# Expected Return

Expected return of a portfolio is the weighted average return expected from the portfolio. It is calculated by multiplying expected return of each individual asset with its percentage in the portfolio and the summing all the component expected returns.

Expected return on different asset classes in portfolio, i.e. stocks, bonds, real estate, commodities, etc. and different individual assets in each asset class is determined by formulating overall capital market expectations. Historical returns are a good starting point which are adjusted keeping in view the overall macroeconomic environment such as growth rate, inflation, unemployment, government expenditure, central bank’s policy rate, open market operations, etc.

Expected return in an important input in calculation of Sharpe ratio which measures expected return in excess of the risk-free rate per unit of portfolio risk (measured as portfolio standard deviation).

Unlike the portfolio standard deviation, expected return on a portfolio is not affected by the correlation between returns of different assets.

## Formula

Expected return for a portfolio can be calculated as follows:

$$ E_r=w_1\times R_1+w_2\times R_2+....+w_n\times R_n $$

Where E_{r} is the portfolio expected return, w_{1} is the weight of first asset in the portfolio, R_{1} is the expected return on the first asset, w_{2} is the weight of second asset and R_{2} is the expected return on the second asset and so on.

Where a portfolio has a short position in an asset, for example in case of a hedge fund, its weight is negative.

## Example

You purchased 100 shares of Apple, Inc. at $156.41 each and 30 shares of Google at $1,046.27 each. Your expected return for each stock over the next year is 10% and 14%. Calculate expected return on your portfolio.

Investment in Apple

= 100 × 156.41 = 15,641

Investment in Google

= 30 × 1,046.27 = 31,388

$$ Weight\ of\ Apple\ in\ the\ Portfolio \\=\frac{15,641}{15,641+31,388}=33\% $$

$$ Weight\ of\ Google\ in\ the\ Portfolio \\= \frac{31,388}{15,641+31,388}=67\% $$

$$ Portfolio\ Expected\ Return\\=33\%\times10\%+67\%\times14\%=12.67\% $$

You might be interested in reviewing how to calculate portfolio standard deviation.

Written by Obaidullah Jan