# Portfolio Risk and Return: Expected returns of a portfolio

05/02/2024

Portfolio risk and return are central concepts in the field of investment management, focusing on how to maximize returns for a given level of risk through diversification and strategic asset allocation.

Expected Returns of a Portfolio

The expected return of a portfolio is the weighted average of the expected returns of its individual assets, where the weights are the proportion of each asset’s value relative to the total value of the portfolio. This metric provides investors with an estimate of the average return that the portfolio is expected to generate over a future period.

Formula for Expected Portfolio Return

If a portfolio contains n assets, with Ri​ representing the expected return of asset i and wi​ representing the weight of asset i in the portfolio, the expected return of the portfolio (Rp​) can be calculated as:

Rp ​= w1​R1​+w2​R2​+…+wnRn

Rp​ = ∑i=1nwiRi

where:

• Rp​ = Expected return of the portfolio
• wi​ = Weight of asset i in the portfolio (the proportion of the portfolio’s total value invested in asset i)
• Ri​ = Expected return of asset i
• n = Number of assets in the portfolio

Example Calculation

Suppose a portfolio consists of three assets. Asset A has an expected return of 5%, Asset B has an expected return of 10%, and Asset C has an expected return of 15%. If 50% of the portfolio is invested in Asset A, 30% in Asset B, and 20% in Asset C, the expected return of the portfolio can be calculated as follows:

Rp ​= (0.50×5%)+(0.30×10%)+(0.20×15%)

Rp​ = 2.5%+3%+3%

Rp​ = 8.5%

Thus, the expected return of the portfolio is 8.5%.

Importance

Calculating the expected return of a portfolio is crucial for investors as it helps in:

• Portfolio Construction:

Guiding the allocation of assets to achieve desired return objectives while managing risk.

• Performance Measurement:

Serving as a benchmark to evaluate the actual performance of the portfolio against its expected performance.

• Risk Management:

Assisting in understanding the trade-offs between risk and return, facilitating adjustments in portfolio composition to align with an investor’s risk tolerance.