Finance Case involving Fama-French Model

You are a new hire of Teachers Retirement System of Texas (TRS). TRSs pension fund assets have

been fluctuating and took a large hit during the financial crisis, but membership growth combined

with reasonably strong returns have increased the funds size to $201.2 billion. Approximately 56%

of the fund is invested in global public equities. Approximately 40% of TRSs allocation to public

equities are externally managed. You have been hired by TRS to

find and assess external money management firms.

The Chief Investment Officer (CIO) of TRS has been approached by Dimensional Fund Advisors

(DFA). DFA is trying to convince TRS of their ability to produce positive returns with relatively

low fees. You have been asked to prepare a report for the CIO that describes the overall viability of

the DFA approach. Your main job is to evaluate DFA and decide whether TRS should invest with them.

Nevertheless, you are given a few questions as good places to start.

1. You realize that the numbers you have regarding value and small cap investing are not updated to take into account recent events. You would like to see how the size and book-to market strategies would have performed recently. You decide to calculate the growth of wealth that someone would have earned from a small minus big (SMB) and a value minus growth (HML) portfolio from July 1, 2002 to June 30, 2022. To do this, you need to compute the growth of wealth of a small cap (value) portfolio and subtract this from the growth of wealth from a large cap (growth) portfolio.

Plot the growth of wealth (July 1, 2002 to June 30, 2022) from investing $1 in the small cap, large cap, value, and growth portfolio (with small and large together & value and growth together). This is done by using the 6-Portfolios Formed on Size and Book-toMarket (2x3) and computing the returns of the four portfolios and cumulating the growth of $1. Details of computing the long and short leg of the portfolio strategy can be found here:

Description of Fama/French Factors

Daily Returns: July 1, 1926 - July 31, 2022

Weekly Returns: July 2, 1926 - July 31, 2022

Monthly Returns: July 1926 - July 2022

Annual Returns: 1927 - 2021

Construction: The Fama/French factors are constructed using the 6 value-weight portfolios formed on size and book-to-market. (See the description of the 6 size/book-to-market portfolios.)

SMB (Small Minus Big) is the average return on the three small portfolios minus the average return on the three big portfolios,

SMB = 1/3 (Small Value + Small Neutral + Small Growth) - 1/3 (Big Value + Big Neutral + Big Growth).

HML (High Minus Low) is the average return on the two value portfolios minus the average return on the two growth portfolios,

HML =1/2 (Small Value + Big Value) - 1/2 (Small Growth + Big Growth).

Rm-Rf, the excess return on the market, value-weight return of all CRSP firms incorporated in the US and listed on the NYSE, AMEX, or NASDAQ that have a CRSP share code of 10 or 11 at the beginning of month t, good shares and price data at the beginning of t, and good return data for t minus the one-month Treasury bill rate (from Ibbotson Associates).

Stocks: Rm-Rf includes all NYSE, AMEX, and NASDAQ firms. SMB and HML for July of year t to June of t+1 include all NYSE, AMEX, and NASDAQ stocks for which we have market equity data for December of t-1 and June of t, and (positive) book equity data for t-1.

For example, to compute the small cap portfolio, compute the average return from the small caps (given in the Excel spreadsheet as SMALL LoBM, ME1 BM2, and SMALL HiBM).

(Google this to find spreadsheet: 6 Portfolios Formed on Size and Book-to-Market (2 x 3) Ken French it is first one under subheading Bivariate sorts on Size, B/M, OP and Inv)

End of Month 0: $1

End of Month 1: $1 x (1+return in Month 1)

End of Month 2: End of Month 1 x (1+return in Month 2)

End of Month t: End of Month t-1 x (1+return in Month t)

What did $1 invested in July 2002 grow to for the small caps, large caps, value, and growth portfolios by the end of June 2022? Should you have stayed invested in small and value as DFA claims?

Value strategies have not been performing well over the past decade as shown by the HML portfolio returning -3.04% on average annually. To gain some historical perspective on this performance, use monthly data from July 1926 to June 2022 and compute the percentage of rolling (forward) 1-year periods with negative value premiums. For example, to compute the rolling 1-year return of value in July 1926, compute the cumulative return from July 1926 to June 1927. For August 1926, compute the cumulative return from August 1926 to July 1927. Repeat the same for growth and define the value premium to be the difference.

How many total rolling 1-year periods are there?

What percentage of them had a negative value premium (value minus growth)?

How does the percentage change when looking at rolling 3-year periods?

After thinking about your answers to parts c and d, what do you think of the claim that value tends to be a long-term driver of expected returns?

2. DFA recently released exchange-traded funds (ETFs). What are the major potential benefits

of the ETF structure compared that of mutual funds?

3. DFAs emphasis on small cap strategies dates back to the start of the firm, with its first fund being the US Micro Cap Portfolio (DFSCX) in 1981. What do you think are the challenges of building an effective small-cap strategy? How might DFA implement things in a particular way that gives them an advantage in the small cap space relative to their competitors?

4. In your research, you find that there are also other drivers of expected returns, or factors, besides SMB (size) and HML (value) such as profitability (more profitable stocks tend to do better).

a. How would you suggest that DFA integrate this additional information into their strategies?

5. Part of the challenges of tilting towards value or growth is to have a theoretical framework as to why one should outperform the other and to test it empirically. Based on valuation theory, if you were running TRS, would you recommend tilting the portfolio towards value or growth? Based on the empirical evidence from this case study, would you tilt the portfolio towards value or growth?

6. Compare recent DFA mutual fund fees with other fees for similar passive products.

a. How do DFA fees compare?

b. Please explain what aspects of DFA you consider as similar to an active fund and

what aspects as similar to a passive fund. Would you consider DFA primarily active

or passive? Why?

c. Would you invest in DFA funds on behalf of your pensioners? Why or why not?

7. DFA tells you that their portfolio investment process uses all available information about a companys expected return and market prices on a daily basis. Index funds, which seek to mirror the performance of an index, however, need to mirror the changes in the indexs holdings at the time of its reconstitution (when stocks are added to or dropped from the index). Announcements of an addition of a stock to an index happen before the reconstitution date (when the stock is actually added/deleted).

a. On average, DFA says they expect the stock to rise following an announcement of being added to an index. Do you agree or disagree?

b. Why might an investment process that rebalances daily help investors in terms of trading costs?

c. How might a daily investment process help with targeting portfolio exposure relative to an index tracking approach? Use a hypothetical example of a portfolio manager mandated to target small cap stock exposure.

8. AQR Capital Management, a global investment fund with strong ties to the academic community, was founded in 1998 by Cliff Asness who also studied under Eugene Fama. While DFA holds a strong belief in efficient markets, AQR relaxes that assumption implicitly by its belief in its ability to capture arbitrage opportunities in the market.

a. Give an example of an arbitrage strategy that AQR uses and explain its intuition.

b. Suppose you estimate an alpha for the AQR Fund to be 2% per year. What important aspects of the portfolio would you consider before investing?

c. Given the philosophical differences between AQR and DFA, explain whether you would choose one over the other as an investment manager.