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Asset Allocation & Portfolio Management: Measuring Expected Return
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The asset allocation and portfolio management techniques we will describe mainly use statistical indicators you should be familiar with. If you are not, first visit our statistical tutorial.

To estimate the future rate of return of an asset or a portfolio, financial analysts are blessed with an enormous quantity of data on security prices and return.

Based on the historical data, we can easily compute an average rate of return and, under the assumption that the future will be like the past, use this rate of return to evaluate future return.

Unfortunately, this is not the way to do it because the average return of the assets are not stable over time.

The return of each asset is made of two components:

• the risk free interest rate (not stable over time because linked to external factors like the inflation).
• risk premium attached to the specific asset.

The crucial assumption in the portfolio theory is that the risk premium follows a normal law and, therefore, can be measured by the average past risk premium.

Some practical allocation examples: Click here

As we will see in the next sections, the risk premium will be measured by asset type and even by asset.

To compute the expected return, you simply add all the possible returns weighted by their respective probabilities (normal law).

The Formula of the expected return is:

Where

E[r] is the expected return
P(s) the probability that the rate r_s occurs.
r_s the return at s level.

Let's take a practical example:

The current price of the stock X is USD 10. You expect the stock to be traded:

•  10% higher at the end of the year if the economic growth is as you expect with a probability of 50%.
• 25% higher at the end of the year if the economic growth is higher than expected with a probability of 25%.
• 5% lower  at the end of the year if the economic growth is lower than expected with a probability of 25%.

The expected return is : 25% * 25% + 50% * 10% + 25% * -5% = 10%

We will see in the next sections how this concept can be used in practice but, beforehand, we have to introduce the concept of risk measurement.

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