Volatility and Correlation: The Math in the Core of Financial Markets

I will start with a small disclaimer, I love mathematics. I’ve always been fascinated by the ability to take parameters, numbers, and signs, and turn them into a function, a function that can predict the future (the result) perfectly. The love of numbers, functions, and problem solving led me to a career choice of a Quantitative Analyst (or quant, in finance jargon), and later to the hedge fund business, where I implemented my quantitative strategies and knowledge. During the course of my career, I was drawn to two fields in quantitative analysis: Volatility and Correlation.

These two fields have always been a mystery to me (and many other traders and analysts), as they are in the core of financial markets, trading, and frankly, they are all around us (despite the fact that we don’t even know it).

 

 

Volatility – The Risk That Keeps the Market Going

 

What is Volatility?

Volatility is the uncertainty surrounding the future. As most of us most likely don’t have the ability to predict the future, we live in peace knowing that we have no way to foresee the future. In financial markets, however, this imposes a problem, as the essence of investment management/trading is to find buying/selling opportunities that will yield profits in the FUTURE. In fact, the entire Option Pricing Theory revolves around the modeling of Volatility and its applications. Dozens of theories tried answering a simple question: “How much would an option on asset xyz cost today?” The only way we can answer that is by GUESSING the asset volatility.

Why is volatility so important?

Volatility represents the risk in financial markets. It represents the unknown, and in financial markets, the unknown is what investors fear. Option traders refer to volatility as the “Risk Premium”, meaning, how much it would cost to protect ourselves of uncertainty (the higher the fear/nervousness in the market, the more costly the risk-premium).  You have probably heard of the VIX (S&P500 Volatility Index). This index, which captures the “Implied Volatility” of the S&P500 acts a gauge to the market fear.

As we can see in the chart above, during periods of retracements in the S&P500, the VIX rises sharply.

When investors/traders look at trading opportunities, they asses the expected return (profit), but also take into consideration the risk (volatility).

Risk Management units at banks and investment firms always review their portfolios and run scenarios (and simulations) to value the possible drawdowns, given a negative shock to the portfolio. They must also estimate the level of volatility, as the outcomes of the scenarios are highly dependent on the assumed volatility.

As you can see by now, volatility is in the core of financial market. Over the last few years, more and more hedge funds, sophisticated investors, and even private investors actually trade the volatility as if it was an actual asset.

 

 

Correlation – What’s Math Got to Do with That?

 

So we understand that volatility is the uncertainty, but why is correlation so important in financial markets?

In statistics, the correlation coefficient measures the dependence (or the co-movement) of two variables (however it doesn’t indicate which variable leads the other). For those of you who don’t remember Statistics 101 course, I will just refresh your memory:

The correlation coefficient ranges between (+1) to (-1), where +1 indicates that two variables move in lockstep, while (-1) represents two variables that move in the exact opposite direction.

The investment theories that were developed in the 20th century rely heavily on correlation assumption. Portfolio Diversification reduces the risk by reducing assets’ correlation (the more diversified the portfolio is, the less risk it has, as one asset’s loss will be offset by another one’s gain).

Equity Indices are a perfect example to the benefit of diversification (correlation reduction). A stock can have a significant volatility, yet, may not have effect on the overall performance of the index. That is due to two factors:

1. Its weight in the index: the lower the weight, the less effect it will have

2. The correlation to the rest of the stocks in the index: the higher the correlation between the different stocks, the more volatile the index will be

Looking at the chart below, we can see that the historical volatility of the Dow Jones Index is persistently below its constituencies’ historical volatility, which empathizes the benefit of dispersion

As we can see, correlation, the same as volatility is in the core of financial markets, and it is a risk, as any other risk in the market.

As investors trade the volatility, there is a growing niche in financial market of correlation trading, which is exploiting mispricing of correlation by the market participants.

 

 

Why I Don’t Like Being the Markets’ Insurance Company

 

As we already understand by now, the entire financial market revolves around the volatility and correlation. However, we need to bear in mind that these are variables, and as such, they tend to change over time, and are dependent on a wide range of factors. Our ability to predict them will be the key to our success.

In general, investors (and traders) in the financial market like to be optimistic. They like to put their trust on the “Law of Averages”, which means that they believe that on average, the market is going to stay calm, and that correlation is going to remain stable. In fact, insurance companies are based on statistic models, and their profits are derived from the ability of their models to predict Volatility, and more importantly Correlation.

When an insurance company sells an insurance policy, it is basically selling risk. It tries to predict the likelihood of an insurance claim given the client’s profile. As these are merely statistical models that may go wrong sometimes.

The best example of that is the burst of the housing bubble in the USA in 2007. The flawed assumption by the insurance companies (and Wall St.) was that the correlation between the different mortgage borrowers was low, and they assumed the rate of default, as a consequences, would not be significant. That turned out to be a big mistake, as the correlation (and the default rate) turned out to be very high. When the market is in stress, all theories are thrown out of the window.

I don’t like to be on the short side of that trade. When we sell risk, which is assumed to have low probability of occurring, in most cases we will collect premium and nothing will happen. But in the rare case that these events do happen, we can find ourselves out of the game (as discussed in our last article: A Flock of Black Swans). I like to sleep well at night. So, if anything, I always look to buy these options if they are offered for cheap.

 

Good Luck,

EZTRADER Market Analysis Team.