# What is Correlation?

Correlation is a useful financial measure that describes how the prices of different assets move with respect to each other.

## 🤔 Understanding correlation

Correlation is the degree to which the prices of different assets move together. If the prices move in a similar proportion and in the same direction, they have a high correlation. If they move in opposite directions, they have a high negative correlation. If the prices of different assets move in a way generally unrelated to each other, they have a low correlation. Correlation is usually measured across various asset classes like stocks, bonds, currencies, and commodities. It can also be measured with regard to securities of the same asset class, such as between two separate stocks. Correlation is typically calculated for a specific time period. Understanding the correlation of different assets is important in managing the level of risk in a portfolio — If the assets are all highly correlated with each other, the risk is greater.

Let's look at an example with two fictional companies. One is called Lead Corp, while the other is called Apex Tech. Over the last five days, Lead Corp's fictional stock has closed at: 1. $200 2. $195 ($5 drop) 3. $197 ($2 rise) 4. $202 ($5 rise) 5. $204 ($2 rise)

Whereas, Apex Tech's stock has closed at: 1. $100 2. $110 ($10 rise) 3. $115 ($5 rise) 4. $112 ($3 drop) 5. $110 ($2 drop)

As you can see, the stock prices of the two company’s don’t appear to be moving in tandem –- This means that two stocks had a low correlation — or even a negative correlation — over those five days. Only performing some mathematical calculations could confirm which it is.

## Takeaway

Correlation is like fish moving about in an ocean...

In an ocean, you will usually find two kinds of fish. One type moves in a school, with all fish moving in unison with coordinated movements (high correlation). The other type of fish moves independently and in different directions (low correlation). Similarly, the prices of some assets move in tandem while the prices of others move independently.

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## What is correlation?

In finance correlation is the relationship between the prices of different assets. It is numerically represented by the correlation coefficient. There are several kinds of correlation coefficients, but usually, Pearson's coefficient is used in finance and investing. It is measured on a scale of 1 to -1:

- A correlation of 1: The two assets have a perfect positive correlation (the prices of both move together). Think of it as a butterfly flapping its wings — Both its wings move in sync.
- A correlation of -1: The two assets have a perfect negative correlation (the prices move in opposite directions). It’s like the way our hands move when we walk — One swings forward while the other goes back.
- A correlation of 0: The two assets have no connection to each other (the price movement is not at all linked). It’s like a room full of children running around randomly — Their movements have no relation whatsoever.

The correlation coefficient also describes the strength of the relationship between the prices of two assets. For example, if the correlation of two fictional assets is 0.2, then they have a weak but positive correlation. On the other hand, if two assets have a correlation of 0.85, they have a strong and positive correlation.

Correlation simply measures the movement in prices of different assets — not what’s causing that movement. Correlation is also not permanent and may change over time and across different periods. For example, the correlation between US stocks and international stocks was 0.35 in the 1980s, while it was 0.8 in September 2018.

## What is stock correlation?

Stock correlation is how stock prices move in relation to each other. Several factors affect stock prices. Stocks in the same sector may tend to move together. Companies having interconnected or auxiliary businesses may also have a positive correlation. For example, in a hypothetical scenario, if the stock of a company that makes cars goes up, a tire company's stock may also go up.

Similarly, stocks that have a negative correlation may have businesses that affect each other. For example, a rise in oil prices tends to cause oil stocks to go up. But, in turn, aviation stocks may go down as they have to pay for more expensive fuel.

Stock correlation can also be used to find out how a particular stock moves with respect to an index like the S&P 500.

## What is the formula for correlation?

Correlation = Covariance of both assets / (Standard deviation of Asset 1 * Standard deviation of Asset 2)

Correlation is calculated by comparing how assets move together and how much they move from their average price.

The official mathematical equation for it is: Correlation = covariance of both assets (the rate at which one asset’s price changes relative to the other) divided by the product of their standard deviation (dispersion of an asset price from its mean).

## How is correlation calculated?

Calculating correlation involves finding out the covariance and standard deviation for both the assets.

Let’s go through it step by step.

- Select two assets and a time frame. Let’s consider two fictional companies called Red and Yellow, and look at their correlation for the past five days.
- Add the stock prices for Red and Yellow for all five days and then divide it by five days to get an average stock price for both companies. Let's say the mean stock price for Red is $25.2 and for Yellow is $46.8 over five days.
- Subtract the actual stock price from the mean for each day for both stocks. For example, if the Red’s price on day one is $25 and its mean is $25.2, then it has deviated by -$0.2 on day 1. Do this for all days for both stocks. Then multiply each subtracted value of Red with the subtracted value of Yellow. Add them up. The sum you get is the covariance of Red and Yellow.
- Square all the subtracted values for Red and Yellow. Add them separately. Multiply the added value of Red and the added value of Yellow. Calculate the square root of the product. This process would give you the standard deviation of Red and Yellow.
- You would get the correlation between the two stocks by dividing the covariance by the standard deviation.

Here’s what the calculation would look like:

## How can correlation be interpreted?

Apart from knowing the strength of the relationship between asset prices, correlation can also provide investors more insight into the stock market as a whole.

If most of the stocks in an index (like the S&P 500) have a high correlation, their prices are moving in a similar direction. The factors affecting their movement may be generally macroeconomic issues –- Think big picture stuff like changes in interest rates, government policies, and trade wars. These types of factors tend to affect the entire stock market as a whole, causing the stocks in an index to have a higher correlation.

On the other hand, if the correlation amongst stocks in an index is low, the prices of individual stocks move in different directions. Usually, in such cases, company-specific news is causing the movement in stock prices. Some investors believe that a lower correlation amongst stocks is a good opportunity to invest in companies as fundamentals (revenue, profits, growth) are driving stock prices instead of economic policies that affect the most of the stock market.

Here’s a real-life example of interpreting correlation. Stock correlation in the S&P 500 reduced to 0.23 in November 2019, the lowest since May 2019 (when it was suspected to be high because of growing trade war concerns). The five-year average correlation is 0.30 (Source: Wall Street Journal, November 25, 2019).

## What’s the importance of correlation?

Attempting to predict the direction and price of stocks is a complicated process. (No one can predict how stocks will move. All investment carries risk.) Correlation could be a useful tool that investors may use in asset allocation and while picking stocks.

Diversifying — having a mixture of different assets and securities — is one of the ways investors lower the risk to their portfolio. Diversification is not a foolproof strategy, but it may limit losses. The key while diversifying is picking investments that do not move together or that move in opposite directions. That's where knowing the correlation of the stocks or assets you own or want to invest in can be beneficial.

If a majority of the stocks in your portfolio are positively correlated, they will tend to fall and rise together. For example, if you invest only in technology stocks, your portfolio may grow when the technology sector is growing. But if that sector does not perform well, your portfolio’s value will go down all the more because you aren’t diversified.

Adding low and negatively correlated stocks to your existing portfolio may act as a balance and can reduce risk.

Just like with selecting stocks, investors can also diversify by investing in different types of assets. By investing in assets that have a historically low or negative correlation, like for example, stocks and bonds, they can further reduce their portfolio’s risk.

However, diversifying your portfolio with the help of correlation has its pros and cons. Investors may get smoother returns (there are no big upward or downward jumps in value), but thy are limiting their potential upside.

Positive returns in the stock market are never guaranteed. Having a well-diversified portfolio is generally considered a sound investing strategy. All investments carry risk. Always keep investment objectives — and your own tolerance for risk — in mind.

Additional Disclosure: Diversification does not ensure a profit and does not protect against losses in declining markets.

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