Chapter 8. Investment Science || Part.1

8.2 Factor Models

 

Inputs of M-V model

• n개의 주식이 있을 때, mv모델을 만드려면
  • n mean value
  • n variance
  • n(n-1)/2 covariances
• 총 2n+n(n-1)/2 개의 파라미터가 필요하다. n이 크면 클수록 더 많은 값들이 필요함

 

Factor Models

• 여러개의 주식을 아우를 수 있는 어떠한 Factors를 찾으면 간단하게 표현할 수 있음
• Factor와 개별 mean 간의 연관성을 나타내는 Factor model은 asset 간 공분산 구조를 단순화한다. 
• For common stocks, the factors might be the size of a company, gross domestic product (GDP), unemployment rate, and so forth

Single - Factor Model

• Single-factor models are the simplest of the factor models

• There is a single factor f which is a random quantity
• We assume that some value y and the factor are related by

• The b’s are termed factor loadings because they measure the sensitivity of the return to the factor
  b는 factor에 의존하는 정도를 나타내는~

 

• 이번에는 y가 r_i(수익률)이라고 생각해보자. 

• single-factor model은 linear fit으로 보여질 수 있다.
•  Imagine that several independent observations are made of both the return  r_i and the factor f
• Since both are random quantities, the points are likely to be scattered
• A straight line is fitted through these points

 

• single-factor 모델을 사용하면, mean-variance model의 파라미터들을 결정할 수 있다. 

=> Now we just need a total of 3n+2 parameters

• When asset returns are described by a single-factor model, the return of any portfolio of these assets is described by a factor model