The rate of return on a portfolio is "a weighted average

Weighted mean

The weighted mean is similar to an arithmetic mean , where instead of each of the data points contributing equally to the final average, some data points contribute more than others...

 of the rates of return

Rate of return

In finance, rate of return , also known as return on investment , rate of profit or sometimes just return, is the ratio of money gained or lost on an investment relative to the amount of money invested. The amount of money gained or lost may be referred to as interest, profit/loss, gain/loss, or...

 on the various assets with the weights being equal to the fractions of the individual's wealth held in these assets" This equates to an average of the average returns on a portfolio

Portfolio

Portfolio literally means "a case for carrying loose papers," ....

  taking into account what portion of the portfolio each individual return represents.

Example

• rate of return on a mining
  Mining
  Mining is the extraction of valuable minerals or other geological materials from the earth, from an ore body, vein or seam. The term also includes the removal of soil. Materials recovered by mining include base metals, precious metals, iron, uranium, coal, diamonds, limestone, oil shale, rock...
  
   stock also called r_m equals 10%
• rate of return on a child care
  Childcare
  Child care means caring for and supervising child/children usually from 0–13 years of age. In the United States child care is increasingly referred to as early childhood education due to the understanding of the impact of early experiences of the developing child...
  
   centre also called r_c equals 8%
• rate of return on a fishing
  Fishing
  Fishing is the activity of trying to catch wild fish. Fish are normally caught in the wild. Techniques for catching fish include hand gathering, spearing, netting, angling and trapping....
  
  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.