Investment: How to Look for Covariance in Assets

Manage your risk: diversify by understanding covariance.

There are many ways in which someone can manage risks in their investment portfolio. Diversification has been one of the most sought ways. There are many ways in which you can diversify your portfolio, but if you’re thinking of sticking to only stocks, or only stocks in one particular industry, then you might want to know about covariance.

What is covariance?

Covariance is essentially a statistical concept that measures how one thing corresponds with another — or you could also say how closely associated are the two.

In the context of investment, covariance measures the interconnectivity between two assets (usually stocks) by measuring how their returns move — is it in correspondence or independent of one another.

This method is used to diversify portfolios by looking for companies that are not closely interrelated. There are generally three results of covariance analysis.

Types of Covariance



When the number is more than 0, it means that there is a positive relationship, the further away it is from 0, the more interrelated they are. Once it reaches 1, you can say that the two assets are almost like identical twins, there are strong correlations with each other.

Getting strongly related assets together will not be much for your diversification effort since it’s almost like you’re buying one single asset.



The closer the value is to zero, the less interrelated the movements of the two assets are. Making sure that the assets in your portfolio are not closely interrelated would be good in terms of diversification.



A negative value indicates that the two assets are moving in the opposite direction of each other. However, getting something that is too close to -1 may not be a good idea, since your portfolio will be of assets that cancel out each other. If Asset 1 moves up by 10%, Asset 2 will most likely move down by 10%. In the end, your portfolio will move at a constant 0%.

Also read: How to diversify your portfolio

How to calculate the covariance

Covariance can be calculated by using the formula below:

Cov(x,y) = covariance between x (asset 1) and y (asset 2)
Σ = Summation of all of the calculations.
x(i) = Day return of x (asset 1)
y(i) = Day return of y (asset 2)
x̄ = Average return of x (asset 1) over the period
ȳ = Average return of y (asset 2) over the period
N = number of data value (sample size)

We know the formula above may not be sufficient. So, let’s go through it step-by-step.

Let’s say we have this table for the daily returns of Asset 1 and Asset 2:

How to calculate it is as follows:

1. To make things easier, we will look for the x̄ and ȳ values first.


x̄ (Average return for Asset 1): (2.5+2.7+2.4+2.5+2.8) ÷ 5 = 2.58

ȳ (Average return for Asset 2): (3+3+3.2+3.3+3.1) ÷ 5 = 3.12


x̄ = 2.58

ȳ = 3.12


2. Now we move to the Σ (x(i) — x̄) × (y(i) — ȳ) part, it’s not as complex as it looks. Let’s go.


Day 1: (2.5–2.58) × (3–3.12) = 0.0096

Day 2: (2.7–2.58) × (3–3.12) = -0.0144

Day 3: (2.4–2.58) × (3.2–3.12) = -0.0144

Day 4: (2.5–2.58) × (3.3–3.12) = -0.0144

Day 5: (2.8–2.58) × (3.1–3.12) = -0.0044


3. Now add the result of each day above.


0.0096–0.0144–0.0144–0.0144–0.0044 = -0.038


4. Now we move to the N-1 part.


5–1 = 4


5. Finally divide the result of each day with the N — 1 above.


-0.038 ÷ 4 = -0.0095

Ta-da! The result is -0.0095; which means that the assets are inversely related, but not very much related.

How do you use covariance for portfolio diversification?

The whole point of diversification is to look for companies with different levels of risk exposure, or ones that are exposed to different types of risk. The reason behind it is to ensure that if there is any unfortunate development in the market, some of the assets in your portfolio might be taking the fall, but not all of it.

As mentioned above, there are 3 types of covariance, what you want is to make sure that the companies in your portfolio have a covariance that is closest to 0, that is to make sure that they’re not interrelated at all (if that is possible).

Why? The whole point of diversification is to make sure that your portfolio will not crumble upon one bad stroke of luck.

Here’s an analogy: There’s a person with a gun who’s going to shoot you one time, the rule is that the bullet will definitely hit, but the person isn’t a very good shot, so the impact location is randomized. Should you cuddle up into a ball or just spread yourself wide open?

In this case, one bullet will definitely hit you, but the location is randomized. In this situation, it’s not wise to cuddle up into a ball, as many of your vitals will be closely packed together.

So, if the bullet hits, it might pierce through and damage your vitals which are closely located to each other. We know that this isn’t the best way to put it, but as long as the point comes across.

Bottom line

  • Diversifying your portfolio will make sure your portfolio is well-cushioned for any fall.
  • Covariance measures how identical an asset moves in relation to another.
  • The main concern is to look for covariance close to 0.
  • Covariance is just one of the many methods to look into your investment portfolio.
  • Even if the covariance is near 0, you’ll have to see if the assets are volatile.
  • A portfolio with covariance close to 0 but all of them are risky assets wouldn’t be as good.

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None of the material above or on our website is to be construed as a solicitation, recommendation or offer to buy or sell any security, financial product or instrument. Investors should carefully consider if the security and/or product is suitable for them in view of their entire investment portfolio. All investing involves risks, including the possible loss of money invested, and past performance does not guarantee future performance.

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