In finance, the performance of an asset is often quantified by alpha (the excess returns above a benchmark return) and beta (the volatility or risk of the asset relative to a benchmark). In this post, we develop time-varying, probabilistic versions of alpha and beta, and go through the process of using these new metrics to build a dynamic stocks/bonds portfolio to improve on the classic 60/40 portfolio.
In this post we will take a closer look at the expected return that is often stated for investments like stocks and other financial assets, or for certain outcomes in gambling. The point we want to convey is that the expected return is only valid for one period or a single “iteration” (say, one year, … Read more
This is the forth and final post of a short series of posts on extreme events in financial time series. In the first post, we have introduced power-law theory to describe and extrapolate the chance of extreme price movements of the S&P500 index. In the second post, we took a closer look at how statistical moments … Read more
This is the third post of a short series of posts on extreme events in financial time series. In the first post, we have introduced power-law theory to describe and extrapolate the chance of extreme price movements of the S&P500 index. In the second post, we took a closer look at how statistical moments may become … Read more
This is the second post of a short series of posts on extreme events in financial time series. In the previous post, we have introduced power-law theory to describe and extrapolate the chance of extreme price movements of the S&P500 index. In this post, we will explore how the power-law tails of a return distribution … Read more
This is the first post of a short series of posts on extreme events in financial time series. We will investigate the return distribution of financial assets, use power-law theory to describe its tails, see how estimating higher moments such as kurtosis becomes meaningless, and finally discuss a fundamental flaw in popular models such as … Read more