This Expected Return Calculator helps you determine the potential returns and associated risks for two different stocks. By inputting probabilities and expected returns, you can calculate the expected return, variance, and standard deviation for each stock. It’s a useful tool for evaluating the performance and risk of investments in various market conditions.
Formulas and Calculations: A Detailed Explanation
Calculating expected return involves summing the weighted average of all possible outcomes, where each outcome is weighted by its probability of occurring.
The formula for Expected Return is as follows:
\(\text{Expected Return} = \sum P_i \times R_i\)Where:
- Pi is the probability of outcome i
- Ri is the return for outcome i
In addition to calculating the expected return, it’s essential to assess the investment’s risk through variance and standard deviation.
The formula for Variance is:
\(\text{Variance} = \sum P_i \times (R_i – \text{Expected Return})^2\)Variance helps measure the spread of possible returns, while Standard Deviation is simply the square root of variance, providing a direct measure of volatility:
The formula for Standard Deviation is:
\(\text{Standard Deviation} = \sqrt{\text{Variance}}\)How to Interpret Your Expected Return Results
Here’s how you can interpret the key metrics calculated from your expected return results:
| Metric | High Value Interpretation | Low Value Interpretation |
|---|---|---|
| Expected Return | Potential for high profits but with risk | Stable but possibly lower returns |
| Variance | Greater dispersion, more volatile returns | Less dispersion, more predictable returns |
| Standard Deviation | High volatility, riskier investment | Lower volatility, safer investment |
What is Expected Return and Why Is It Important?
Expected Return represents:
- The potential profit or loss based on the probabilities of different outcomes.
- An estimate of how much return can be expected from an investment over time.
Why It’s Important:
- Benchmarking: Expected return provides a benchmark for comparing different assets.
- Goal Alignment: It helps assess whether an investment aligns with the investor’s goals and risk tolerance.
- Risk-Return Balance: Higher expected returns often indicate greater potential profits but also come with higher risk.
- Decision-Making: Understanding expected return aids in constructing a balanced and diversified portfolio.
Expected Return vs. Actual Return: What’s the Difference?
The difference between expected and actual return can be explained as follows:
| Metric | Expected Return | Actual Return |
|---|---|---|
| Definition | Forecasted average return based on probabilities | The return realized over a specific period |
| Nature | Forward-looking, estimated | Retrospective, based on actual performance |
| Impact of Market | Can be affected by market changes but is theoretical | Directly impacted by market conditions |
| Example | Expected return: 7% | Actual return: 5% due to market downturn |
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