# Calculating Expected Portfolio Returns

## A portfolio's expected return is the sum of the weighted average of each asset'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.

#### Terms

• 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.

#### Figures

1. ##### A Fruitful Portfolio

How would you calculate the expected return on this portfolio?

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.

Figure 1

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:

$E(R_{FMP}) = W_{A}(A*E(R_{A}))+W_{B}(B*E(R_{B}))+W_{C}(C*E(R_{C}))$

Where A stands for apple, B is banana, C is cherry and FMP is farmer’s market portfolio. W is weight and E(RX) 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:

$E(R_{FMP})=1.1$

In reality, a portfolio is not a fruit basket, and neither is the formula. A math-heavy formula for calculating the expected return on a portfolio, Q, of n assets would be:

$E(R_{Q}) =\sum_{ i=1 }^{ n }{ { w }_{ i }\bullet { R }_{ i } }$

What does this equal?

$\sum _{ i=1 }^{ n }{ { w }_{ i } }$

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 Glossary

asset
Something or someone of any value; any portion of one's property or effects so considered.
##### Appears in these related concepts:
diversifiable risk
the potential for loss which can be removed by investing in a variety of assets
##### Appears in these related concepts:
expected return
Considering the magnitude and likelihood of exogenous events, the yield that an investor predicts s/he will earn on average.
##### Appears in these related concepts:
Expected Return
The expected return of a potential investment can be computed by computing the product of the probability of a given event and the return in that case and adding together the products in each discrete scenario.
##### Appears in these related concepts:
investment
A placement of capital in expectation of deriving income or profit from its use.
##### Appears in these related concepts:
portfolio
The group of investments and other assets held by an investor.
##### Appears in these related concepts:
the price above par value at which a security is sold
##### Appears in these related concepts:
return
Gain or loss from an investment.
##### Appears in these related concepts:
risk
The potential (conventionally negative) impact of an event, determined by combining the likelihood of the event occurring with the impact, should it occur.
##### Appears in these related concepts:
Risk
The potential that a chosen action or activity (including the choice of inaction) will lead to a loss (an undesirable outcome).
##### Appears in these related concepts:
A risk premium is the minimum amount of money by which the expected return on a risky asset must exceed the known return on a risk-free asset, or the expected return on a less risky asset, in order to induce an individual to hold the risky asset rather than the risk-free asset.
##### Appears in these related concepts:
strategy
A plan of action intended to accomplish a specific goal
##### Appears in these related concepts:
weighted average
An arithmetic mean of values biased according to agreed weightings.
##### Appears in these related concepts:
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.