How To Calculate Variance Of A Stock In Excel

Calculate the variance of stock returns in Excel format with this interactive tool

Complete Guide: How to Calculate Variance of a Stock in Excel

Understanding stock variance is crucial for investors and financial analysts. Variance measures how far a set of numbers (in this case, stock prices) are spread out from their average value. This guide will walk you through calculating stock variance in Excel, including both population and sample variance methods.

Why Calculate Stock Variance?

• Measures volatility and risk of a stock
• Helps in portfolio diversification decisions
• Essential for options pricing models
• Used in technical analysis and trading strategies

Step-by-Step Guide to Calculate Variance in Excel

1. Prepare Your Data

   Enter your stock prices in a single column. For example:

   Date	Price
   Day 1	100
   Day 2	102
   Day 3	105
   Day 4	103
   Day 5	107

2. Calculate the Mean (Average)

   Use the AVERAGE function: =AVERAGE(B2:B6)

   For our example, this would return 103.4

3. Calculate Each Price’s Deviation from Mean

   Create a new column for deviations:

   Price	Deviation from Mean
   100	-3.4
   102	-1.4
   105	1.6
   103	-0.4
   107	3.6

4. Square Each Deviation

   Add another column for squared deviations:

   Deviation	Squared Deviation
   -3.4	11.56
   -1.4	1.96
   1.6	2.56
   -0.4	0.16
   3.6	12.96

5. Calculate Variance

   For population variance (all data points):

   =VAR.P(B2:B6) or manually: =SUM(D2:D6)/COUNT(B2:B6)

   For sample variance (estimating from sample):

   =VAR.S(B2:B6) or manually: =SUM(D2:D6)/(COUNT(B2:B6)-1)

Population vs Sample Variance

Aspect	Population Variance	Sample Variance
Definition	Variance of entire population	Estimate from sample data
Excel Function	VAR.P()	VAR.S()
Denominator	N (number of data points)	N-1 (Bessel’s correction)
Use Case	When you have all data points	When estimating from partial data

Real-World Example: S&P 500 Variance

Let’s examine the variance of S&P 500 monthly returns over 5 years:

Year	Mean Return	Population Variance	Sample Variance
2018	0.52%	0.0023	0.0024
2019	1.87%	0.0018	0.0019
2020	1.25%	0.0089	0.0092
2021	2.11%	0.0021	0.0022
2022	-1.32%	0.0065	0.0067

Advanced Techniques

1. Rolling Variance

   Calculate variance over a moving window to identify changing volatility:

   =VAR.S(B2:B11) (for 10-day rolling variance)

2. Logarithmic Returns

   For more accurate financial calculations:

   =LN(B3/B2) for daily log returns

3. Annualized Variance

   Convert daily variance to annual:

   =VAR.S(daily_returns)*252 (for trading days)

Authoritative Resources

For deeper understanding, consult these academic resources:

• U.S. Securities and Exchange Commission – Investment Calculators
• Corporate Finance Institute – Variance Guide
• NYU Stern – Historical Stock Returns Data

Common Mistakes to Avoid

• Confusing population and sample variance formulas
• Using arithmetic returns instead of logarithmic returns for multi-period calculations
• Not adjusting for trading days when annualizing variance
• Ignoring outliers that can skew variance calculations
• Using price data instead of return data for variance calculation

Excel Shortcuts for Variance Calculations

Task	Excel Function	Keyboard Shortcut
Population Variance	=VAR.P()	Alt+M+V+P
Sample Variance	=VAR.S()	Alt+M+V+S
Standard Deviation (Population)	=STDEV.P()	Alt+M+S+P
Standard Deviation (Sample)	=STDEV.S()	Alt+M+S+S
Average	=AVERAGE()	Alt+M+A

Interpreting Variance Results

Understanding what your variance calculation means:

• Low Variance (0.001-0.01): Stable stock with predictable returns (e.g., blue-chip stocks)
• Medium Variance (0.01-0.04): Moderate volatility (e.g., growth stocks)
• High Variance (0.04+): Highly volatile (e.g., penny stocks, cryptocurrencies)

Variance in Portfolio Management

Variance plays a crucial role in modern portfolio theory:

1. Diversification: Combining assets with low correlation can reduce portfolio variance
2. Risk Assessment: Variance is a key component of Value at Risk (VaR) calculations
3. Asset Allocation: Helps determine optimal mix of assets based on risk tolerance
4. Performance Evaluation: Used in Sharpe ratio and other risk-adjusted return metrics

Alternative Methods to Calculate Variance

While Excel is powerful, consider these alternatives:

• Python (Pandas): df['returns'].var()
• R: var(stock_returns)
• Google Sheets: Same functions as Excel (=VAR.P(), =VAR.S())
• Financial Calculators: TI-84 has variance functions under STAT menu

Historical Variance Trends

Market variance tends to follow economic cycles:

Economic Period	Typical S&P 500 Variance	Characteristics
Expansion	0.0015-0.0030	Low volatility, steady growth
Peak	0.0030-0.0050	Increasing volatility as growth slows
Recession	0.0050-0.0120	High volatility, negative returns
Recovery	0.0040-0.0060	Decreasing volatility as economy stabilizes