Investment Analysis: FF Three Factor Model

Investment Analysis #5

Prepared by Anh Nguyen

Instructed by Dr. Jay Chen

I. Three-factor model

Although the relationship between risks and returns are scientifically acceptable, Eugene Fama and Jenneth French say that the CAPM model is insufficient in capturing all of the risk components, therefore miscalculate the expected return. High beta stocks do not necessarily mean high expected returns. A new model to price assets is essential for investors now as beta is no longer a perfect sole way to predict and explain the returns.

One of the useful tools is the Three Factor Model combining small stock effect (SMB), value stock effect (HML), and market risk premium (Mkt-RF).

• Value = HML = book equity/market equity = BE/ME (a good indicator for a stock's value)

• Size = SMB = market equity or market capitalization (ME).

Value investors always buy cheap and good stocks. They do careful research on fundamentals and annual financial reports of companies to ensure safety margin. They separate apart falling angel stocks and dying stocks, and they bet against high value stocks. Therefore, their safety margin is very huge; even though they are unlucky, they still make good money in the end.

II. VTV

If you are looking for a huge safety margin in your investments, it is a good idea to find value ETFs (exchange traded funds). Vanguard Value (ticker: VTV) could be one of the choices.

VTV is a value ETF with the longest history. It is considered as an index fund, passively managed like SPY. While actively managed funds (mutual funds) are more likely to outperform the benchmark through investment decisions, Index funds like VTV are more stable in returns with less associated fees.

The expense ratio of VTV indicates how much of a fund’s assets for administrative and other operating expenses is 0.04%. VTV also tracks the performance of the largest US’s capitalization stocks such as JP Morgan Chase & Co., Johnson & Johnson, Procter & Gamble Co.. The convenience and the large cap makes it an attractive ETF for investors.

Let's take a look at VTV's performance from the time when they went public to now:

VTV Performance

Using Google Sheet, I could pull out the data for VTV's monthly returns, market risk premiums, small stock risk premiums, and value stock risk premiums. HERE is the detailed for data and calculation. The p-value indicates whether the data is statistically significant or not. The summary tables are represented below for further discussion.

Table 1: VTV's Means

Measures	Calculation	Note
VTV returns' mean	0.52	Annual return= 6.235
VTV returns' standard deviation	5.132
Monthly Sharpe Ratio	0.101	Reward to risk ratio
Annual Sharpe Ratio	0.351
VTV SMB's mean	0.102
VTV HML's mean	-0.265	BE/ME ratio
Market risk premium's mean	0.880	Annual return= 10.565
Market premium's standard deviation	4.415

VTV holds potential high risks but yield relatively low average monthly return. The annual reward-to-risk ratio is also low. Compared to the market risk premium, VTV's average returns and standard deviation are both not at an advantage.

Table 2: CAPM Method

Measures	Calculation	Note
Beta	1.032	Statistically significant
Alpha	-0.389	Statistically significant​

Alpha is negative and statistically significant, indicating an unfavorable abnormal return. Beta is positive and high, indicating that VTV delivers a very high systematic risk.

Table 3: FF Three-Factor Model

Measures	Calculation	Note
Alpha	-0.226	Instatistically significant
Market risk premium beta	0.985	Statistically significant
Small stock premium beta	-0.131	Statistically significant
Value stock premium beta	0.408	Statistically significant

VTV's not highly correlated with market risk factor, small stock risk factor, and value stock risk factor. VTV's alpha is statistically insignificant. Therefore, VTV does not yield any alpha (returns) but delivers beta riss sfrom the market. After reviewing the number, I do not recommend VTV to investors.

III. BRK.A

Warren Buffett is also a value follower. He follows investment philosophy of Graham (his teacher), the founding father of the belief in modern value investing. Buffett becomes famous for his investments in deep value investments and owns many growth stocks, such as Coca-Cola and American Express. I can take a look at Berkshire Hathaway (ticker: BRK.A) to understand whether Buffett is really a value investor.

BRK.A Performance

Using Google Sheet, I could pull out the data for BRK.A's monthly returns, market risk premiums, small stock risk premiums, and value stock risk premiums. HERE is the detailed for data and calculation. The p-value indicates whether the data is statistically significant or not. The summary tables are represented below for further discussion.

Table 1: BRK.A's Means

Measures	Calculation	Note
Returns' mean	1.049	Annual return = 12.597
Returns' standard deviation	5.858
Monthly Sharpe Ratio	0.179	Reward to risk ratio
Annual Sharpe Ratio	0.621
SMB's mean	0.134
HML's mean	0.095	BE/ME ratio
Market risk premium's mean	0.771	Annual return = 9.251
Market premium's standard deviation	4.358

BRK's high returns come with high risks. BRK yield a very good annual returns and beats the market. The annual reward-to-risk ratio is good overall. Compared to the market risk premium, BRK does outperform the market premium.

Table 2: CAPM Method

Measures	Calculation	Note
Beta	0.598	Statistically significant
Alpha	0.589	Statistically significant​

Both alpha and beta turn out positive and statistically significant. The numbers indicate that BRK.A has decent abnormal returns and associates with relatively low systematic risks.

Table 3: FF Three-Factor Model

Measures	Calculation	Note
Alpha	2.029	Statistically significant
Market risk premium beta	0.703	Statistically significant
Small stock premium beta	-0.389	Statistically significant
Value stock premium beta	0.488	Statistically significant

BRK has a good positive and statistically significant alpha. It indicates that BRK should deliver a good abnormal return. BRK.A is slightly correlated with market risk factor, and value stock factor. However, it is against with small stock factor. Also, small stock factor is negative while beta is positive. Those make BRK.A have less expected monthly return than it should do.

Time Series Momentum

I will break down BRK's long period into three following time periods with the respective value stock risk premiums:

1. 1990/05-2000/02: value stock premium beta is 0.055 2. 2000/03-2009/02: value stock premium beta is 0.593 3. 2009/03-2020/02: value stock premium beta is 0.345

With the breakdowns, I can further understand Buffett’s exposure to the value factor. The sub-period factors increased over the time and the whole period as indicated above is the highest value stock premium. It explains the momentum factor in the model that a stop is in a top-performing group this year is likely to be in the same group next year. Once the momentum factor is established, investors just need to watch how the stock moves with the momentum portfolio.

In conclusion, Buffett is definitely a value investor and BRK is doing very well over the time. I do recommend investing in BRK and might do more analysis into VTV before making an investing decision.