# How to Calculate the Expected Return of a Portfolio

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An investment’s “expected return” is a critical number, but in theory it is fairly simple: It is the total amount of money you can expect to gain or lose on an investment with a predictable rate of return. Basically, it tells you what you can expect to get out of a given investment, and by extension, what kind of return you can expect when you build an investment portfolio with a particular mix of investments. If you have questions about investing, consider speaking with a financial advisor.

## What Is Expected Return?

Every investment has a speculative component. The degree of that speculation typically defines the product’s rate of return. A stock can bring in enormous rewards or total losses, with no guarantees either way. A bond guarantees that you’ll see every penny of this money back, but it’s worthless if the borrower doesn’t keep this promise.

Expected return, therefore, is not about knowing what will happen to an investment for certain. Instead it measures the likely return you should expect on an investment based on a series of likely outcomes.

As a result, an investment’s expected return represents a probability distribution. It is a statistical model that tells you an investment’s general worth. Based on each of the investment’s likely outcomes, and based on how likely it is that you’ll see each of those outcomes, here is how you should value it.

For a portfolio, expected return takes that logic and extends it one step further. A portfolio’s expected return represents the combined expected rates of return for each asset in it, weighted by that asset’s significance. It tells you what to expect out of this portfolio’s total likely gains and losses based on how you chose the portfolio’s component parts.

## How to Calculate the Expected Return of a Portfolio

A portfolio’s expected return is based on the rate of return of each component asset, and each asset’s weight in the portfolio.

• Rate of return: An asset’s rate of return measures how much money you, as an investor, would have made or lost had you invested in this asset over a specific period of time. For example, say you assume a \$1,000 investment in a stock over a one-year period after which you sold it. Between dividends and the sale of the stock you would have made \$150. The rate of return on this stock would have been 0.15%.

It can also be used to calculate the results of an actual investment. In this case you would use your actual initial investment and the period of time you held it.

• Asset weight: The percent of your portfolio that any given asset makes up. You calculate this by dividing the value of each given asset by the total value of the portfolio. For example, say your portfolio is worth \$50,000. A single asset in it is worth \$18,000. This asset’s weight in your portfolio would be 36%.

To calculate expected rate of return, you multiply the expected rate of return for each asset by that asset’s weight as part of the portfolio. You then add each of those results together. Written as a formula, we get:

• Expected Rate of Return (ERR) = R1 x W1 + R2 x W2 … Rn x Wn

In this formula, “R” equals rate of return, while “W” is equivalent to the asset weight.

Let’s look at a sample portfolio with five stocks in it. The total value of our portfolio is \$100,000, and we have already calculated each stock’s rate of return.

1. Stock A – \$25,000
1. Rate of return = 10%
2. Weight = 25%
2. Stock B – \$10,000
1. Rate of return = 15%
2. Weight = 10%
3. Stock C – \$30,000
1. Rate of return = 4%
2. Weight = 30%
4. Stock D – \$15,000
1. Rate of return = 5%
2. Weight = 15%
5. Stock E – \$20,000
1. Rate of return = -6%
2. Weight = 20%

The process for finding the expected return on this portfolio would go as follows:

• R1 x W1 + R2 x W2 … Rn x Wn = Expected Rate of Return (ERR)
• RA x WA + RB x WB + RC x WC + RD x WD + RE x WE = ERR
• (0.1 x 0.25) + (0.15 x 0.1) + (0.04 x 0.3) + (0.05 x 0.15) + (-0.06 x 0.2) = ERR
• 0.025 + 0.015 + 0.012 + 0.0075 + -0.012 = ERR
• 0.0475 = 4.75% = ERR

We should expect a return of 4.75%. This reflects the strong gains posted by nearly a third of this portfolio’s assets, set against the more modest gains and outright losses posted by the rest.

## Understanding the Limits of Expected Return

It’s important to understand that expected return is closer to an educated guess than a firm prediction. Whether you’re calculating this for an individual stock or an entire portfolio, the formula depends on getting your assumptions right.

For a portfolio, you will calculate expected return based on the expected rates of return of each individual asset. But expected rate of return is an inherently uncertain figure. As an investor you calculate it by assuming that the asset’s growth and yield in the past will continue unabated into the future.  If your stock returned dividends in the past year, it will continue to pay those dividends in future years. If it grew 10% in the past year, it will grow by at least another 10% this year.

These are not completely speculative assumptions, but neither are they necessarily reliable. While past performance can indicate future results, there are no guarantees.

## Bottom Line

A portfolio’s ERR is a probability distribution that reflects the gains and losses you should expect based on asset weight and past performance. It is neither completely speculative nor necessarily reliable.