volatility...

Diversification is a core concept in Asset Management. Yet diversification can mean different things to different people and there no consensus on how it is measured nor is there a broadly accepted metric for reporting of diversification. Sometimes, there is confusion in understanding...

In this paper we propose a new risk decomposition technique. Taking an example of a portfolio of assets that can be decomposed into sub portfolios and also represented using a factor model, investment professionals have access to tools that can represent risk from three different perspectives...

In the wide panorama of investment strategies, the Liability-Driven one aims at creating an optimal portfolio by beating a chosen liability. In this paper we will extend the problem by considering as utility function, to be maximized, the joint probability that the Funding Ratio is above a...

In Liability Driven Investing (LDI) the profile of future liabilities is an explicit component of the asset allocation process. Similarly, Assets and Liabilities Management (ALM) deals with mismatches between assets and liabilities in banking books. Since extreme events have become the rule in...

In this paper, we propose a multivariate market model with returns assumed to follow a multivariate normal tempered stable distribution. This distribution, defined by a mixture of the multivariate normal distribution and the tempered stable subordinator, is consistent with two stylized facts...