When we talk about the risk of investing in stocks, corporate bonds, etc., we can distinguish between two main sources of risk: Systematic risk and unsystematic risk. The former relates to sources of risk that affect the entire market whereas the latter is risk specific to individual securities.

Learning objectives

- Understand the distinction between systematic risk and unsystematic risk.
- Learn how unsystematic risk can be reduced (or even be eliminated) via diversification.

## Don’t put all your eggs in one basket

Earlier in this course, we emphasized the fact that portfolio risk depends on covariances between the returns of asset pairs in a portfolio as well as the variance of each asset’s returns. Imagine that you invest all your savings in a single stock. If the stock increases in value over time, that is great. However, there is no guarantee of that. Stocks are risky investments. If the stock you invested in loses substantial value, you have nothing else to offset that loss. In such a scenario, you would be upset and would regret your decision to put money in that stock.

Compare this with the case where you hold a portfolio of 50 stocks instead of a single stock. In any given year, it would be unlikely that all of those stocks would lose value or gain value. The most likely scenario will be that some of the stocks will go down and the rest will go up. In that case, even if some of your stocks lose value, those losses would be (more than) offset by the gains you realize from the remaining stocks in your portfolio. Thus, holding a large portfolio of securities would reduce the volatility of your returns over the years.

Have you ever heard of the saying “don’t put all your eggs in one basket”? If you drop that basket along the way, you lose all your eggs and are left with nothing. This saying captures the spirit of portfolio theory. It advises investors to spread their risks. If you put all your wealth in a single asset, and if that asset turns sour, you are in big trouble.

## How many stocks should you have in your portfolio?

It is wise to invest your funds in a variety of assets to reap the benefits of diversification. In fact, diversification is one of the rare “free lunches” available to investors. By investing in a well-diversified portfolio, you can achieve higher returns at the same level of risk compared to investing in a single asset or a small, inefficient portfolio.

If that is the case, how many assets should we hold in our portfolio? 10, 100, 1000? When investing in stocks, we would like to have 30 or more stocks in our portfolio to fully benefit from diversification. We refer interested readers to a classical paper on this topic by Statman (1987), which is fully referenced at the bottom of this post.

## The power of diversification

Can the portfolio risk be completely eliminated if we keep adding assets into a portfolio? In practice, portfolio risk can be reduced by adding more securities to the portfolio. However, once the portfolio is large, each additional security would only result in an increasingly small reduction in portfolio risk. That is, we can reduce but cannot fully eliminate portfolio risk. Moreover, the lower the correlation between assets, the higher the proportion of portfolio risk that can be eliminated by increasing the size of your portfolio.

We illustrate this in Figure 1. The red curve represents a market where the average correlation between securities is relatively high. And, the green curve depicts a market where there is a low degree of correlation between securities. In both markets, we can reduce portfolio risk by increasing the number of securities in the portfolio. Moreover, in both markets, once the portfolio contains a large number of securities, we can’t reduce portfolio risk further by adding more securities to the portfolio. However, the proportion of portfolio risk that can be shed via increasing portfolio size is higher for the “low-correlation market” than the “high-correlation market”.

## Splitting total risk into systematic risk and unsystematic risk

In general, the portion of portfolio risk that can be eliminated via diversification is the **unsystematic risk**. And, the remaining portion of portfolio risk that stays regardless of how many securities you have in your portfolio is the **systematic risk**. We illustrate this more clearly in Figure 2. Furthermore, a portfolio’s **total risk** is the sum of its systematic risk and unsystematic risk.

We use the variance of returns *σ _{P}^{2}* as the measure of a portfolio’s total risk. The portfolio’s systematic risk is related to the beta of the portfolio

*β*and the variance of returns of the market portfolio

_{P}*σ*. Finally, we denote the unsystematic risk as

_{M}^{2}*σ*Then, we have the following relationship:

_{e}^{2}.*σ _{P}^{2}* =

*β*

_{P}*σ*^{2}_{M}^{2}+*σ*

_{e}^{2}As you add more assets into a portfolio, the unsystematic risk *σ _{e}^{2}* begins to go down to zero. This means that for a well-diversified portfolio, the variance of portfolio returns

*σ*(i.e., the total risk) is mainly driven by the portfolio beta

_{P}^{2}*β*, which is a measure of systematic risk.

_{P}## Market risk, firm-specific risk, idiosyncratic risk, …

Practitioners may use different terms when they refer to systematic risk and unsystematic risk. Let’s focus on the former first. Because systematic risk affects all securities in a market, we sometimes refer to it as **market risk** as well. Furthermore, it cannot be eliminated by portfolio diversification as all securities are affected by systematic risk. So, we can also call it **non-diversifiable risk**.

In contrast, unsystematic risk is all about risk factors that are specific to a security. Therefore, a common alternative name is **firm-specific risk**. The term **idiosyncratic risk** is also often used to refer to unsystematic risk. Furthermore, because we can eliminate unsystematic risk in a portfolio through diversification, we can call it **diversifiable risk** as well.

### Wrapping up

According to portfolio theory, investors should hold diversified portfolios. That is, we shouldn’t put all our eggs in the same basket. This is because, we can get rid of unsystematic risk through investing in a large number of securities. Usually, it is a good idea to diversify across asset classes (stocks, bonds, etc.) as well. However, no matter how large our portfolio is, we can’t eliminate systematic risk as this type of risk affects all securities in the market.

##### What is next?

This post is part of our free course on investments. We elaborated on the market portfolio in our previous post. Next, we will be moving on to the capital asset pricing model (capm), which is arguably the most well-known asset pricing model in finance.

Further reading

- Statman (1987) ‘How Many Stocks Make a Diversified Portfolio?‘,
*The Journal of Financial and Quantitative Analysis*, Vol. 22 (3), 353-363.

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