大浩浩的笔记课堂——FRM考试学习笔记134

Topic 63 The Low-Risk Anomaly and Alpha

1.Low-risk anomaly:

⑴definition:

It violates the CAPM and suggests that low beta stocks will outperform high-beta stocks.

⑵comparison:

Higher risk,as measured by beta,should have a higher return.But in the low-risk anomaly,firms with lower betas and lower volatility have higher returns over time.

⑶explanations:

①The potential explanations for the risk anomaly are:

data mining:

It is not well supported.

②investor constraints(leverage):

leverage constraints on retail investors(that drive them to buy pre-leveraged investment in the form of high-beta stocks)

③institutional manager constraints:

institutional investor constraints such as prohibitions against short selling or tracking error tolerance bands

④preference theory:

the preferences of investors

2.Formulas related to alpha:

3.Benchmark selection for alpha:

⑴If the benchmark is riskier than the investment in question,then both the alpha and the information ratio will be too low.

⑵The best combination for a benchmark is for it to be well-defined,tradable,replicable and adjusted for the risk of the underlying pool of investments.

4.Fundamental law of active management:

⑴formula:

A tradeoff between the number of investment bets placed(breath) and the required degree of forecasting accuracy(information coefficient):

⑵investor:

①place a large number of bets and not be very concerned with forecasting accuracy

②need to be very good at forecasting if he places only a small number of bets

5.Factors regression and portfolio sensitivity:

⑴models:

①traditional capital asset pricing model:

Only accounts for co-movement with a market index.

②multifactor models:

To enhance the informational value of regression output.

⑵Fama-French 3-factor model:

①formula:

A.(R_M-R_F):CAPM single factor model

B.SMB:size premium

C.HML:value premium

②explanation:

A momentum effect could also be added to help explain excess returns.

6.Measurement of time-varying factors:

⑴Style analysis is a form of factor benchmarking where the factor exposures evolve over time.

⑵The traditional Fama-French 3-factor model can be improved by using indices that are tradable,such as the SPDR S＆P value ETF (SPYV) and incorporating time-varying factors that change over time.

7.Issues with alpha measurement for nonlinear strategies:

⑴Alpha is computed using regression,which operates in a linear 

framework.So there are nonlinear strategies that can make it appear that alpha exists when it actually does not.

⑵This 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.

8.Volatility and beta anomalies:

They 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.

大浩浩的笔记课堂之FRM考试学习笔记合集