As an investor, it is important to understand how to calculate the expected return of a portfolio. The expected return is an estimate of the average return an investor can expect to receive from a portfolio over a specific period of time. The expected return is a critical metric to determine if the portfolio is meeting the investor’s investment goals and if it is providing adequate compensation for the risk taken.

There are a few different methods to calculate the expected return of a portfolio. Here are some of the most common methods:

1. ### Weighted Average Return

The weighted average return is the most straightforward method to calculate the expected return of a portfolio. It involves calculating the weighted average of the returns of each investment in the portfolio, where the weights are the percentages of the portfolio allocated to each investment.

For example, if a portfolio is comprised of two investments with returns of 10% and 5%, and the portfolio is allocated 60% to the first investment and 40% to the second investment, the expected portfolio return can be calculated as follows:

Expected portfolio return = (0.6 x 10%) + (0.4 x 5%) = 7%

1. ### Historical Average Return

The historical average return method involves calculating the average return of the portfolio over a specific period of time, such as the past five or ten years. This method assumes that the future performance of the portfolio will be similar to its historical performance.

For example, if the historical average return of a portfolio over the past ten years was 8%, the expected portfolio return using this method would be 8%.

1. ### Capital Asset Pricing Model (CAPM)

The Capital Asset Pricing Model (CAPM) is a widely used method to calculate the expected return of a portfolio. It takes into account the risk-free rate of return, the expected market return, and the portfolio’s beta.

The risk-free rate of return is the return an investor can expect to earn on an investment that is considered to be risk-free, such as a U.S. Treasury bond. The expected market return is the average return of the overall stock market. The portfolio’s beta measures the portfolio’s sensitivity to the overall market.

### The CAPM formula to calculate the expected portfolio return is as follows:

Expected portfolio return = Risk-free rate of return + (Expected market return – Risk-free rate of return) x Portfolio’s beta

For example, if the risk-free rate of return is 2%, the expected market return is 10%, and the portfolio’s beta is 1.2, the expected portfolio return using the CAPM method can be calculated as follows:

Expected portfolio return = 2% + (10% – 2%) x 1.2 = 11.6%

1. ### Monte Carlo Simulation

The Monte Carlo simulation is a statistical method that uses probability distributions to model the potential outcomes of a portfolio. It involves generating a large number of random scenarios, each with its own set of expected returns and probabilities.

For example, a Monte Carlo simulation can be used to model the expected returns of a portfolio during a recession, a market downturn, and a market boom. The simulation generates a distribution of possible outcomes, from which the expected portfolio return can be calculated.