## Implications Across Portfolios

Read this section and learn more about risk and return, implications across portfolios, and the beta coefficient for portfolios. Why are these topics important to businesses? The answer is contained in this section. This section discusses how a beta coefficient compares how much a particular stock fluctuates in value daily.

### 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.

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.

A Fruitful Portfolio: How would you calculate the expected return on this portfolio?

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:

$E(R_Q)=∑^{n}_{i=1}w_i∙R_i$

What does this equal?

$∑^{n}_{i=1}w_i$

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.

Source: Boundless