$$$$
Calculating the Rate of Return in a Portfolio
The expected rate of return on a portfolio is determined using a different approach than the one used for the rate of return of a single security. Since the portfolio contains multiple securities, each security’s individual return must be calculated first. The portfolio’s overall return is then determined as the weighted average return of all the securities in the portfolio.
Category: Expected Portfolio Returns
$$
\text{Expected Return} = (R_1 \times W_1) + (R_2 \times W_2) + \ldots + (R_n \times W_n)
$$
Where:
- R = The expected return on a particular security
- W = The weight or proportion of the portfolio held in the security, based on its dollar value
- n = The number of securities in the portfolio
Here’s a visual representation in Mermaid:
pie title Portfolio Breakdown
"ABC Co." : 60
"DEF Co." : 40
Example Calculation
Let’s illustrate this with an example. Suppose a client invests $100 in two securities: $60 in ABC Co. and $40 in DEF Co. The expected returns from these securities are 15% and 12% respectively.
Step-by-step Calculation
Because the total investment amount is $100, ABC Co. represents 60% of the portfolio, and DEF Co. represents 40% of the portfolio. These proportions can be calculated as follows:
-
ABC Co.:
$$
\frac{60}{100} = 0.60 , (or , 60% )
$$
-
DEF Co.:
$$
\frac{40}{100} = 0.40 , (or , 40% )
$$
Using these proportions, we can calculate the expected return for the portfolio as:
-
Expected Return from ABC Co.:
$$
0.15 \times 0.60 = 0.09 , (or , 9% )
$$
-
Expected Return from DEF Co.:
$$
0.12 \times 0.40 = 0.048 , (or , 4.8% )
$$
Adding these together gives us the total expected portfolio return:
$$
\text{Expected Return} = 0.09 + 0.048 = 0.138 , (or , 13.8% )
$$
Therefore, the expected rate of return for the portfolio is 13.8%.
Key Takeaways
- The rate of return for a portfolio is calculated as a weighted average of the returns for the individual securities it contains.
- The weight of each security in the portfolio is determined based on the proportion of the total portfolio value that the money invested in the security represents.
- The expected return provides an indication of the portfolio’s overall performance.
Frequently Asked Questions
Q: Why do we use weighted averages in portfolio returns?
A: Weighted averages account for the varying proportions of different securities in the portfolio, providing a more accurate reflection of overall performance.
Q: Can the weights (percentages) of securities change over time?
A: Yes, as the values of individual securities change, their proportions within the portfolio also change. Periodic rebalancing may be required to maintain the desired asset allocation.
Glossary and Definitions
- Rate of Return (RoR): The net gain or loss on an investment, expressed as a percentage of the initial investment cost.
- Weighted Average: A calculation method where each value in a set is multiplied by a weighted factor reflecting its proportion within the set.
- Rebalancing: The process of adjusting the weights of securities in a portfolio to maintain a desired asset allocation.
For a deeper understanding, consult the Canadian Securities Course materials and additional financial literature.
📚✨ Quiz Time! ✨📚
## What is the formula used to calculate the expected return on a portfolio?
- [ ] Sum of individual returns of each security in the portfolio
- [ ] Average of the returns of each security in the portfolio
- [x] Weighted average return of all the securities in the portfolio
- [ ] Difference between the highest and lowest returns in the portfolio
> **Explanation:** The expected return on a portfolio is calculated as the weighted average return of all the securities held in the portfolio. Each security's return is multiplied by its weight in the portfolio, and these products are summed to get the portfolio's overall expected return.
## In the formula for the expected return of a portfolio, what does 'R' represent?
- [x] The expected return on a particular security
- [ ] The proportion (weight) of the portfolio held in the security
- [ ] The total return of the portfolio
- [ ] The number of securities in the portfolio
> **Explanation:** In the formula for the expected return of a portfolio, 'R' represents the expected return on a particular security.
## In the formula for the expected return of a portfolio, what does 'W' represent?
- [ ] The expected return on a particular security
- [x] The proportion (weight or %) of the portfolio held in the security based on the dollar value of the security
- [ ] The total return of the portfolio
- [ ] The number of securities in the portfolio
> **Explanation:** 'W' represents the proportion (weight or percentage) of the portfolio held in a specific security based on the dollar value of that security.
## How do you calculate the weight of a security in the portfolio?
- [x] By dividing the dollar value of the security by the total portfolio value
- [ ] By adding the individual security returns
- [ ] By averaging the security prices
- [ ] By subtracting the security's cost from its return
> **Explanation:** The weight of a security in a portfolio is calculated by dividing the dollar value of the security by the total value of the portfolio.
## If a portfolio consists of two investments, one with a 15% return and another with a 12% return, what is the expected return if $60 is invested in the first and $40 in the second?
- [ ] 12.0%
- [x] 13.8%
- [ ] 14.5%
- [ ] 15.0%
> **Explanation:** The expected return can be calculated using the formula. Here, 60% of the portfolio is invested in the first security and 40% in the second. Thus, expected return = (0.15 * 0.60) + (0.12 * 0.40) which equals 13.8%.
## What do you need to first calculate to determine the expected return on the whole portfolio?
- [ ] The dividend yield of each security
- [ ] The market value of each security
- [ ] The purchase price of each security
- [x] The return generated by each security
> **Explanation:** To determine the expected return on the whole portfolio, you must first calculate the return generated by each individual security.
## How do you denote the number of securities in the portfolio in the formula for expected portfolio return?
- [x] 'n'
- [ ] 'R'
- [ ] 'W'
- [ ] 'P'
> **Explanation:** In the formula, 'n' denotes the number of securities in the portfolio.
## What is the key difference in calculating the expected return of a portfolio versus a single security?
- [ ] Single security returns do not require weighting.
- [x] The portfolio return is a weighted average of individual security returns.
- [ ] Portfolio returns are always higher.
- [ ] Single security returns involve compounding.
> **Explanation:** The key difference is that the portfolio return is a weighted average of the individual security returns whereas for a single security, you only calculate the direct return without any weighting.
## If a security represents 40% of a portfolio, and the expected return is 12%, what is the contribution of this security to the portfolio's expected return?
- [ ] 12%
- [ ] 40%
- [x] 4.8%
- [ ] 6%
> **Explanation:** The contribution to the portfolio's expected return is calculated by multiplying the security's expected return by its weight in the portfolio i.e., 0.12 * 0.40 = 4.8%.
## In the example provided, if ABC Co. earned a return of 10% instead of 15%, what would the new expected return of the portfolio be?
- [ ] 10%
- [ ] 12%
- [x] 11.2%
- [ ] 13.8%
> **Explanation:** With ABC Co. returning 10%, the calculation would be: (0.10 * 0.60) + (0.12 * 0.40) = 0.06 + 0.048 = 0.108 = 10.8%.