Expected Value of a Portfolio

Using the same properties, we can calculate the expected value (returns), variance and standard deviation of a portfolio.

Expected Value (Expected returns)

The formula for portfolio returns is presented below:

w represents the weights of each asset, and r represents the returns on the assets. For example, if an asset constitutes 25% of the portfolio, its weight will be 0.25. Note that sum of all the asset weights will be equal to 1, as it will represent 100% of the investment. The returns here are single period returns with same periods for each asset’s returns.

Let’s take an example of a two asset portfolio to understand how portfolio returns are calculated. Let’s say that our portfolio comprises of two assets A and B and has the following details.

The table presents the amount invested in each asset and the returns from each asset. The total amount invested is $100,000. We can calculate the weights for each asset as follows:

wA = 25000/100000 = 0.25

wB = 75000/100000 = 0.75

We can now calculate the portfolio returns as follows:

The same calculation can be extended for multiple assets.