FIN302/502 Empirical Methods in Finance
Due: June 29th 2018 (Late submission are not accepted.)
Note: This project is a group assignment. Don’t copy paste other groups’ report, otherwise
both your group and other groups that share reports with you will get zero score.
Using the two EXCEL les \ nalproject.csv" and \market.csv" in the directory \Final-
Project" of the course website in SAKAI, do the following empirical analyses.
Present your empirical results in a table format, and interpret your ndings
as best as you can. Send me a report of your analyses in an EXCEL and your
programming code by email. Name your email title and your excel le by
\Student names in the group". My email address is . Cc
your email to TA: Bozhi Wang, .
Data description:
1. \ nalproject.csv" contains quarterly excess returns on all U.S. stocks listed in
major exchanges from 1973/12/31 to 2015/06/30. Column 1 is stock ID (ticker)
for stock i. Column 2 is its estimated market beta (estimated using historical
returns), denoted as i;t 1. Column 3 is its quarter-t excess return in percentage
(Ri;t Rft ), denoted as ~Rei;t. Column 4 is the date of the quarterly excess return.
Column 5 is the logarithm of the market value of equity, denoted as logMEi;t 1.
Column 6 is the cumulative return over past month-t 12 to month-t 2, denoted
as ~Ri;t 12;t 2. Column 7 is the gross pro tability, denoted as gpi;t 1. Column 8
is the book-to-market ratio, denoted as BMi;t 1. Note that, column 2, 5, 6,
and 7 are observed at one quarter before column 3, excess return.
For instance, the rst row is a stock with ID 10006. Its excess return in the
fourth quarter of 1973 (over 1973/9/28-1973/12/31) is 23.82%. Thus the date
of the quarterly excess return is 1973/12/31. Its market beta, logarithm of the
market value of equity, past cumulative return, and gross pro tability, and book-
to-market ratio, at the end of the third quarter of 1973 (1973/9/28), is
0.6441, 5.56, -11.41(%), 0.2, and 1.01, respectively.
2. \market excess return.csv" contains the quarterly excess returns (in percentage)
on the U.S market index, denoted as ~Rem;t, and the dates of excess returns.
Project assignment:
1. Import the data from \ nalproject.csv" and perform. the following six Fama-MacBeth
cross sectional regressions. The goal is to explore which rm-level attributes (market
betas or characteristics) are useful for predicting the cross section of stock returns.
(a) ~Rei;t = at + 1;t i;t 1 + i;t
(b) ~Rei;t = at + 1;t i;t 1 + 2;tlogMEi;t 1 + i;t
(c) ~Rei;t = at + 1;t i;t 1 + 3;tBMi;t 1 + i;t
(d) ~Rei;t = at + 1;t i;t 1 + 4;t ~Ri;t 12;t 2 + i;t
(e) ~Rei;t = at + 1;t i;t 1 + 5;tgpi;t 1 + i;t
(f) ~Rei;t = at + 1;t i;t 1 + 2;tlogMEi;t 1 + 3;tBMi;t 1 + 4;t ~Ri;t 12;t 2 + 5;tgpi;t 1 + i;t
Recall that a Fama-MacBeth regression is to run period by period cross-sectional re-
gressions to get quarter-t estimated coe cient t, average them over t to obtain , and
conduct a t-test using the time series of f tgTt=1 for the hypothesis E[ t] = 0.
You should report the time series average coe cients , and their t-statistics,
for the six speci cations separately, in the following table format. Discuss
your ndings in detail. Cover these questions: 1) Is market beta a signi cant predic-
tor for stock returns? 2) Which rm-level characteristics are signi cant predictors for
stock returns, controlling for market betas? 3) Are your ndings consistent with the
CAPM? Why or why not. 4) Are the signs of the average coe cients consistent with
the implication of the dividend discount model discussed in the course?
PtBt =1Xj=1Et[Yt+j 4Bt+j]=(1 +r)jBt
5) Based on these ndings, what kinds of trading strategies can you develop to get
positive CAPM alpha?
Table I: Fama-MacBeth regression
(I) (II) (III) (IV) (V) (VI)
2. Using the data from \ nalproject.csv" and conduct portfolio sorting exercises. For a
given rm-level characteristic, at each the end of each quarter-t, sort all stocks into
ve equal-numbered portfolios, based on their rankings in the characteristics (Note:
some stocks’ characteristics at a particular quarter are missing. Skip these stocks at
this quarter.). Portfolio 5 contains stocks with the largest values of the characteristic,
while portfolio 1 contains stocks with smallest values of the characteristic. Compute
the equally-weighted quarterly portfolio excess return over [t;t + 1], that is, ~Rep;t+1 =
j;t+1=Np, where Np is the number of stocks in the portfolio p. Repeat above
steps for each quarter to obtain the time series of the quarterly excess returns (Note:
Since the four rm-level characteristics are already lagged return by one
quarter, the sorting actually starts at 1973/9/28. The rst return date
is 1973/12/31.). Because there are four characteristics (LogME;BM, ~Rt 12;t 2;gp),
you should get 20 series of portfolio excess returns (4 characteristics 5 portfolios.)
Report time average excess returns, their standard deviations and t-statistics,
and CAPM alpha and associated t-statistics for the twenty portfolios ex-
cess returns and four long-short portfolios (buying portfolio 5 and short
selling portfolio 1 for each characteristics) in the following table format,
for each group of 5 characteristic-sorted portfolios. Thus you should have
4 tables separately for logME, BM, ~Rt 12;t 2, and gp. Discuss your nding in
detail. Cover these questions: 1.Do these portfolios have average excess returns that
are signi cantly di erent from 0? 2. Can the four rm-level characteristic predict the
cross-section of stock returns? (Hint: examine the hypothesis E[ReH ReL]=0) 3. Do
these portfolios have CAPM alpha that are signi cantly di erent from 0? 4. Do the
results indicate a CAPM anomaly? Why or why not? (Hint: examine the intercept
in the time series regression ReH;t ReL;t = + Rem;t +et) 5) are your portfolio sorting
results consistent with the previous results from Fama-MacBeth regressions? You may
compare the magnitude/sign/signi cance RHt RLt with t in previous Fama-MacBeth
regressions.
3. Then use the market excess return from \market.csv", compute the GRS statistic of
the above 20 portfolio quarterly excess returns (The preceding 20 portfolios. Do not
use the 4 long-short portfolios). You should match the dates of \market.csv" with
the dates of \ nalproject.csv". Recall the GRS statistic tests whether the intercepts
of the time series regressions of portfolio excess returns on market excess returns are
JOINTLY zero.
~Rei;t = i + i ~Rem;t +ei;t; t = 1;:::;T; i = 1;:::;20 (1)
where ~Rei;t is the quarterly excess return on portfolio i (i = 1;2;:::;20) and ~Rem;t is
the quarterly excess return on the market index. The GRS statistic tests whether
i;i = 1;2;:::20 are JOINTLY zero.
Report the Sharpe ratio of the market portfolio
Report the GRS-statistic and its p-value. Does the statistic reject the CAPM?
Report the Sharpe ratio of the tangency portfolio formed by the market portfolio
and the 20 portfolios. (Hint: use the second formula of the GRS statistic).