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Calculating Expected Portfolio Returns
A portfolio's expected return is the sum of the weighted average of each asset's expected return.
Learning Objective

Calculate a portfolio's expected return
Key Points

To calculate the expected return of a portfolio, you need to know the expected return and weight of each asset in a portfolio.

The figure is found by multiplying each asset's weight with its expected return, and then adding up all those figures at the end.

These estimates are based on the assumption that what we have seen in the past is what we can expect in the future, and ignores a structural view on the market.
Term

weighted average
In statistics, a weighted average is an average that takes each object and calculates the product of its weight and its figure and sums all of these products to produce one average. It is implied that all the individual weights add to 1.
Full Text
Let's say that we have a portfolio that consists of three assets, and we'll call them Apples, Bananas, and Cherries. We decided to invest in all three, because the previous chapters on diversification had a profound impact on our investment strategy, and we now understand that diversifiable risk doesn't pay a risk premium, so we try to eliminate it.
The return of our fruit portfolio could be modeled as a sum of the weighted average of each fruit's expected return. In math, that means:
Where A stands for apple, B is banana, C is cherry and FMP is farmer's market portfolio. W is weight and E(R_{X}) is the expected return of X. A good exercise would be to calculate this figure on your own, then look below to see if you completed it accurately.
Here's what you should get:
In reality, a portfolio is not a fruit basket, and neither is the formula. A mathheavy formula for calculating the expected return on a portfolio, Q, of n assets would be:
What does this equal?
Remember that we are making the assumption that we can accurately measure these outcomes based on what we have seen in the past. If you were playing roulette at a casino, you may not know if red or black (or green) is coming on the next spin, but you could reasonably expect that if you bet on black 4000 times in a row, you're likely to get paid on about 1900 of those spins. If you go to Wikipedia, you can review a wide variety of challenges to this model that have very valid points. Remember, the market is random: it is not a roulette wheel, but that might be the best thing we have to compare it to.
Key Term Reference
 Assets
 Appears in this related concepts: What is a Financial Statement?, Defining a LongLived Asset, and Secured vs Unsecured Funding
 asset
 Appears in this related concepts: Introduction to the Balance Sheet, What is a Balance Sheet, and The Demand for Money
 diversifiable risk
 Appears in this related concepts: Defining the Security Market Line and The Capital Asset Pricing Model
 expected return
 Appears in this related concepts: Expected Return, Types of Financial Decisions: Investment and Financing, and Arbitrage Pricing Theory
 investment
 Appears in this related concepts: The Upper Class, Agencies, and Shifts in investment due to shocks
 portfolio
 Appears in this related concepts: Impact of Inflation, Overview of Warrants, and FamaFrench ThreeFactor Model
 premium
 Appears in this related concepts: The Term Structure, The Freemium Model, and Health Insurance
 return
 Appears in this related concepts: Dollar Returns, Finance, Economics, and Accounting: Differences and Commonalities, and Disadvantages of the Payback Method
 risk
 Appears in this related concepts: The ExportImport Bank of the United States, Portfolio Risk, and Defining Risks in Capital Budgeting
 risk premium
 Appears in this related concepts: Understanding Future Stock Value, Measuring and Managing Risk, and The Value of Diversification
 strategy
 Appears in this related concepts: Making Strategy Effective, Defining Strategic Planning, and Strategic Planning
Sources
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Cite This Source
Source: Boundless. “Calculating Expected Portfolio Returns.” Boundless Finance. Boundless, 03 Jul. 2014. Retrieved 26 May. 2015 from https://www.boundless.com/finance/textbooks/boundlessfinancetextbook/introductiontoriskandreturn8/implicationsacrossportfolios80/calculatingexpectedportfolioreturns3493894/