LO 64.9: Describe potential explanations for the risk anomaly.

LO 64.9: Describe potential explanations for the risk anomaly.
A comprehensive explanation for the risk anomaly is elusive. It has been speculated that the true explanation is some combination of data mining, investor leverage constraints, institutional manager constraints, and preference theory.
Some academics have wondered if the risk anomaly is the result of data mining. Ang et al. (2006) found that the risk anomaly appears during both recessions and expansions. Frazzini and Pedersen (2014)6 found that low beta portfolios have high Sharpe ratios in U.S. stocks, international stocks, Treasury bonds, and corporate bonds. Cao and Flan (2013)7 also found evidence of the risk anomaly in option and commodity markets. The argument of data mining is not well supported.
Another possible explanation is the prevalence of leverage constrained investors. This is sometimes an occurrence with institutional investors, but it is very much a constraint of retail investors. Since certain investors are leverage constrained, meaning that they cannot borrow funds for investing, they choose to invest in stocks with built-in leverage in the form of high betas. The additional demand for high-beta stocks will bid up their respective prices until the assets are overvalued and they deliver a decreased risk-adjusted return with regard to lower beta stocks. This same theory works to lower the prices of low beta stocks and, therefore, results in higher risk-adjusted returns due to lower entry prices.
Institutional managers also have constraints that could help to explain the risk anomaly. Consider a scenario with two competing portfolios. Portfolio A has positive alpha because the portfolio is undervalued, while Portfolio B has a negative alpha because it is overvalued. In a perfect world, an investor would buy (go long) Portfolio A and short sell Portfolio B to capture the perceived alphas. Many institutional investors will have constraints against short selling. Most also have tracking error constraints that only permit a specified deviation from their benchmark. Under either of these constraints, an institutional investor would not be able to capture the alpha that they think exists. One solution for the tracking error constraint is to change the benchmark or the tracking error tolerance bands, but this can be a difficult process requiring formal approval from the investment committee of the fund.
Sometimes investors simply have a preference for high-volatility and high-beta stocks. This could occur because their capital market expectations are very bullish, so they want to amplify their returns. The end result is that investors buy the higher-beta investments and bid up their prices to the point where future returns will be much lower. There will always be a group of investors that desire to shun safe and boring lower-volatility stocks. The good news is that this creates less emotionally driven entry points for long-term investors who desire lower volatility.
6. Andrea Frazzini and Lasse Heje Pederson, Betting Against Beta, The Journal o f Financial
Economics 111, no. 1 (2014): 1-25. Jie Cao and Bing Han, Cross Section of Option Returns and Idiosyncratic Stock Volatility, The Journal o f Financial Economics 108, no. 1 (2013): 231-A9.
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Topic 64 Cross Reference to GARP Assigned Reading – Ang, Chapter 10
Investors holding heterogeneous preferences (disagreeing on investment potential) and having investment constraints could explain a portion of the risk anomaly. Hong and Sraer (2012)8 found that when disagreement is low and investors are long-only constrained, then the CAPM holds the best. When disagreement is high, some investments become overpriced and future returns are decreased. Significant disagreement can lead to an inverse relationship between beta and returns.
Harrison Hong and David Sraer, Speculative Betas, NBER Working Paper 18548, November 2012.
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Topic 64 Cross Reference to GARP Assigned Reading – Ang, Chapter 10
Ke y Co n c e pt s
LO 64.1 The capital asset pricing model (CAPM) states that there should be a positive relationship between risk and return. Higher risk, as measured by beta, should have a higher return. The low-risk anomaly appears to suggest the exact opposite. This anomaly finds that firms with lower betas and lower volatility have higher returns over time.
LO 64.2 Alpha is the average performance of an investor in excess of their benchmark. Excess return is often called active return, and the standard deviation of the active return is known as tracking error.
The ratio of active return to tracking error is called the information ratio, which is one way to easily rank competing investment alternatives.
If an investor is using the risk-free rate as their benchmark, then their alpha is any return earned in excess of the risk-free rate, and the best risk-adjusted return measurement is the Sharpe ratio.
Sharpe ratio =
LO 64.3 A benchmark is very important for investment comparisons. If the benchmark is riskier than the investment in question, then both the alpha and the information ratio will be too low. The best combination for a benchmark is for it to be well-defined, tradeable, replicable, and adjusted for the risk of the underlying pool of investments.
LO 64.4 Grinolds fundamental law of active management suggests a tradeoff between the number of investment bets placed (breadth) and the required degree of forecasting accuracy (information coefficient).
I R r s I C x Vb R
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Topic 64 Cross Reference to GARP Assigned Reading – Ang, Chapter 10
An investor either needs to place a large number of bets and not be very concerned with forecasting accuracy, or he needs to be very good at forecasting if he places only a small number of bets.
LO 64.5 The traditional capital asset pricing model only accounts for co-movement with a market index. Multifactor models, like the Fama and French three-factor model, add other explanatory factors in an attempt to better predict the alpha for an asset. Multifactor models have been shown to enhance the informational value of regression output. The Fama-French three-factor model is expressed as:
Ri – RF – a + (3i>MKT x (Rm R f ) + 3i,SMB x (SMB) + 3i?HML x (HML)
This model adds a size premium (SMB) and a value premium (HML) to the CAPM single-factor model. A momentum effect (UMD) could also be added to help explain excess returns. This factor suggests that upward trending stocks will continue their upward movement while downward moving stocks will continue their downward trend.
LO 64.6 Style analysis is a form of factor benchmarking where the factor exposures evolve over time. The traditional Fama-French three-factor model can be improved by using indices that are tradeable, such as the SPDR S&P Value ETF (SPYV), and incorporating time-varying factors that change over time.
LO 64.7 Alpha is computed using regression, which operates in a linear framework. There are nonlinear strategies that can make it appear that alpha exists when it actually does not. This situation is encountered when payoffs are quadratic terms or option-like terms. This may be a significant problem for hedge funds because merger arbitrage, pairs trading, and convertible bond arbitrage strategies all have nonlinear payoffs.
LO 64.8 The volatility anomaly and the beta anomaly both agree that stocks with higher risk, as measured by either high standard deviation or high beta, produce lower risk-adjusted returns than stocks with lower risk.
LO 64.9 A comprehensive explanation for the risk anomaly is elusive. It has been speculated that the true explanation is some combination of data mining, investor leverage constraints, institutional manager constraints, and preference theory.
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Topic 64 Cross Reference to GARP Assigned Reading – Ang, Chapter 10
Co n c e pt Ch e c k e r s
Which of the following statements is correct concerning the relationship between the low-risk anomaly and the capital asset pricing model (CAPM)? A. The low-risk anomaly provides support for the CAPM. B. The notion that the low-risk anomaly violates the CAPM has not been proven
C. The low-risk anomaly violates the CAPM and suggests that low-beta stocks will
D. Both CAPM and the low-risk anomaly point to a positive relationship between
outperform high-beta stocks.
risk and reward.
Which of the following statements is not a characteristic of an appropriate benchmark? An appropriate benchmark should be: A. B. C. well-defined. D. equally applied to all risky assets irrespective of their risk exposure.
tradeable. replicable.
Grinolds fundamental law of active management suggests that: A.
investors should focus on increasing only their predictive ability relative to stock price movements.
B. sector allocation is the most important factor in active management. C. a small number of investment bets decreases the chances of making a mistake
and, therefore, increases the expected investment performance.
D. to maximize the information ratio, active investors need to either have high- quality predictions or place a large number of investment bets in a given year.
Why would an investor include multiple factors in a regression study?
I. To attempt to improve the adjusted R2 measure. II. To reduce the r-stat value on the respective regression coefficients. A. I only. B. II only. C. Both I and II. D. Neither I nor II.
Which of the following characteristics is a potential explanation for the risk anomaly? A. Investor preferences. B. The presence of highly leveraged retail investors. C. Lack of short selling constraints for institutional investors. D. Lack of tracking error constraints for institutional investors.
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Topic 64 Cross Reference to GARP Assigned Reading – Ang, Chapter 10
Co n c e pt Ch e c k e r An s w e r s
1. C The low-risk anomaly violates the CAPM and suggests that low beta stocks will outperform
high-beta stocks. This has been empirically proven with several studies. The CAPM points to a positive relationship between risk and reward, but the low-risk anomaly suggests an inverse relationship.
2. D An appropriate benchmark should be well-defined, replicable, tradeable, and risk-adjusted. If the benchmark is not on the same risk scale as the assets under review, then there is an unfair comparison.
3. D Grinolds fundamental law of active management focuses on the tradeoff of high quality predictions relative to placing a large number of investment bets. Investors can focus on either action to maximize their information ratio, which is a measure of risk-adjusted performance. While sector allocation is a very important component of the asset allocation decision, Grinold focused only on the quality of predictions and the number of investment bets made.
4. A An investor should consider adding multiple factors to the regression analysis to potentially improve the adjusted R2 measurement, potentially increase the tests of statistical significance, and to search for a benchmark that is more representative of a portfolio s investment style.
5. A Potential explanations for the risk anomaly include: the preferences of investors, leverage
constraints on retail investors that drive them to buy pre-leveraged investments in the form of high-beta stocks, and institutional investor constraints like prohibitions against short selling and tracking error tolerance bands.
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The following is a review of the Risk Management and Investment Management principles designed to address the learning objectives set forth by GARP. This topic is also covered in:
Il l i q u i d A s s e t s
Topic 65
Ex a m Fo c u s
This topic examines illiquid asset market characteristics and the relationship between illiquidity and market imperfections. Reported return biases are discussed as well as the illiquidity risk premium within and across asset classes. For the exam, understand that all markets, even highly liquid markets such as commercial paper, can be illiquid at some points in time. Also, know the three biases that impact reported returns of illiquid asset classes (survivorship bias, sample selection bias, and infrequent sampling). Finally, understand the factors that influence the decision to include illiquid asset classes in a portfolio.
Il l iq u id As s e t M a r k e t s

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