Overview Overview

Price action is always in a random walk, so no quantitative strategy can cover all price actions. Different quantitative strategies or asset allocations are suitable for different market conditions. For example, grid trading is more suitable for volatile market conditions. The purpose of this article is to introduce more diverse analysis models to investors, so that investors can have more choices and judgments in the random changes in the market.

Report report

Report report

Introduction to Multifactor Models
The multi-factor model has become the mainstream method of investment practice, and has superior performance in measuring and controlling risks.

• In investing, factors refer to the common characteristics among the returns of different assets. Multi-factor models are used by investors for asset portfolio construction, portfolio management, risk management, and attribution analysis. Compared with the single factor model, the explanatory power of the multifactor model is stronger and more flexible. Multifactor models can help investors:

• Build asset portfolios to track specified indices or characteristics

• Adjust the exposure of the portfolio under the identified risk category

• Attributing risk and return to active investment management

• Understand the comprehensive risk exposure of large categories of assets such as equity and fixed income

• Active investment decisions based on specified benchmarks and measure the market capacity for that decision

Ensure that the risk-return of the investor's asset portfolio matches its cost

The origin of the multifactor model

In 1952, Markowitz proposed a new framework for constructing securities investment portfolios. Different from treating different securities separately in the past, this framework comprehensively considers the return and risk characteristics of different securities. This is the well-known Modern Portfolio Theory (MPT) . Markowitz assumes that the returns of different securities obey a normal distribution. The core conclusion of the theory is that as long as the correlation between the two given assets is not 1, the risk can be diversified by allocation of different proportions. In 1964, Sharp introduced the Capital Asset Pricing Model (CAPM) based on mean-variance theory. CAPM theory and related literature have brought some new concepts to investors, such as systematic risk. Systematic risk is the key to understanding multi-factor models, each asset has different kinds of risk, but these risks are not equally important. The theory holds that risk can be reduced by adjusting the proportion of different assets on the premise that the expected return remains unchanged. However, systemic risk cannot be diversified, so this part of risk has a corresponding return requirement. In the CAPM theory, the systematic risk of an asset is an increasing function of its beta value, which measures the sensitivity of asset returns to market returns. According to the CAPM theory, the asset return value is related to a factor, that is, the market return. The higher the systematic risk, the higher the beta value, and the higher the required return. But a lot of data show that the CAPM theory provides an incomplete description of risk. Modeling asset returns will be more effective if a model takes more systematic risk into account. Thus the multifactor model was born.

Types of Multifactor Models

According to the type of factor can be divided into 3 categories

macro factor model
Factors represent unexpected changes in macroeconomic variables that can significantly affect returns. Taking equity as an example, the main consideration is the factors that affect future cash flow and discount rate. For example, interest rates, inflation risk, business cycles, and credit spreads.

Macrofactor models assume that factor returns depend on unexpected changes in some macroeconomic variable, such as inflation or real output. The unexpected change is defined as the difference between the actual value and the predicted value. The unexpected change of a factor is the component of the factor's unexpected return, and the unexpected changes of all factors constitute the independent variables of the model. For example, the risk premium of the GDP growth rate factor is positive, but the risk premium of the inflation rate factor is negative. Therefore, if the sensitivity of an asset to the inflation rate factor is evidence, then as the inflation rate rises, the expected return on the asset will decrease, and this type of asset has a good anti-inflation feature.

Inflation rate and GDP growth factor matrix

Fundamental Factor Model

Factor principal represents the main factors that explain the cross-sectional variance of securities. For example, book-to-market ratio, even, price-to-earnings ratio, and leverage ratio.

statistical factor model

By making statistics on the historical performance of securities and extracting the main factors affecting the return. The main factor statistical models include factor analysis model and principal component analysis model. In a factor analysis model, factors adequately explain the covariance of historical returns. In a PCA model, factors can adequately explain the variance of historical returns.

Among them, principal component analysis (PCA) is a commonly used method for constructing statistical factor models, the purpose is to find uncorrelated factors, and make the observed security returns can be well explained by the linear combination of factor returns. For complex combinations of multiple securities, PCA can effectively reduce dimensions and filter noise, and extract fewer factors to perform linear regression. Principal component analysis is a statistical method for dimensionality reduction. It transforms the original random vector whose components are related into a new random vector whose components are uncorrelated by means of an orthogonal transformation, which is expressed algebraically as the original random vector The covariance matrix of the transformation is transformed into a diagonal matrix, which is geometrically expressed as transforming the original coordinate system into a new orthogonal coordinate system, making it point to the p orthogonal directions where the sample points are scattered the most, and then reducing the multi-dimensional variable system. Dimensional processing, so that it can be transformed into a low-dimensional variable system with a higher precision, and then the low-dimensional system can be further transformed into a one-dimensional system by constructing an appropriate value function.

The main role of principal component analysis
1. Principal component analysis reduces the dimensionality of the data space under study. That is, replace the p-dimensional X space with the m-dimensional Y space (m
2. Sometimes some relationship among X variables can be clarified through the conclusion of factor loading aij.
3. A graphical representation of multidimensional data. We know that geometric figures cannot be drawn when the dimension is greater than 3, and most of the problems in multivariate statistical research have more than 3 variables. It is impossible to represent the research question graphically. However, after principal component analysis, we can select the first two principal components or one of the two principal components, and draw the distribution of n samples on a two-dimensional plane according to the scores of the principal components, which can be seen intuitively from the graph The status of each sample in the principal component can be obtained, and then the samples can be classified, and the outliers far away from most sample points can be found by the graph.
4. The regression model was constructed by principal component analysis. That is, each principal component is used as a new independent variable to replace the original independent variable x for regression analysis.

Through principal component analysis, investors can more effectively refine core factors, filter out noise interference, and make the decision-making process of the entire investment analysis more accurate and effective. At the same time, the refinement of core factors can also help investors avoid certain unnecessary risks.

Conclusion

Conclusion