<p>Consider <span class="math-container">$\mathbf{r} = (r_1, r_2 ... r_n)$</span> to be the vector of expected returns - i.e., <span class="math-container">$r_i$</span> represents the expected annual return for asset class <span class="math-container">$i$</span></p>
<p>Consider <span class="math-container">$\mathbf{w} = (w_1, w_2 ... w_n)$</span> to be the vector of allocation weights - i.e., <span class="math-container">$w_i$</span> represents the weight of asset class <span class="math-container">$i$</span> within your portfolio, such that <span class="math-container">$\sum\limits_{i=1}^{n}w_i =1$</span></p>
<p>Then the expected return of your portfolio is <span class="math-container">$ \mathbf{r} \cdot \mathbf{w} = \sum\limits_{i=1}^{n}r_iw_i$</span></p>
<p>More concisely, it will be the weighted average of the average returns for each asset class, where the weights are the allocation within the portfolio.</p>

CC BY-SA 4.0
2024-12-08T19:19:49.717Z
I like your answer but it does assume that the allocation within the portfolio is constant. However,  it is implied by the problem that it is constant.
Bob
CC BY-SA 4.0
2024-11-08T08:51:06.270Z
2024-11-08T08:51:06.270Z
shgwani2804
<p>&quot;I have 20 years of returns for stocks, bonds, and real estate, and I need to calculate the expected return from this data. I have both the annual returns and the allocation information. How can I calculate the expected return?&quot; <a href="https://i.sstatic.net/F0bhYJhV.png" rel="nofollow noreferrer"><img src="https://i.sstatic.net/F0bhYJhV.png" alt="enter image description here" /></a></p>

<stock-market><portfolio-theory>
portfolio expected return how
Batsaikhan Uransanaa
# portfolio expected return how

(Asked by: username_0 on 2024-11-07)

"I have 20 years of returns for stocks, bonds, and real estate, and I need to calculate the expected return from this data. I have both the annual returns and the allocation information. How can I calculate the expected return?" [![enter image description here](https://i.sstatic.net/F0bhYJhV.png)](https://i.sstatic.net/F0bhYJhV.png)

**Tags:** stock-market, portfolio-theory


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## 1 answers

### Answer by username_1 on 2024-11-08. Score: 0

Consider $\mathbf{r} = (r\_1, r\_2 ... r\_n)$ to be the vector of expected returns - i.e., $r\_i$ represents the expected annual return for asset class $i$

Consider $\mathbf{w} = (w\_1, w\_2 ... w\_n)$ to be the vector of allocation weights - i.e., $w\_i$ represents the weight of asset class $i$ within your portfolio, such that $\sum\limits\_{i=1}^{n}w\_i =1$

Then the expected return of your portfolio is $ \mathbf{r} \cdot \mathbf{w} = \sum\limits\_{i=1}^{n}r\_iw\_i$

More concisely, it will be the weighted average of the average returns for each asset class, where the weights are the allocation within the portfolio.

> **Comments:**
> **username_2**: I like your answer but it does assume that the allocation within the portfolio is constant. However,  it is implied by the problem that it is constant.  

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