Implications Across Portfolios
buttons.Calculating Expected Portfolio Returns
A portfolio's expected return is the sum of the weighted average of each asset's expected return.
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. We now understand that diversifiable risk doesn't pay a risk premium, so we try to eliminate it.
| Fruit | Investment | Expected Return | Weight |
|---|---|---|---|
| Apples | $50,000 | 12% | 0.5 |
| Bananas | $25,000 | 6% | 0.25 |
| Cherries | $25,000 | 10% | 0.25 |
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:
\(E(R_{FMP})=W_A(A∗E(R_A))+W_B(B∗E(R_B))+W_C(C∗E(R_C))\)
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 independently, 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:
\(E(RQ)=∑_{i=1}^n w_i ∙ R_i \)
What does this equal?
\(∑_{i=1}^n w_i\)
Remember that we are assuming 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 various challenges to this model with valid points.
Remember, the market is random: it is not a roulette wheel, but that
might be the best thing to compare it to.
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.
Source: Boundless Finance, https://ftp.worldpossible.org/endless/eos-rachel/RACHEL/RACHEL/modules/en-boundless-static/www.boundless.com/finance/textbooks/boundless-finance-textbook/introduction-to-risk-and-return-8/implications-across-portfolios-80/index.html
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