Machine learning (ML) has made a lot of progress in recent years. However, there are still skeptics, especially when it comes to its application in finance. In this post, I will feature articles that discuss the pros and cons of ML. In future editions, I’ll explore specific techniques. How

nd Strategies Subscribe to newsletter Calendar anomalies in the stock market refer to recurring patterns or anomalies that occur at specific times of the year, month, or week, which cannot be explained by traditional financial theories. These anomalies often defy the efficient market hypothesis and

A catastrophe (CAT) bond is a debt instrument designed to transfer extreme event risks from insurers to capital market investors. They’re important for financial institutions, especially insurers and reinsurers, because they offer a way to manage large, low-probability. In this post, I feature

Implied volatility is an important concept in finance and trading. In this post, I further discuss its breakdown into diffusive volatility and jump risk components. Decomposing Implied Volatility: Diffusive and Jump Risks Implied volatility is an estimation of the future volatility of a security’s

Cryptocurrencies are becoming mainstream. In this post, I feature some strategies for trading and managing risks in cryptocurrencies. Arbitrage Trading in the Cryptocurrency Market Arbitrage trading takes advantage of price differences in different markets and/or instruments. Reference [1] examined

Portfolio allocation is an important research area. In this issue, we explore not only asset allocation but also the allocation of strategies. Specifically, I discuss tactical asset and trend-following strategy allocation. Tactical Asset Allocation: From Simple to Advanced Strategies Tactical Asset

The volatility risk premium is a well-researched topic in the literature. However, less attention has been given to specific techniques for capturing it. In this post, I’ll highlight strategies for harvesting the volatility risk premium. Long-Term Strategies for Harvesting Volatility Risk Premium

In a previous newsletter, I discussed momentum strategies. In this edition, I’ll explore mean-reverting strategies. Mean reversion is a natural force observed in various areas of life, including sports performance, portfolio performance, volatility, asset prices, etc. In this issue, I specifically

The breakdown of the volatility risk premium into overnight and intraday sessions is an active and emerging area of research. It holds not only academic interest but also practical implications. ETF issuers are launching new ETFs to capitalize on the overnight risk premium, and the shift toward

Credit risk, also known as default risk, is the likelihood of loss when a borrower or counterparty fails to meet its obligations. A lot of research has been conducted on credit risk, and an emerging line of study explores the connection between the equity and credit markets. In this post, we’ll

Tail risk hedging aims to protect portfolios from extreme market downturns by using strategies such as out-of-the-money options or volatility products. While effective in mitigating large losses, the challenge lies in balancing cost and long-term returns. In this post, we’ll discuss tail risk

Momentum strategies have long been a cornerstone of investing, relying on the premise that past winners continue to outperform in the near future. This post explores the effectiveness of momentum strategies, analyzing their ability to generate abnormal returns and assessing their viability in

Dividend yield has long been a cornerstone of equity valuation. In this post, we explore how dividend yield predicts stock returns, its impact on stock volatility, and why it holds unique significance for mature, dividend-paying firms. Relationship Between Implied Volatility and Dividend Yield

Monte Carlo simulations are widely used in science, engineering, and finance. They are an effective method capable of addressing a wide range of problems. In finance, they are applied to derivative pricing, risk management, and strategy design. In this post, we discuss the use of Monte Carlo

Principal Component Analysis (PCA) is a dimensionality reduction technique used to simplify complex datasets. It transforms the original variables into a smaller set of uncorrelated variables called principal components, ranked in order of their contribution to the dataset’s total variance. In

Beta is a measure of an asset’s sensitivity to market movements, indicating how much its price is expected to change in relation to the overall market. Beta is often used in CAPM and the calculation of WACC. However, it can also be applied in trading, specifically in arbitrage. In this post,

Gold, one of the oldest and most enduring asset classes, had an exceptional run in 2024, capturing attention across financial markets. Its role in investment portfolios continues to spark interest, acting as a hedge against uncertainty. On the other end of the spectrum, cryptocurrencies represent

Financial models and strategies are usually universal and can be applied across different asset classes. However, in some cases, they must be adapted to the unique characteristics of the underlying asset. In this post, I’m going to discuss option pricing models and trading strategies in

It’s well known that there is a negative relationship between an equity’s price and its volatility. This can be explained by leverage or, alternatively, by volatility feedback effects. In this post, I’ll discuss practical applications to exploit this negative correlation between equity prices

One of my favourite ways to characterize the market regime is by using the Hurst exponent. However, its applications are not limited to identifying market regimes. There are innovative ways to utilize it. In this post, I will discuss two approaches to applying the Hurst exponent. Using the Hurst

In this post, I will continue exploring various aspects of the volatility index and the associated volatility futures. Data To conduct this study, data is essential. Below are the data sources: Spot VIX: Yahoo Finance provides data but no longer allows direct downloads. With some programming, a

Building on the first paper, Reference [2] investigates machine learning techniques for trading VIX futures. It proposed using Constant Maturity Futures (CMF) to generate trading signals for VIX futures. It applied machine learning models to create these signals. Findings The experiment results show

Pairs trading is a market-neutral strategy that involves trading two correlated stocks or assets. The idea is to identify pairs that historically move together, and then take a long position in one and a short position in the other when they diverge, with the expectation that they will eventually

The weekend (or Monday) effect in the stock market refers to the phenomenon where stock returns exhibit different patterns on Mondays compared to the rest of the week. Historically, there has been a tendency for stock prices to be lower on Mondays. Various theories attempt to explain the weekend

Would you rather choose a trading system that wins small amounts most of the time but when it loses, the loss is big? Or would you rather choose a trading system that loses small amounts most of the time but when it wins, the gain is big? In this blog post, we will examine such systems from the risk

In a previous post, we discussed how the dynamics of assets are priced in the options prices. We recently came across a newly published article [1] that explored the same topic but from a different perspective that does not involve options. The conclusion of the new article [1] is consistent with

The VIX index is an important market indicator that everyone is watching. VVIX, on the other hand, receives less attention. In this post, we are going to take a look at the relationship between the VIX and VVIX indices. While the VIX index measures the volatility risks, VVIX measures the

When trading options, we often use the VIX index as a measure of volatility to help enter and manage positions. This works most of the time. However, there exist some differences between the VIX index and at-the-money implied volatility (ATM IV). In this post, we are going to show such a difference

A lot of research has been devoted to answering the question: do options price in the volatility risks correctly? The most noteworthy phenomenon (or bias) is called the volatility risk premium, i.e. options implied volatilities tend to overestimate future realized volatilities. Much less attention

This post is a follow-up to the previous one on a simple system for hedging long exposure during a market downturn. It was inspired by H. Krishnan’s book The Second Leg Down, in which he referred to an interesting research paper [1] on the power-law behaviour of the equity indices. The paper

In a previous post, we showed that the spot volatility index, VIX, has a strong mean reverting tendency. In this follow-up installment we’re going to further investigate the mean reverting properties of the VIX. Our primary goal is to use this study in order to aid options traders in positioning

In this post, we are going to examine a trading system with the goal of using it as a hedge for long equity exposure. To this end, we test a simple, short-only momentum system. The rules are as follows, Short at the close when Close of today Cover at the close when Close of today > lowest Close

wn Day a Black Swan? On February 5, the SP500 experienced a drop of 4% in a day. We ask ourselves the question: is a one-day 4% drop a common occurrence? The table below shows the number of 4% (or more) down days since 1970. 4% down 4% down and bullish From 1970 40 5 On average, a 4% down day

In the previous post, we looked at some statistical properties of the empirical distributions of spot SPX and VIX. In this post, we are going to investigate the mean reverting and trending properties of these indices. To do so, we are going to calculate their Hurst exponents. There exist a variety

VIX related products (ETNs, futures and options) are becoming popular financial instruments, for both hedging and speculation, these days. The volatility index VIX was developed in the early 90’s. In its early days, it led the derivative markets. Today the dynamics has changed. Now there is strong

This post is the continuation of the previous one on the riskiness of OTM vs. ATM short put options and the effect of leverage on the risk measures. In this installment we’re going to perform similar studies with the only exception that from inception until maturity the short options are

Traders often debate whether short out-of-the-money (OTM) or at-the-money (ATM) puts are riskier. The argument for OTM put options being riskier is that their Speeds (or dGamma/dspot) are higher than the ATMs’ ones, thus the Gamma, which is negative, can increase (in absolute value) substantially

In the previous installment, we discussed the use of a popular asset allocation/market timing rule (10M SMA rule hereafter) to size a short option position. The strategy did not work well as it was the case in traditional asset allocation. We thought that the poor performance was due to the fact

Position sizing and portfolio allocation have not received much attention in the options trading community. In this post we are going to apply a simple position sizing rule and see how it performs within the context of volatility trading. An option position can be sized by using, for example, a

The spot VIX index finished last Friday at 11.28, a relatively low number, while the SKEW index was making a new high. The SKEW index is a good proxy for the cost of insurance and right now it appears to be expensive. A high reading of SKEW means investors are buying out of the money puts for

In previous blog posts, we explored the possibility of using various volatility indices in designing market timing systems for trading VIX-related ETFs. The system logic relies mostly on the persistent risk premia in the options market. Recall that there are 3 major types of risk premium:

A recent post on Bloomberg website entitled Rising VIX Paints Doubt on S&P 500 Rally pointed out an interesting observation: While the S&P 500 Index rose to an all-time high for a second day, the advance was accompanied by a gain in an options-derived gauge of trader stress that usually

In previous posts, we presented 2 volatility trading strategies: one strategy is based on the volatility risk premium (VRP) and the other on the volatility term structure, or roll yield (RY). In this post we present a detailed comparison of these 2 strategies and analyze their recent performance.