Statistical Measures of Asset Returns (With Easy Formulas!)
Understanding the statistical measures of asset returns is essential for any investor. These measures help you evaluate risk, reward, and how assets behave in different market conditions.
Let’s explore the key metrics with easy-to-use formulas you can copy directly into your blog!
1️⃣ Mean (Expected Return)
The mean is the average return you can expect from an asset over a period.
Formula:
-
R̄ = Mean return
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Rᵢ = Return in period i
-
n = Number of periods
This tells you the typical return you might expect.
2️⃣ Variance (σ²)
Variance measures how much returns fluctuate around the mean — a key indicator of risk.
Formula:
3️⃣ Standard Deviation (σ)
Standard deviation is the square root of variance, giving you a measure of risk in the same units as returns.
Formula:
4️⃣ Sharpe Ratio
The Sharpe Ratio measures the risk-adjusted return — how much return you get per unit of risk.
Formula:
-
Rf = Risk-free rate (e.g., return on government bonds)
A higher Sharpe Ratio means better reward for risk taken.
5️⃣ Covariance
Covariance shows how two assets move together — do they rise and fall in sync, or move in opposite directions?
Formula:
6️⃣ Correlation (ρ)
Correlation standardizes covariance between -1 and +1, helping you quickly see the relationship between two assets.
Formula:
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σₓ and σᵧ = Standard deviations of X and Y
A correlation of:
-
+1 means perfect positive relationship
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0 means no relationship
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-1 means perfect negative relationship
7️⃣ Beta (β)
Beta measures an asset’s sensitivity to market movements. It tells you if an asset is more or less volatile than the market.
Formula:
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β < 1: Less volatile than the market
📈 Quick Example: Stock ABC
Let’s say you have the following monthly returns for Stock ABC:
| Month | Return (%) |
|---|---|
| 1 | 5 |
| 2 | -2 |
| 3 | 4 |
| 4 | 3 |
| 5 | 6 |
✅ The mean return is:
✅ The variance is approximately:
✅ The standard deviation is:
✅ The Sharpe Ratio (assuming risk-free rate = 1%):
✅ The beta can be calculated if you know the market returns!
🎯 Final Thoughts
These statistical measures are the foundation for understanding risk and return in finance. Whether you’re managing a single stock or a diversified portfolio, knowing these numbers helps you make smarter investment decisions.
