Rate of return on a portfolio

The rate of return on a portfolio is "a weighted average of the rates of return on the various assets with the weights being equal to the fractions of the individual's wealth held in these assets" ^[1] This equates to an average of the average returns on a portfolio taking into account what portion of the portfolio each individual return represents.

Example

rate of return on a mining stock also called r_m equals 10%
rate of return on a child care centre also called r_c equals 8%
rate of return on a fishing company also called r_f equals 12%

Now assume that 40% of the portfolio is in the mining stock (weighting for this stock also called A_m), 40% is in the child care centre (weighting for this stock also called A_c) and the remaining 20% is in the fishing company (weighting for this stock also called A_f). To determine the rate of return on this portfolio, multiply the weighting of each asset by its rate of return and add these figures together:

for the mining stock, its weighting is 40% and its rate of return is 10% so it equals 40% x 10% = .04 = 4%
for the child care centre, its weighting is 40% and its rate of return is 8% so it equals 40% x 8% = .032 = 3.2%
for the fishing company, its weighting is 20% and its rate of return is 12% so it equals 20% x 12% = .024 = 2.4%

Adding these percentages gives 4% + 3.2% + 2.4% = 9.6% therefore the rate of return on this portfolio = 9.6%

Mathematically this whole process may be written as r_p = A_mr_m + A_cr_c + A_fr_f where r_p equals the rate of return on the portfolio.

References

^ Levy,A 2009, ECON331 'Uncertainty, risky assets (activities) and portfolio choice', lecture notes accessed 22 May 2009 elearning.uow.edu.au