Liquidity and Liquidity Risk in Small Firms

Liquidity and Liquidity Risk in Small Firms

The file Project 3.xls in the Projects folder contains the end-of-month prices of the
Columbia Small Cap Core fund (ticker: FSCRX) in the period from November 2000 to
December 2014. The file Project 3.xls also provides you with the Fama-French factors
(MKT-RF, SMB, HML) and the risk-free rate (RF) in the same time period. Project 3.xls
also provides, for a longer sample from January 1964 to December 2014, the market-wide
liquidity measure called Pastor-Stambaugh gamma we discussed in class (Gamma column),
as well as its innovations computed by Pastor and Stambaugh (IGamma column) and the
value-weighted returns to the five portfolios sorted on market capitalization. Use these
data to answer the questions below:
i. Estimate the Fama-French model for the Small Cap fund. Does the fund beat the
Fama-French model by a statistically significant amount? (5 points)
ii. Partition Pastor-Stambaugh gamma into the expected part and the innovation using
the first-order autoregression. Please write down the regression equation for the autoregression
(with estimated coefficients) and report means and standard deviations
of the illiquidity measure and its news component. (10 points)
iii. Your colleague suggests that you can avoid doing the regression in (ii) and take the
simple change in Pastor-Stambaugh gamma as a proxy for the innovation. Looking
at the estimation output in (ii), what would be wrong with doing that? (5 points)
iv. Construct the simple change suggested in (iii). Look at the correlation between
IGamma column and your version of the innovation to Gamma from (ii) and the
correlation between IGamma and the simple change in Gamma. Comment on their
magnitude and how they compare with each other. (You can assume that IGamma
is the true innovation and the other two are proxies for IGamma). (10 points)
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v. (Bonus question) Compute two more correlations: between Gamma and IGamma
and between the innovation from (ii) and Gamma. Why do you think you get the
results you get? (10 points)
vi. Regress the fund returns on MKT, SMB, HML, and IGamma. What do you learn
from the sign of the slope on IGamma? Does it help to understand where the alpha
is coming from or does it make the alpha more puzzling? (15 points)
vii. Form the factor-mimicking portfolio for IGamma using the five size portfolios. Please
report the factor-mimicking regression with the estimated coefficients and R-square.
(Hint: You may want to multiply the news component by 100 for scaling purposes).
Does it look like a good factor-mimicking regression? (10 points)
viii. (Bonus question) Look at the slopes from the factor-mimicking regression in (vii).
Are their signs and the relations between them consistent with your expectations?
(Hint: Think about the flight-to-quality effect we discussed in class). (10 points)
ix. Project 3.xls also has the PS-VW tradable factor we discussed in class (it starts
in January 1968). Estimate the correlation between the factor-mimicking portfolio
from (vii) and PS-VW. Comment on its sign and its magnitude. Do you expect it
to be positive? Do you expect it to be large? (5 points)
x. Estimate the Fama-French model for the PS-VW portfolio and the factor-mimicking
portfolio you formed in (vii) using all the data you have. What do the signs of the
alphas and the Fama-French betas tell you about whether either of them is a good
liquidity risk factor? Are you surprised about the signs of the alphas and betas or
did you expect them to turn out this way? (15 points)
xi. Regress the fund returns on MKT, SMB, HML, and PS-VW. What do you learn from
the slope on PS-VW? Is the slope on PS-VW consistent with the slope on IGamma
in (vi)? Explain your reasoning. (15 points)
xii. What do you learn from the alpha in (xi) and how it compares with the alpha in (i)?
What is the main difference between the intercept in (vi) and (xi)? (10 points)

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