Historical volatility (HV) is a useful measure to gauge market uncertainty. Recall that, In finance, volatility (usually denoted by σ) is the degree of variation of a trading price series over time, usually measured by the standard deviation of logarithmic returns. Historic volatility measures a time series of past market …

In the previous installments, we presented the concept of Modern Portfolio Theory. We also provided an optimization algorithm, written in Python, for searching for the optimal portfolio. To continue, we are going to perform some numerical experiments. Specifically, we are going to use the portfolio optimization program developed in the …

In the previous installment, we presented a description of the Model Portfolio Theory and provided a concrete example in Python. We also explained the concept of an Efficient Frontier and provided a visual presentation of it. Recall that, … the efficient frontier (or portfolio frontier) is an investment portfolio which …

Convertible bonds are complex, hybrid securities. In finance, a convertible bond or convertible note or convertible debt (or a convertible debenture if it has a maturity of greater than 10 years) is a type of bond that the holder can convert into a specified number of shares of common stock …

Modern Portfolio Theory (MPT) is a theory developed by Harry Markowitz in 1952, which later earned him a Nobel Prize in Economics. The theory states that investors can create an ideal portfolio of investments that can provide them with maximum returns while also taking an optimal amount of risk. The …

In a previous post, we presented statistical tests for the Australia/Canada country ETF pair. Specifically, we calculated the return correlation and performed cointegration tests using a training set consisted of 8 years of data. The high correlation and the fact that the pair spread passed 2 cointegration tests made this …

Harry M. Markowitz is the founder of Modern Portfolio Theory (MPT) which originated from his 1952 essay on portfolio selection. He was later awarded a Nobel Prize in Economics. His work founded the concept of an efficient frontier, and it allows for the determination of portfolio mixes that provide an …

Pair trading, or statistical arbitrage, is one of the oldest forms of quantitative trading. In this post, we are going to present some relevant statistical tests for analyzing the Australia/Canada pair. We chose this pair because these countries’ economies are tied strongly to the commodity sector, therefore they share similar …

A recent podcast on Bloomberg offers some interesting perspectives on quantitative investing. Interest in quantitative investing strategies continues to grow; however, as the space gets more competitive, making money and winning gets harder and harder. Computation costs alone can be prohibitive. On the latest episode, we speak with Columbia Business …

In a previous post, we presented theory and a practical example of calculating implied volatility for a given stock option. In this post, we are going to implement a model for forecasting the implied volatility. Specifically, we are going to use the Autoregressive Integrated Moving Average (ARIMA) model to forecast …