As a well-informed investor, you naturally want to know the expected return of your portfolio—its anticipated performance and the overall profit or loss it's racking up. Expected return is just that: expected. It is not guaranteed, as it is based on historical returns and used to generate expectations, but it is not a prediction.
The expected return of a portfolio will depend on the expected returns of the individual securities within the portfolio on a weighted-average basis. A well-diversified portfolio will therefore need to take into account the expected returns of several assets.
Key Takeaways
- To calculate a portfolio's expected return, an investor needs to calculate the expected return of each of its holdings, as well as the overall weight of each holding.
- The basic expected return formula involves multiplying each asset's weight in the portfolio by its expected return, then adding all those figures together.
- In other words, a portfolio's expected return is the weighted average of its individual components' returns.
- The expected return is usually based on historical data and is therefore not guaranteed.
- The standard deviation or riskiness of a portfolio is not as straightforward of a calculation as its expected return.
How to Calculate Expected Return
To calculate the expected return of a portfolio, the investor needs to know the expected return of each of the securities in their portfolio as well as the overall weight of each security in the portfolio. That means the investor needs to add up the weighted averages of eachsecurity's anticipated rates of return (RoR).
An investor bases the estimates of the expected return of a security on the assumption that what has been proven true in the past will continue to be proven true in the future. The investor does not use a structural view of the market to calculate the expected return. Instead, they find the weight of each security in the portfolio by taking the value of each of the securities and dividing it by the total value of the security.
Once the expected return of each security is known and the weight of each security has been calculated, an investor simply multiplies the expected return of each security by the weight of the same security and adds up the product of each security.
Formula for Expected Return
Let's say your portfolio contains three securities. The equation for its expected return is as follows:
Ep = w1E1 + w2E2 + w3E3
where: wn refers to the portfolio weight of each asset and En its expected return.
A portfolio's expected return and its standard deviation (i.e., its risk) are used together in modern portfolio theory (MPT). In particular, it uses a process of mean-variance optimization (MVO) to provide the best asset allocations that maximize expected return for a given level of risk (or, alternatively minimize the risk for a given expected return).
Limitations of Expected Return
Since the market is volatile and unpredictable, calculating the expected return of a security is more guesswork than definite. So it could cause inaccuracy in the resultant expected return of the overall portfolio.
Expected returns do not paint a complete picture, so making investment decisions based on them alone can be dangerous. For instance, expected returns do not take volatility into account. Securities that range from high gains to losses from year to year can have the same expected returns as steady ones that stay in a lower range. And as expected returns are backward-looking, they do not factor in current market conditions, political and economic climate, legal and regulatory changes, and other elements.
How Do I Calculate the Standard Deviation of a Portfolio?
The standard deviation of a portfolio is a proxy for its risk level. Unlike the straightforward weighted average calculation for portfolio expected return, portfolio standard deviation must take into account the correlations between each asset class. The implication is that adding uncorrelated assets to a portfolio can result in a higher expected return at the same time it lowers portfolio risk. As a result, the calculation can quickly become complex and cumbersome as more assets are added. For a 2-asset portfolio, the formula for its standard deviation is:
σ= (w12σ12+ w22σ22+ 2w1w2Cov1,2)1/2
where: wn is the portfolio weight of either asset, σn2 its variance, and Cov1,2, the covariance between the two assets.
How Can I Find the Expected Return of a Portfolio?
Some online brokers or certain financial advisors may be able to provide you with your portfolio's standard deviation at a glance, as it is automatically calculated via software in the background. To compute it by hand, you simply need to work out the weighted average of the expected returns of each individual holding.
What Is the Excel Formula for Investment Portfolio Returns?
Excel can quickly compute the expected return of a portfolio using the same basic formula.
- Enter the current value and expected rate of return for each investment.
- Indicate the weight of each investment.
- Multiply the weight by its expected return
- Sum these all up
