Beta Portfolio Calculator
This tool calculates the overall beta of your investment portfolio. Portfolio beta is the weighted average of the individual betas of the assets within the portfolio. It measures the portfolio's sensitivity to overall market movements.
Enter the Beta and the corresponding Weight (e.g., dollar value or percentage) for each asset in your portfolio. Ensure you use consistent units for all weights. Add rows as needed for all your holdings.
Enter Portfolio Assets
Understanding Beta and Portfolio Beta
What is Beta?
Beta (β) is a measure of the volatility—or systematic risk—of a security or portfolio compared to the market as a whole. Systematic risk is the non-diversifiable risk that affects the entire market, not just a specific company or industry.
- A beta of **1.0** indicates that the security's price will move with the market.
- A beta **less than 1.0** means the security is theoretically less volatile than the market.
- A beta **greater than 1.0** means the security is theoretically more volatile than the market.
- A beta of **0** means the security's price is uncorrelated with the market (like cash or a risk-free asset).
- A **negative beta** means the security's price moves in the opposite direction to the market (very rare, e.g., some derivatives).
What is Portfolio Beta?
Portfolio beta is the weighted average of the individual betas of all assets in the portfolio. It provides a single number indicating the portfolio's sensitivity to market risk. A higher portfolio beta suggests higher systematic risk but potentially higher returns in a rising market; a lower beta suggests lower systematic risk but potentially lower returns, especially beneficial in a falling market.
Portfolio Beta Formula
The formula is a simple weighted average:
Portfolio Beta = Σ (Asset Beta * Asset Weight) / Σ (Asset Weight)
Where:
- Σ (Asset Beta * Asset Weight) is the sum of each asset's beta multiplied by its weight.
- Σ (Asset Weight) is the sum of all asset weights (the total portfolio value).
The weights can be dollar values, percentages, or any consistent unit representing the proportion of each asset in the total portfolio value.
Beta Portfolio Calculation Examples
Click on an example to see the calculation details:
Example 1: Simple 2-Asset Portfolio
Scenario: Calculate the portfolio beta for a simple portfolio with two stocks.
Assets:
- Stock A: Beta = 1.2, Weight = $10,000
- Stock B: Beta = 0.8, Weight = $10,000
1. Calculate Weighted Beta Sum:
(1.2 * $10,000) + (0.8 * $10,000) = $12,000 + $8,000 = $20,000
2. Calculate Total Weight:
$10,000 + $10,000 = $20,000
3. Calculate Portfolio Beta:
$20,000 / $20,000 = 1.0
Conclusion: This portfolio has a beta of 1.0, suggesting it will move roughly in line with the market.
Example 2: Unequal Weights
Scenario: Calculate the portfolio beta with different allocations.
Assets:
- Stock X: Beta = 1.5, Weight = $5,000
- Stock Y: Beta = 0.5, Weight = $15,000
1. Calculate Weighted Beta Sum:
(1.5 * $5,000) + (0.5 * $15,000) = $7,500 + $7,500 = $15,000
2. Calculate Total Weight:
$5,000 + $15,000 = $20,000
3. Calculate Portfolio Beta:
$15,000 / $20,000 = 0.75
Conclusion: With a beta of 0.75, this portfolio is expected to be less volatile than the market.
Example 3: Including Cash (Beta = 0)
Scenario: Calculate the portfolio beta when including a cash position.
Assets:
- Stock Z: Beta = 1.3, Weight = $8,000
- Cash: Beta = 0, Weight = $2,000
1. Calculate Weighted Beta Sum:
(1.3 * $8,000) + (0 * $2,000) = $10,400 + $0 = $10,400
2. Calculate Total Weight:
$8,000 + $2,000 = $10,000
3. Calculate Portfolio Beta:
$10,400 / $10,000 = 1.04
Conclusion: The cash position lowered the portfolio beta from what it would be if only Stock Z was held ($10,400 / $8,000 = 1.3).
Example 4: Portfolio of Just Cash
Scenario: What is the beta of a portfolio consisting entirely of cash?
Assets:
- Cash: Beta = 0, Weight = $50,000
1. Calculate Weighted Beta Sum:
(0 * $50,000) = $0
2. Calculate Total Weight:
$50,000
3. Calculate Portfolio Beta:
$0 / $50,000 = 0
Conclusion: A portfolio of cash has a beta of 0, meaning it has no systematic market risk.
Example 5: Portfolio with Negative Beta Asset
Scenario: Calculate the portfolio beta including a rare negative beta asset.
Assets:
- Stock Q: Beta = 1.1, Weight = $7,000
- Asset R: Beta = -0.5, Weight = $3,000
1. Calculate Weighted Beta Sum:
(1.1 * $7,000) + (-0.5 * $3,000) = $7,700 - $1,500 = $6,200
2. Calculate Total Weight:
$7,000 + $3,000 = $10,000
3. Calculate Portfolio Beta:
$6,200 / $10,000 = 0.62
Conclusion: The negative beta asset helps lower the overall portfolio beta, providing a hedge against market downturns.
Example 6: Using Percentages as Weights
Scenario: Calculate portfolio beta using percentage allocations.
Assets:
- Stock A: Beta = 1.2, Weight = 40%
- Stock B: Beta = 0.8, Weight = 60%
1. Calculate Weighted Beta Sum:
(1.2 * 40) + (0.8 * 60) = 48 + 48 = 96
2. Calculate Total Weight:
40 + 60 = 100
3. Calculate Portfolio Beta:
96 / 100 = 0.96
Conclusion: Using percentages or dollar values yields the same beta result if consistent.
Example 7: Portfolio of 3 Stocks
Scenario: Calculate portfolio beta for three different stocks.
Assets:
- Stock M: Beta = 0.9, Weight = $20,000
- Stock N: Beta = 1.4, Weight = $30,000
- Stock P: Beta = 1.0, Weight = $50,000
1. Calculate Weighted Beta Sum:
(0.9 * $20,000) + (1.4 * $30,000) + (1.0 * $50,000) = $18,000 + $42,000 + $50,000 = $110,000
2. Calculate Total Weight:
$20,000 + $30,000 + $50,000 = $100,000
3. Calculate Portfolio Beta:
$110,000 / $100,000 = 1.10
Conclusion: This portfolio has a slightly higher beta than the market.
Example 8: Portfolio with a Low Beta Stock
Scenario: Including a stable stock with a low beta.
Assets:
- Stock S: Beta = 0.4, Weight = $15,000
- Stock T: Beta = 1.2, Weight = $25,000
1. Calculate Weighted Beta Sum:
(0.4 * $15,000) + (1.2 * $25,000) = $6,000 + $30,000 = $36,000
2. Calculate Total Weight:
$15,000 + $25,000 = $40,000
3. Calculate Portfolio Beta:
$36,000 / $40,000 = 0.90
Conclusion: The presence of Stock S (Beta 0.4) helps lower the portfolio's overall beta compared to a portfolio solely of Stock T.
Example 9: Portfolio Heavily Weighted in High Beta
Scenario: A portfolio with most capital in high beta assets.
Assets:
- Stock U: Beta = 1.8, Weight = $80,000
- Stock V: Beta = 0.7, Weight = $20,000
1. Calculate Weighted Beta Sum:
(1.8 * $80,000) + (0.7 * $20,000) = $144,000 + $14,000 = $158,000
2. Calculate Total Weight:
$80,000 + $20,000 = $100,000
3. Calculate Portfolio Beta:
$158,000 / $100,000 = 1.58
Conclusion: The portfolio beta is significantly higher than 1, indicating higher market risk.
Example 10: Portfolio Heavily Weighted in Low Beta
Scenario: A portfolio with most capital in low beta assets.
Assets:
- Stock W: Beta = 0.6, Weight = $70,000
- Stock Z: Beta = 1.3, Weight = $30,000
1. Calculate Weighted Beta Sum:
(0.6 * $70,000) + (1.3 * $30,000) = $42,000 + $39,000 = $81,000
2. Calculate Total Weight:
$70,000 + $30,000 = $100,000
3. Calculate Portfolio Beta:
$81,000 / $100,000 = 0.81
Conclusion: The portfolio beta is significantly lower than 1, indicating lower market risk.
Frequently Asked Questions about Portfolio Beta
1. What is Portfolio Beta?
Portfolio Beta is the weighted average beta of all assets within a portfolio. It measures the portfolio's sensitivity to overall market movements, indicating its systematic risk.
2. How is Portfolio Beta calculated?
It's calculated using the formula: Portfolio Beta = Σ (Asset Beta * Asset Weight) / Σ (Asset Weight). You multiply each asset's beta by its weight (value or percentage), sum these products, and then divide by the sum of all weights (total portfolio value).
3. What does a Portfolio Beta of 1 mean?
A portfolio beta of 1 suggests the portfolio's value is expected to move up or down in line with the overall market.
4. What does a Portfolio Beta greater than 1 mean?
A beta greater than 1 indicates the portfolio is expected to be more volatile than the market. It might see larger gains in a rising market but also larger losses in a falling market.
5. What does a Portfolio Beta less than 1 mean?
A beta less than 1 suggests the portfolio is expected to be less volatile than the market. It might lag the market in gains but also experience smaller losses during downturns.
6. Can Portfolio Beta be negative?
Yes, although rare, a portfolio can have a negative beta if it contains assets (like some derivatives or short positions) that are expected to move inversely to the market. A negative beta portfolio would generally increase in value when the market falls.
7. Do I use dollar values or percentages for the asset weights?
You can use either, as long as you are consistent across all assets in the same calculation. Using dollar values is often simpler if you know the current market value of each holding. The calculator will work correctly with either.
8. How does cash affect Portfolio Beta?
Cash is considered to have a beta of 0 (it's uncorrelated with market movements). Including cash in a portfolio will lower the overall portfolio beta, reducing its sensitivity to market risk.
9. Why is Portfolio Beta important?
Portfolio beta helps investors understand the systematic risk of their portfolio. It's a key input in portfolio management and asset allocation decisions, helping investors align their portfolio's risk profile with their risk tolerance.
10. Does Beta account for all risks?
No, Beta only measures systematic risk (market risk). It does not account for unsystematic risk (specific risk related to individual assets or industries), which can often be reduced through diversification.
