The most popular factor model in finance is probably the Fama-French 3 factor mo

Question

The most popular factor model in finance is probably the Fama-French 3 factor model which can be implemented using a linear regressions of the following form: ri = a + b*(MRP) + b*(SMB) + b*(HML) + e Please explain what each factor captures and why you think it is included in the model. Please explain how to construct the SMB and HML factors. Suppose you want to add a fourth factor, the liquidity factor (LIQ), to the model above. Do you think this would be a good factor to include? How would you construct the liquidity factor? Now suppose you want to back test a trading strategy and you want to ensure you are compensated for all of the risks of the three factor model, plus LIQ. How would you determine if your trading strategy is providing you with a positive risk adjusted return?

Explanation / Answer

1. Factors Explained

ri = a + b*(MRP) + b*(SMB) + b*(HML) + e

Here a = Minimum Risk free return
b (beta somehwat different from capital Asset Pricing model)
MRP = Km-a = Market return - risk free return
SMB - Small -Big (in terms of capitalization)
HML = High minus low (book to market ratio)
e - Factor determined by linear regression

2. Constructing SMB -= Small minus big & HML

a. Divide stock into 2 groups by comparing its mean (if stock market capitalization is great than the mean, classify it under big, else small).Do this exercise and arrange in ascendign order for small and big. divide them into 3 groups (top30 (small high-SH), middle 30 (Small medium-SM) and bottom 30(small low-SL)).

Similarly ((big low-BL, big medium-BM, big high-BH)

do the similar exercise for ration of Small Book/ price and high book/price.

Now you shall get SMB = ((SL+SM+SH)-(BL+BM+BH))/3
                  HMB = ((Small High+Big High)-(small low+big Low))/2

3. Liqudity factor is a function of trading quantity, speed, costs and price impact.

Here we can add liqudity factor as investors seek a premium in return for holding a illiquid stock and also stocks with price has higher trading costs as well.

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.