FRM Exam Part II · Alpha (and the Low-Risk Anomaly)

Low-Volatility and Betting-Against-Beta Strategies Explained

Updated 11 October 2026 · Fact-checked

The low-risk anomaly is exploited in two main ways. A low-volatility or minimum-variance portfolio holds low-risk stocks long-only. Betting against beta goes long leveraged low-beta assets and short high-beta assets, scaled so net beta is zero. Both face turnover, sector bias and factor exposure issues.

Understand Exploiting the Anomaly: Strategies and Implementation

The low-risk anomaly says low-beta or low-volatility stocks have earned returns higher than CAPM predicts, while high-beta stocks have earned less. Exploiting it means building a portfolio that tilts toward low risk and then living with the practical side effects.

There are two routes. The first is a long-only low-volatility portfolio. You rank stocks by volatility or beta and hold the lowest group, or you build a minimum variance portfolio that uses the covariance matrix to get the lowest total portfolio volatility. The result usually has beta below 1 and a lower drawdown than the market. It is easy to hold, but it does not remove market risk.

The second route is betting against beta (BAB). You go long low-beta assets and short high-beta assets. Because low-beta assets have small market exposure, you lever the long side up and scale the short side down so each leg has beta of 1 in the BAB construction. The net portfolio is then market-neutral. This isolates the beta effect, but it needs borrowing and shorting.

A minimum variance portfolio and a low-beta portfolio are not the same. Low beta ranks stocks on market sensitivity only. Minimum variance uses volatility and correlations together, so it can hold a stock with high beta if it diversifies well. Minimum variance also depends heavily on the estimated covariance matrix, which is noisy.

Practical issues matter for the exam. Low-risk portfolios tend to concentrate in sectors such as utilities, consumer staples and financials. They load on other factors, such as value, quality and negative momentum or interest-rate sensitivity. Rebalancing creates turnover and transaction costs, and constraints on weights and sectors are often added to control this. Leverage in BAB brings funding cost, margin and crash risk when low-beta assets fall sharply.

Key formulas to remember

Beta of a portfolio: β_p = Σ w_i × β_i; Weights include leverage and shorts. Short positions carry negative weights.
BAB leverage on the long leg: Long leverage = 1 ÷ β_L; Scales the low-beta basket to beta of 1. Needs borrowing, so the leveraged amount is financed at the funding rate.
BAB short leg scaling: Short size = 1 ÷ β_H; The high-beta basket is scaled down to beta of 1 before shorting.
BAB portfolio return: r_BAB = (1 ÷ β_L)(r_L − r_f) − (1 ÷ β_H)(r_H − r_f); Net beta is zero by construction. The risk-free terms matter because the long leg is financed.
Minimum variance weights (fully invested, no constraints): w = Σ⁻¹ 1 ÷ (1ᵀ Σ⁻¹ 1); Σ is the covariance matrix. Weights depend on estimated covariances, so estimation error matters.
Two-asset minimum variance weight in asset 1: w₁ = (σ₂² − ρσ₁σ₂) ÷ (σ₁² + σ₂² − 2ρσ₁σ₂); Valid when short selling is allowed. Weights can be negative if correlation is high.

How to solve Exploiting the Anomaly: Strategies and Implementation questions

Use this order for most questions on low-risk strategy implementation.

1Identify the strategy: long-only low-vol, minimum variance, low beta, or betting against beta.
2Note what is given: betas, volatilities, correlations, returns and the risk-free rate.
3For BAB, compute the scaling for each leg as 1 ÷ beta and check the net beta equals zero.
4Compute the return, remembering to subtract the risk-free rate on the leveraged long leg and the short leg scaling.
5For minimum variance, use the weight formula or compare portfolio variances, and say it depends on covariance estimates.
6Name the implementation issue the question points to: turnover, sector concentration, factor exposure, leverage or funding.
7State the interpretation: what risk is removed, what remains, and what could go wrong.
8Check the answer against the options for sign and size before choosing.

Quickest way: Beta-neutral check in 30 seconds

When to use it: Use for any BAB calculation or a question asking whether a portfolio is market-neutral.

Write long leverage as 1 ÷ β_L and short size as 1 ÷ β_H.
Multiply each by its beta: both give 1, so net beta is 1 − 1 = 0.
Compute excess returns of each leg over the risk-free rate.
Apply the scaling and subtract the short leg from the long leg.
If asked about risk, link low-vol tilts to sector bias and BAB to leverage and funding.

Common mistakes in Exploiting the Anomaly: Strategies and Implementation

Treating minimum variance and low beta as the same thing.
Both produce low-risk portfolios, so they look alike.
Fix: Low beta ranks on market sensitivity alone. Minimum variance uses full covariances and can hold higher-beta stocks that diversify.
Forgetting the risk-free rate in BAB returns.
Students use raw returns instead of excess returns.
Fix: Subtract r_f from each leg before scaling. Leverage is financed at the funding rate.
Saying a long-only low-vol portfolio is market-neutral.
Low beta is confused with zero beta.
Fix: It still has positive beta, usually below 1. Only BAB with matched scaling targets zero net beta.
Ignoring sector and factor bias.
Focus stays on the beta number.
Fix: Remember low-risk portfolios tilt to defensive sectors and load on other factors such as value and quality, so alpha may partly be factor return.
Assuming the strategy has low turnover and no cost.
Low volatility sounds stable.
Fix: Betas and volatilities change, so rebalancing creates turnover. Constraints can reduce it at some cost to the tilt.
Scaling the short leg up instead of down.
Students apply the same leverage to both legs.
Fix: The long leg has beta below 1, so it is levered up. The short leg has beta above 1, so its size is cut by 1 ÷ β_H.

Worked examples

Example 1

A BAB strategy is long a low-beta basket with β_L = 0.5 and short a high-beta basket with β_H = 1.5. The risk-free rate is 2%. The low-beta basket returns 8% and the high-beta basket returns 10%. Find the long leverage, short size, net beta and BAB return.

Show the solution

Long leverage = 1 ÷ 0.5 = 2.0.
Short size = 1 ÷ 1.5 = 0.6667.
Net beta = 2.0 × 0.5 − 0.6667 × 1.5 = 1.0 − 1.0 = 0.
Long leg excess return = 8% − 2% = 6%. Scaled: 2.0 × 6% = 12%.
Short leg excess return = 10% − 2% = 8%. Scaled: 0.6667 × 8% = 5.333%.
BAB return = 12% − 5.333% = 6.667%.

Answer: Long leverage 2.0, short size 0.6667, net beta 0, BAB return about 6.67%.

Example 2

Two assets have volatilities of 10% and 20%, and correlation 0. Short selling is allowed and weights sum to 1. What weight in the 10% volatility asset gives the minimum variance portfolio, and what is that portfolio's volatility?

Show the solution

With ρ = 0, w₁ = σ₂² ÷ (σ₁² + σ₂²).
σ₁² = 0.01 and σ₂² = 0.04, so w₁ = 0.04 ÷ 0.05 = 0.8.
w₂ = 0.2.
Variance = 0.8² × 0.01 + 0.2² × 0.04 = 0.0064 + 0.0016 = 0.008.
Volatility = √0.008 = 0.08944, about 8.94%.

Answer: Weight 80% in the 10% volatility asset; portfolio volatility about 8.94%, below either asset alone.

Exam tips

Expect applied questions asking you to pick the right implementation issue: turnover, sector concentration, leverage or factor exposure.
In BAB questions, always scale by 1 ÷ beta and use excess returns.
Know that minimum variance relies on estimated covariances and that estimation error is a weakness.
When asked why low-risk returns may not be pure alpha, point to loadings on other factors and sector tilts.
Remember leverage risk: funding costs and sharp losses when low-beta assets are sold off.

Practice questions from Alpha (and the Low-Risk Anomaly)

Exploiting the Anomaly: Strategies and Implementation: frequently asked questions

How do I build a low volatility portfolio?

Rank stocks by trailing volatility or beta and hold the lowest group, or use covariances to find the minimum variance weights. Add sector and weight caps to limit concentration and turnover. Rebalance on a schedule and monitor factor exposures.

Why does betting against beta need leverage?

Low-beta assets have little market exposure, so their absolute return is small. Leverage scales the long leg to a beta of 1 so it matches the short leg. This makes the portfolio market-neutral and isolates the low-beta premium.

What is the difference between a minimum variance and a low beta portfolio?

A low beta portfolio selects on market sensitivity only. A minimum variance portfolio minimises total volatility using volatilities and correlations, so it can include higher-beta stocks. It also depends more on covariance estimates.

What are the main practical problems in exploiting the low-risk anomaly?

Turnover and transaction costs, sector bias toward defensive industries, loadings on other factors, and for BAB, leverage and funding constraints. These can reduce or explain part of the apparent return.