Expected Value of Return 🔮
In finance, we can never be 100% sure about the future. Will the market boom, crash, or stay stagnant? Since we don't have a crystal ball, we use Probability to estimate what the likely return will be. This weighted average of all possible future outcomes is called the Expected Value of Return.
1. Meaning of Expected Return
The Expected Return (E(R)) is the average return an investor anticipates receiving in the future, based on various possible scenarios and their likelihood of occurrence. It is the central pillar of investment decision-making under uncertainty.
Key Insight: Expected return is a "forecast," not a guarantee. It represents the "mean" of a distribution of possible returns.
2. Probability Distribution of Returns
A probability distribution is a list of possible outcomes (Returns) and the chance (Probability) of each one happening.
- Total Probability must always equal 1.0 (or 100%).
Example Distribution:
| Economic Scenario | Probability (Pi) | Possible Return (Ri) |
|---|---|---|
| Boom | 0.20 (20%) | 25% |
| Normal | 0.50 (50%) | 12% |
| Recession | 0.30 (30%) | -5% |
3. Calculation of Expected Return
The formula for Expected Return is the sum of each outcome multiplied by its probability:
E(R) = Σ (Pi * Ri)
Where:
- Pi: Probability of scenario i.
- Ri: Return in scenario i.
4. Problems on Expected Return
Problem 1: Single Security Return
Using the table from the "Probability Distribution" section above, calculate the expected return for the investment.
Solution:
| Scenario | Pi | Ri | Pi * Ri |
|---|---|---|---|
| Boom | 0.20 | 25 | 5.0 |
| Normal | 0.50 | 12 | 6.0 |
| Recession | 0.30 | -5 | -1.5 |
| Total | 1.00 | 9.5% |
The Expected Return E(R) is 9.5%.
Problem 2: Choosing between Two Stocks
Stock A has a 60% chance of 15% return and a 40% chance of 5% return. Stock B has a 50% chance of 20% return and a 50% chance of 0% return. Which stock has a higher expected return?
Solution for Stock A: E(Ra) = (0.60 * 15) + (0.40 * 5) = 9 + 2 = 11%
Solution for Stock B: E(Rb) = (0.50 * 20) + (0.50 * 0) = 10 + 0 = 10%
Stock A has a higher expected return (11%) compared to Stock B (10%).
Comparison: Historical vs. Expected Return
| Feature | Historical (Realized) Return | Expected Return |
|---|---|---|
| Data Basis | Past performance (Actual results) | Future scenarios (Probabilities) |
| Certainty | 100% Certain (Known) | Uncertain (Estimated) |
| Primary Use | Reporting & Evaluation | Decision-making & Selection |
Summary
- Expected Return is the weighted average of all possible future returns.
- It requires defining scenarios (e.g., Bear/Bull market) and assigning probabilities.
- The sum of all Pi * Ri gives the expected return.
- It is the foundation for calculating Risk (Standard Deviation) which we will learn later.
Quiz Time! 🎯
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