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What is Unsystematic Risk? How to Calculate It?

What is Unsystematic Risk? How to Calculate It?

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In finance and economics, unsystematic risk or firm specific risk, is a type of risk that affects only a specific company. But what is unsystematic risk exactly? What makes it unique to a specific company? And how do we actually calculate it?

Let’s consider and answer all these questions.

Table of Contents hide
1 What is Unsystematic Risk?
1.1 Examples of Unsystematic Risk
2 What is Systematic Risk?
3 How to Calculate Unsystematic Risk
3.1 Generalised Expected Returns
3.2 Rearranging for the Unsystematic Risk Formula
4 Unsystematic Risk Calculation Example
5 Wrapping Up – Unsystematic Risk

First, though, let’s get some jargon out of the way.

Unsystematic risk is also known as:

  • diversifiable risk
  • idiosyncratic risk
  • nonsystematic risk
  • business risk
  • unique risk
  • firm-specific risk

What is Unsystematic Risk?

Despite the barrage of different terms, they all fundamentally mean the same thing. Unsystematic risk is a risk that investors can do something about. It’s a risk that investors can control to some extent.

It’s a risk that an investor can diversify away by holding a diversified portfolio.

From a company’s standpoint, it’s a risk that affects the company, but not necessarily its competitors.

Examples of Unsystematic Risk

Examples of unsystematic risk or idiosyncratic risk include (but aren’t limited to):

  • death of the founder/CEO, especially if no succession plans exist
  • fire, theft, or other damage to the business or property
  • accounting scandals
  • fraudulent activities
  • incompetent management or staff
  • poor internal training programs

By no means is this an exhaustive list of examples of unsystematic risk. There can be a host of other relevant examples.

Notice, though, that all of these risks can affect one firm while leaving its competitors completely unaffected.

Sure, you might argue that some of these risks give competitors a competitive advantage, but in this context, we’re only really focusing on the adverse effects of risk.

Unsystematic risk, or diversifiable risk, is typically contrasted with systematic risk. There’s a good reason for this, so let’s take a look.

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What is Systematic Risk?

Systematic Risk is also known as Market Risk, and it is essentially the risk that you would incur if you invest in any type of investment or market.

The risk that any individual shareholder would be exposed to is Systematic Risk, no matter whether it’s a diversified investor who owns a large number of stocks or an investor who holds only one stock.

Since systematic risk is market-wide, it affects all the investors in a market equally.

Examples of systematic risk include (but aren’t limited to):

  • recession
  • depression
  • inflation, particularly hyperinflation
  • deflation
  • changes in interest rates
  • natural calamities
  • pandemics (e.g., covid/coronavirus)

Similar to the examples of unsystematic risk, this is is not exhaustive whatsoever.

What is clear, however, is that no single individual can control or prevent these risks.

They cannot be diversified away. And this explains why systematic risk is also called non-diversifiable risk.

Systematic risk is also known as:

  • market risk
  • non-diversifiable risk
  • undiversifiable risk
  • non-unique risk

Note that Systematic Risk holds across asset classes. It applies to fixed income securities, equity instruments, real estate, and pretty much any other asset class.

How to Calculate Unsystematic Risk

Now that you know what is unsystematic risk and how it differs from systematic risk, let’s think about how to calculate unsystematic risk.

Calculating unsystematic risk is fairly straightforward. It fundamentally relies on the fact that Total Risk is made up of:

  • Systematic Risk, and
  • Unsystematic Risk

Put differently, we can say:

Total Risk = Systematic Risk + Unsystematic Risk

With this interpretation of total risk, we can simply rearrange to obtain an expression for Unsystematic Risk. Thus we can calculate unsystematic risk as…

Unsystematic Risk = Total Risk – Systematic Risk

Yes, this is a conceptual formula for unsystematic risk, but don’t worry – we’ll go over the exact formula to calculate unsystematic risk further down.

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But given this conceptual formula for unsystematic risk, the obvious next question is how to calculate total risk? And how to calculate systematic risk?

Those are interesting and important questions. Answering them here is a bit of a tall order.

However, we do have an article on estimating total risk and another one on calculating systematic risk. Do give those a read as they’re incredibly important concepts.

Now, assuming you know how to estimate total risk and market risk, we can proceed further.

We’ll start by considering the case of estimating expected returns using the CAPM.

Generalised Expected Returns

Recall that the generalised equation for excess expected returns using the CAPM is this:

    \[r_j - r_f = \alpha + \beta_j (r_m - r_f) + \epsilon_t\]

Of course, this expression applies in an asset pricing framework. So, it’s completely different to say, calculating expected returns using state contingent probabilities.

(Strictly speaking, in the article linked above, we looked at expected returns (r_j), and not excess expected returns (r_j – r_f), but it’s still the same principle).

Here, r_j - r_f reflects the excess return on stock j.

That is, the return over and above the risk-free rate.

The Beta (\beta_j) measures the stock’s exposure to market risk. r_m reflects the market portfolio, and r_m - r_f reflects the market risk premium.

Finally, \epsilon_t reflects the ‘error term’.

For simplicity – and indeed, given the CAPM – we can ignore alpha, or set its value to zero.

This is ultimately because, under the CAPM, the only factor that affects expected returns of securities is the overall market portfolio.

Now, given that the risk-free rate is on both sides, we can essentially ignore it too, and focus on the returns of the firm and the market explicitly, instead of the excess returns of the firm and the market.

Rearranging for the Unsystematic Risk Formula

Now, if you take the variance of both sides (i.e., to express the equation as the variance of returns instead of returns), you’ll end up with this:

    \[var(r_j) = var(\beta_j r_m) + var(\epsilon_t)\]

This is equivalent to writing…

    \[\sigma_j^2 = \beta_j^2 \sigma_m^2 + \sigma_{\epsilon}^2\]

Recall that the variance is just the square of the standard deviation. In other words, it’s the risk of a stock squared.

Remember we said Total Risk = Systematic Risk + Unsystematic Risk?

Here’s what’s incredible…

You can literally see the two types of risk in the equation for the variance!

The first part (\beta_j^2 \sigma_m^2) is the market risk, and the second part (\sigma_{\epsilon}^2) is the firm specific risk.

Subtract the market risk from both sides to get our expression for the firm specific risk (variance) as:

    \[\sigma_{\epsilon}^2 = \sigma_j^2 - \beta_j^2 \sigma_m^2\]

And given that the standard deviation is a measure of risk, we can take the square root of the firm-specific variance to get the firm-specific risk / unsystematic risk formula as:

    \[\sigma_{\epsilon} = \sqrt{\sigma_j^2 - \beta_j^2 \sigma_m^2}\]

And that’s how to measure unsystematic risk mathematically.

Unsystematic Risk Calculation Example

Alright, let’s now consider an example on how to calculate unsystematic risk.

Consider BME stock which has a beta of 1.37 relative to an equities market with risk equal to 18%. The stock’s own total risk is equal to 25%. What is its idiosyncratic risk?

Start by getting our numbers together. We need three things, including:

  • \sigma_{BME} (which is equal to 25%)
  • \beta_{BME} (equal to 1.37), and
  • \sigma_{m} (which in this case is equal to 18%)

Plugging in these numbers into the formula for unsystematic risk gives us…

    \[\sigma_{\epsilon} = \sqrt{\sigma_j^2 - \beta_j^2 \sigma_m^2}\]

    \[\sigma_{\epsilon} = \sqrt{0.25^2 - 1.37^2 \times 0.18^2}\]

This is equivalent to writing…

    \[\sigma_{\epsilon} = \sqrt{0.0625 - 1.8769 \times 0.0324}\]

Solving for this gives us…

    \[\sigma_{\epsilon} \approx 0.0411 = 4.11\%\]

And that’s it!

If any part of this example isn’t quite clear, please re-read the article from the start. It’ll likely make much more sense the second time round!

Wrapping Up – Unsystematic Risk

So there you have it! Now you know how to calculate unsystematic risk.

Importantly, the relevance of firm-specific risk decreases when we look at investing in diversified portfolios (i.e., an asset allocation in multiple assets).

That’s because the individual risks of firms tend to cancel out as a result of portfolio diversification.

RELATED: How to Calculate Portfolio Risk

Thus, the only risk that’s left is the market risk. And that’s ultimately the only one that matters since we can’t get rid of it.

Alright, hopefully now know what is unsystematic risk, why it matters, and what some of the most common examples of unsystematic risk are.

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That’s a wrap from us for now. Keep learning and loving Finance and Investing!

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