How to Calculate Expected Portfolio Return?

Fundamentals · Oct 5, 2019

It’s usually justified to be skeptical about financial forecasting, yet most portfolio managers have certain expectations regarding the future rate of return on the investments they make. How does one figure out an expected return of a financial portfolio?

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In this article, we’ll explain a method that is commonly used to calculate the expected return.

Also, we’ll show how to assess the “riskiness” of a certain asset in order to pick the less risky one within a group of assets with a similar forecasted return. Finally, we’ll present a way to calculate the total future return for a financial portfolio.

Table of Contents

What is Return on Assets?

Return on assets (ROA) reflects the value generated from certain assets at the end of a particular time period, expressed as a fraction of an initial value of those assets at the beginning of that period (usually 1 year). If an investment had a yearly return of 5%, that means its value increased by 5% during the last year so you’d get 1/20 (0.05 or 5%) of your initial investment back if you invested in that asset at the beginning of last year. A return of 1/20 means that you need 20 of such periods to get the return equal to your initial investment. By that time, the value of your investment would double because you get to keep the initial investment too. Please note that this example assumes that the return on assets will remain constant for the next 20 years, which is unlikely, so the sole purpose of this example is only to demonstrate the concept of return on assets.

➤ Read also: Return on Assets - our detailed guide on ROA

Everyone likes money, especially investors and traders, so they always try to maximize their return, or at least match a certain benchmark that can be a stock index, an inflation level, a neighbor’s portfolio, etc.

How to Calculate Historical Return?

Historical returns can be calculated in a similar way to return on assets, as well as any other kind of return in finance. To figure out the rate of return of an asset, simply divide its gains (revenues, income) by its size.

Here is the formula:

$$ R = \frac{FV-IV}{IV} $$

Where:

  • R: Return
  • FV: Final or Future Value
  • IV: Initial Value

So, if you invest $100 and let’s say it’d generate a modest $1 of income at the end of the year, a bank’s savings account, for example that pays an interest, then the rate of return in this case would be:

$$ 101 - 100 = 1 $$

$$ \frac{1}{100} = 0.01 $$

$$ 0.01\times100 = 1 \,percent $$

However, here is a catch: this rate of return is based on the last year’s data and we know exactly how much money this asset has generated for us during that year but this rate of return may not be the same going forward.

How to Calculate Expected Return of an Investment?

No one can predict the future and this holds true for financial forecasting.

Any successful “oracle” would quickly become the richest person alive. Although, it’s also naive to think that the past has no influence on the future and that’s why historical data can play a certain role in our attempts to forecast future returns. You can take a long-term average of the historical rates of return and then, based on this number, assume that the future rates of return would be somewhat similar.

For example, let’s imagine a new company on the market that had its IPO just 5 years ago. To calculate an expected future return, you would take the rates of return for each year and then just find an average (or median) value for the whole period.

Here is a data set for our example investment A:

  • Year 1: Return 2%
  • Year 2: Return 4%
  • Year 3: Return 6%
  • Year 4: Return -5%
  • Year 5: Return 1%

The total average return for 5 years would be:

$$ \frac{2+4+6-5+1}{5} = 1.6\,percent $$

Just 1.6%, eh? Even though, over many years, this asset had a higher than 1.6% return, year 4 had ruined everything. The median value in this scenario is equal to 2%.

Also, from this data set, you can conclude that the maximum historical yearly return was +6% and the minimum was -5%. Those extreme levels are important too because they can help us to estimate the “riskiness” of holding a certain asset.

Obviously, such a small data set is not reliable, that’s why long-term investors usually prefer corporations that have been in the game for a longer time: older companies have a track record of their performance and they also have a reputation to keep.

Standard Deviation and Risk

Calculating an expected return by using the method above is fine but it’s not perfect and it doesn’t show us the full picture. To illustrate why this is the case, let’s take another hypothetical company (Investment B) and its rates of annual return:

  • Year 1: Return 1%
  • Year 2: Return 2%
  • Year 3: Return 3%
  • Year 4: Return 1%
  • Year 5: Return 1%

As you might have already guessed, this is some kind of a conservative and a less risky investment, compared with the first one. Here, the total average return for 5 years would be the same 1.6%, but does it mean that both of those investments are equal in terms of expected outcomes?

Of course not, you can say that just by looking at the lowest and highest points of the data set above in order to make such a conclusion, but better proof would be produced by calculating the standard deviation for these two sets of data.

In our article about volatility we gave an example of how to calculate standard deviation and what it can be used for, so let’s use it here for our data sets in order to find out which investment is actually better.

The standard deviation would be:

  • Investment A: 4.15…
  • Investment B: 0.89…

Basically, what we’ve got here is a kind of “risk as a volatility” metric. Standard deviation shows us how close different values tend to be to the mean (the average), so with the investment A, our data points tend to be much farther from the mean and with the investment B they are much closer.

It’s true that, on average, the rates of return are around 1.6% in both cases, especially if the period is long enough, but the investment B is much better if we want to decrease risk (uncertainty), because it’s less likely that the future rates of return on this investment will deviate from the average value. Sure, with the investment A, you could get lucky and have a great rate of return occasionally, which might be fine for a risk insensitive young person who started investing yearly, but as an older adult you would probably want to choose the investment B just out of the fear of unexpected sharp losses. Older people tend to have a shorter time horizon so they tend to avoid exposure to events that can take decades to recover from.

That’s how two assets with similar average return can be actually very different in terms of their quality.

How to Calculate Expected Return of a Portfolio?

Ok, so we figured out how to calculate an expected return on a certain asset, but what about a big and diversified portfolio?

It’s actually quite similar but you would also need to add up all of the elements of a portfolio (assets) in a weight-adjusted manner.

Let’s say that we have a total capital of $8000 and we purchased 4 assets to build a portfolio:

  • Asset 1 ($1000): Expected return 2%
  • Asset 2 ($3000): Expected return 3%
  • Asset 3 ($2000): Expected return 1%
  • Asset 4 ($2000): Expected return 10%

As you can see, the structure of this portfolio is quite safe with only $2000 (2/8 = 1/4 = 25%) allocated in a relatively risky high-yield asset.

To figure out the expected return on a portfolio, we would add together all of its weighed assets:

$$ (2\times\frac{1}{8}) + (3\times\frac{3}{8}) + (1\times\frac{2}{8}) + (10\times\frac{2}{8}) = 0.25 + 1.125 + 0.25 + 2.5 = 4.125\,percent $$

The result would be 4.125%, this is the rate of return on capital that we can expect from this portfolio.

It’s clear that, in this case, the asset 4 plays a huge role in terms of the total expected return. Without this asset, we wouldn’t be able to expect a return higher than 3%, and even if this asset would perform not as good as we expect, let’s say 5% instead of 10%, it would still be a great pick.

The Main Problem With History-based Forecasts

All these statistical measurements have one major problem: the projected data is constrained by historical numbers. As all future forecasts are based on the past, it’s impossible to predict a scenario out of the scale of such a measurement, but, in reality, history doesn’t always repeat itself. There can be a dramatic fall or rise in the price of a certain asset or even a whole market index.

The most extreme versions of such events are called “black swans”.

It’s true that extreme and unexpected outcomes are unlikely, especially for an investment with a long history, and it’s also true that we don’t actually have other more or less sensible methods which can be used to forecast future except by studying the past and, sometimes, the future surprises us and it can make us rich or poor in a short period of time.

All these methods of predicting future return don’t work as good for the new companies and new markets that have no history, and, in those cases, it’s better to use other techniques to try to forecast the future of a certain asset. Even companies like Tesla are almost impossible to forecast with those methods of historical analysis as they don’t have a big set of historical data and they are also very volatile.

analytics   business   capital   finance   income   investing   money   management   personal finance   statistics   portfolio   risk

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