Uncertainty about signals and price impact

Every model will have signal noise or uncertainty, and every model will have imprecise impact uncertainty from trading. This is a certainty because any training set will have to be imperfect. Hence, we should expect performance problems due to parameter uncertainty. Modelers should take this into account in their work. 

First, the model’s Sharpe ratio will be lower than expected from what is generated from the training set. There will be estimation error and model misspecification. Second, the model will affect transaction costs, with the impact being greater for smaller and less liquid stocks. Notably, weak signals will have less impact on trading costs, while strong signals will have a greater impact on trading costs. See “Trading with Uncertainty about signals and price impact”.

How do you solve these problems? One way to solve the problem is to define a reference model and then assess the costs associated with variations from it. The uncertainty can be managed to lock in a reasonable Sharpe around the reference level. The math in this paper is not easy, but the key is to be aware of the problem and to place bounds on what is possible.  

Beta is sensitive to the level of risk aversion

We have just written about the impact of changing beta. See There is no one beta - It changes across regimes. This is not new information, but researchers have taken a deeper look at the issue and have found some interesting relationships. Another paper that has found an interesting beta relationship is “Risk Appetite and (Mis)Pricing”. It has examined some beta portfolios conditional on high and low risk aversion. The risk aversion index was developed in prior research and is not new, but it has not been used in this type of study.

The results are strong and very thought-provoking. In a high-risk aversion environment, the researchers find a positive relationship between beta and returns. In contrast, in a low-risk aversion environment, there is a slight negative relationship between beta and returns. This can help explain why we do not find the usual CAPM relationship in the data. When risk aversion is high, the market risk premium idominatesother factors that may create distortions, such as sentiment. When risk aversion is low, mispricing becomes more important, and there is a positive relationship with a positive intercept. The study carefully examines the evidence and finds that risk aversion plays a key role in determining whether the CAPM holds or fails. When aversion to risk is low, sentiment-driven mispricing will be the key driver of returns and will offset the market risk premium effect.

 

"Look at your fish" - same with market prices

There is importance in looking closely at the things we study. There is an old parable from Samuel Scudder called "Look at your fish". The story can best be described in "The Student, the Fish, and Agassiz," a 19th-century educational parable in which Harvard professor Louis Agassiz forces a student to study a dead fish for days, using only observation and sketching, to teach that true knowledge comes from intense, firsthand examination. It emphasizes finding "general laws" through detail.

The same process can be applied to markets. We can start with price charts. Look at your charts. Look at the prices, but just don't look once; look deeply into what the markets may be saying. Then, after looking at the prices, look at the news surrounding the prices. This does not mean that everything has to have a pattern, but for any analysis, the first order of business is looking at the data. 

See before starting to analyze. 

There is no one beta - It changes across regimes

 

An interesting but simple paper, “Your Beta Is Wrong Regime-Dependent Alpha & Beta for Major Asset Classes”, explores the issue of regime-dependent beta. Your beta is not stationary, so alpha will not be stable but will move with the regime. This does not mean that you should calculate beta on a rolling basis; assume that beta is regime-dependent, and when the regime changes, so does the beta. Below are two examples of significant changes in beta. One shows silver, and the other is for Alphabet, one of the classic Mag 7 stocks. 

Do not assume there is one beta for any asset. This may seem obvious, but when seen in a distribution, the numbers are stark.