Alpha
Alpha
The excess return of an investment relative to the return predicted by CAPM for its level of systematic risk. Positive alpha indicates outperformance above risk-adjusted expectations, while negative alpha indicates underperformance. Calculated as: α = R_portfolio - [R_f + β(R_market - R_f)].
A mutual fund with a beta of 1.2 returns 15% annually. If the risk-free rate is 3% and the market returns 12%, CAPM predicts 13.8%. The fund's alpha is +1.2% (15% - 13.8%), indicating the manager added value beyond market exposure.
Students often confuse alpha with total return. Alpha measures only the excess return above what CAPM predicts for the portfolio's risk level, not the total return itself. A portfolio can have high total returns but negative alpha if it underperformed relative to its beta.
How This Is Tested
- Calculating alpha given actual return, risk-free rate, beta, and market return
- Interpreting positive vs. negative alpha as outperformance vs. underperformance
- Understanding that alpha measures manager skill beyond market movements
- Recognizing that alpha is risk-adjusted (accounts for systematic risk via beta)
- Comparing funds using alpha to evaluate manager performance net of risk
Calculation Example
α = R_portfolio - [R_f + β(R_market - R_f)] - Calculate expected return: R_f + β(R_market - R_f)
- Substitute values: 3% + 1.2(12% - 3%)
- Calculate market risk premium: 12% - 3% = 9%
- Multiply by beta: 1.2 × 9% = 10.8%
- Add risk-free rate: 3% + 10.8% = 13.8%
- Calculate alpha: 15% - 13.8% = +1.2%
Example Exam Questions
Test your understanding with these practice questions. Select an answer to see the explanation.
Jennifer, a portfolio manager at a large investment firm, is being evaluated for her annual performance review. Her equity portfolio returned 18% over the past year. The portfolio has a beta of 1.3, the market returned 14%, and Treasury bills yielded 2%. Her supervisor wants to determine if Jennifer truly added value beyond simply taking on market risk. What is the most accurate assessment of Jennifer's performance?
B is correct. To evaluate Jennifer's true skill, we calculate alpha: Expected return = R_f + β(R_market - R_f) = 2% + 1.3(14% - 2%) = 2% + 1.3(12%) = 2% + 15.6% = 17.6%. Alpha = 18% - 17.6% = +0.4%. This positive alpha indicates Jennifer added modest value (40 basis points) beyond what CAPM predicted for her portfolio's risk level.
A is misleading because comparing total return to market return (18% vs 14%) ignores the portfolio's higher beta of 1.3, which should have produced higher returns simply from market exposure. C is incorrect because beta of 1.3 is not necessarily "excessive" and the positive alpha shows she performed well for that risk level. D is incorrect because she generated positive alpha, not zero.
The Series 65 exam tests your ability to evaluate manager performance using risk-adjusted measures like alpha. Understanding that total outperformance alone doesn't indicate skill is critical for making appropriate recommendations to clients seeking skilled active managers versus passive market exposure.
What does a portfolio alpha of -2.5% indicate about a manager's performance relative to CAPM expectations?
C is correct. Negative alpha of -2.5% means the portfolio's actual return was 2.5 percentage points below what CAPM predicted based on the portfolio's beta (systematic risk). This indicates the manager underperformed risk-adjusted expectations, suggesting poor security selection or market timing after accounting for market exposure.
A is incorrect because alpha measures excess return relative to expectations, not absolute loss (a portfolio could have +10% return but -2.5% alpha if CAPM predicted +12.5%). B is incorrect because alpha doesn't measure the difference in beta values. D is incorrect because alpha doesn't measure volatility differences; standard deviation or beta would measure risk.
The Series 65 exam frequently tests your ability to interpret alpha values correctly. Understanding that negative alpha indicates underperformance relative to risk-adjusted expectations is essential for evaluating whether to retain or terminate active managers.
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Access Free BetaA growth fund with a beta of 1.4 generated a return of 20% over the past year. During the same period, the S&P 500 returned 14% and 10-year Treasury notes yielded 2%. What is the fund's alpha?
C is correct. Calculate using the alpha formula: α = R_portfolio - [R_f + β(R_market - R_f)]
Step 1: Calculate expected return using CAPM:
Expected return = R_f + β(R_market - R_f)
Expected return = 2% + 1.4(14% - 2%)
Expected return = 2% + 1.4(12%)
Expected return = 2% + 16.8%
Expected return = 18.8%
Step 2: Calculate alpha:
Alpha = Actual return - Expected return
Alpha = 20% - 18.8%
Alpha = +3.2%
The positive alpha of 3.2% indicates the fund manager outperformed CAPM expectations by 320 basis points, suggesting skilled security selection beyond simply taking on market risk.
A (+1.2%) results from calculation errors. B (+2.0%) incorrectly uses the risk-free rate in the calculation. D (+6.0%) confuses alpha with the total outperformance versus market (20% - 14% = 6%), which ignores the portfolio's higher beta.
Alpha calculation questions test your ability to apply CAPM to evaluate manager performance. The Series 65 exam expects you to compute expected returns using beta, then determine if actual returns exceeded or fell short of risk-adjusted expectations.
All of the following statements about alpha are accurate EXCEPT
C is correct (the EXCEPT answer). Alpha is NOT calculated by simply subtracting the risk-free rate from total return. The correct formula is α = R_portfolio - [R_f + β(R_market - R_f)], which subtracts the CAPM-predicted return (not just the risk-free rate) from actual return.
A is accurate: alpha measures excess return above CAPM expectations. B is accurate: positive alpha suggests manager skill beyond market exposure. D is accurate: alpha is risk-adjusted because the CAPM expected return incorporates beta (systematic risk).
The Series 65 exam tests your ability to distinguish alpha from other performance measures. Understanding the correct calculation prevents confusing alpha with simpler metrics like excess return over the risk-free rate, which doesn't account for market risk.
A mutual fund has a beta of 0.8, generated a 10% return over the past year, while the market returned 12% and Treasury bills yielded 3%. Which of the following statements about this fund are accurate?
1. The fund has positive alpha
2. The fund underperformed the market on a total return basis
3. The fund's expected return based on CAPM was 10.2%
4. The fund is appropriate for risk-averse investors seeking market exposure
D is correct. Statements 2, 3, and 4 are accurate.
Statement 1 is FALSE: Expected return = R_f + β(R_market - R_f) = 3% + 0.8(12% - 3%) = 3% + 0.8(9%) = 3% + 7.2% = 10.2%. Alpha = 10% - 10.2% = -0.2%. The fund has NEGATIVE alpha, not positive.
Statement 2 is TRUE: The fund returned 10% while the market returned 12%, so it underperformed on a total return basis by 2 percentage points.
Statement 3 is TRUE: As calculated above, CAPM expected return = 10.2%.
Statement 4 is TRUE: The beta of 0.8 indicates the fund is less volatile than the market (defensive), making it potentially suitable for risk-averse investors who still want equity market exposure with lower volatility.
The Series 65 exam tests detailed understanding of how alpha, beta, and total returns interact. Recognizing that a fund can underperform the market on total return while still having appropriate risk characteristics for certain clients demonstrates comprehensive performance evaluation skills.
💡 Memory Aid
Alpha = "Added value" - What the manager contributed BEYOND what the market gave them for taking risk. Think: "A+ for positive alpha, F for negative alpha." Beta measures the risk taken, alpha measures if the manager earned their fees.
Related Concepts
This term is part of this cluster:
More in Risk & Performance Metrics
Where This Appears on the Exam
This term is tested in the following Series 65 exam topics: