In this lesson, we’ll teach you how to compute the return of a portfolio that consists of multiple assets. We offer a portfolio return calculator as well.

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## Portfolio return calculator

You can use the **portfolio return calculator** below to compute the returns of portfolios containing up to 5 stocks. Please note:

- If the returns you enter are “realized returns”, the calculator gives you the realized return of the portfolio. If they are “expected returns“, you’ll get the expected return of the portfolio.
- The calculator allows for negative investment weights (i.e., short selling) as well as positive investment weights (i.e., long positions).
- Make sure that investment weights add up to 100% (see the “sum of weights (%)” in the last row of the calculator).
- Make sure to enter data as percentage points. For example, if the investment weight of Asset 1 is 80%, simply enter 80 in the “weight (%)” field of that asset.
- If your portfolio consists of less than 5 assets, you can of course use the calculator by leaving 0s in the fields that you don’t need.

## Portfolio return formula

So far in this course on investments, we have focused on investing in a single asset. However, in reality, most investors invest in more than one asset. Therefore, it’s important for them to be able to compute portfolio returns.

Let’s imagine that you have $5,000 to invest. If you invest all that amount in a single asset, say Pfizer shares, the return on your investment will solely depend on the performance of Pfizer shares.

However, if you split your investment such that you invest $4,000 in Pfizer shares and $1,000 in Procter & Gamble shares, then the performance of your portfolio will depend on the performance of Procter & Gamble shares as well as Pfizer shares. In this scenario, you invest $4,000 / $5,000 = 80% of your funds in Pfizer. And, the remaining $1,000 / $5,000 = 20% in Procter & Gamble. In other words, your **investment weights** (or **portfolio weights**) for Pfizer and Procter & Gamble are 80% and 20%, respectively. Given that the investment weight of Pfizer is much bigger than that of Procter & Gamble, the performance of your portfolio will be more heavily influenced by Pfizer shares.

If the returns of Pfizer and Procter & Gamble last month were 2% and −1%, respectively, then your **portfolio return** would simply be the weighted average of these returns:

80% (2%) + 20% (−1%) = 1.4%

Let’s go further and add a third stock to your portfolio: Nike, such that you invest $3,000 in Pfizer, $1,000 in Procter & Gamble, and $1,000 in Nike. Note that the total investment is still $5,000. Now, the updated investment weights are 60% for Pfizer, 20% for Procter & Gamble, and 20% for Nike (this is also referred to as your **portfolio composition**). If Nike’s return last month was 0.5%, your portfolio return would become:

60% (2%) + 20% (−1%) + 20% (0.5%) = 1.1%

In general, the *realized* (or *historical*) return on a portfolio*R _{P}* can be calculated as:

where *w _{i}* is the investment weight for asset

*i*,

*R*is the realized return for asset

_{i}*i*, and

*N*is the total number of assets included in the portfolio.

How about the portfolio expected return *E[*R_{P}*]*? The idea is still the same. In fact, we can simply replace the realized return of each asset in the portfolio with its expected return to obtain the** portfolio expected return formula**:

For example, if the expected returns of Pfizer, Procter & Gamble, and Nike for the next month are 1.4%. 2%, and 0.9%, respectively, then your portfolio’s expected return is:

60% (1.4%) + 20% (2%) + 20% (0.9%) = 1.42%

##### Summary

In this lesson, we have shown that the return of a portfolio depends on (a) the return of each asset within that portfolio and (b) the investments weights for those assets, such that assets with larger investment weights influence the portfolio return more than those with smaller investment weights. We have also provided a handy calculator that functions as both a portfolio expected return calculator (i.e., forward-looking) and a portfolio historical return calculator (i.e., backward-looking).

Further reading:

If you would like to learn more about the historical development of modern portfolio theory, we recommend the following article.

Markowitz (1999), ‘The Early History of Portfolio Theory: 1600–1960,’ *Financial Analysts Journal*, Vol. 55 (4), pp. 5-16.

##### What is next?

This lesson is part of our free course on investments.

**Next lesson**: Now that we have learned how to calculate portfolio return, we will move on to discussing how to calculate portfolio risk.**Previous lesson**: The subject of the previous lesson was the concept of risk premium.

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