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Asset - returns

Creation date：2024-05-09 15:05:13

Belonging category：计算机computer science

Tag GMM

Asset - returns

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Pset 3

Q2: This is an empirical work on GMM. We will work with the Captial Asset Pricing
Models (CAPM). To help better understand the model, you can read the paper (Hansen-
Singleton 1982) in the course reading materials.
For any asset i with return Rit from period t to t+ 1, the representative agent with
utlity function U(C) =
∑∞
q=0 β
qCγq can choose to determine the optimal consumption
path C0, C1, .... β ∈ (0, 1) is the discount factor and γ > 0 is the risk aversion parameter.
1: Show that the Euler equation holds:
E[β(
Ct+1
Ct
)γ−1(Rit + 1)] = 1,
for any asset i and t.
2. Suppose we have data Rit, i = 1, 2, ..., k, t = 1, 2, ..., T . What moment conditions
can we get out of the Euler equations above?
3. Download the data “Asset - returns” from the course website. Estimate the
CAPM model using the data via two-step optimal GMM. You should use the monthly
data between 2011.01 - 2017.07. The consumption data are available to us on the monthly
basis. There are 6 financial assets: AAPL, DJI, GM, MSFT, GSPC, IXIC. The return
of these financial assets should be discounted by the CPI data, which is also given in the
dataset. Report your estimation results.
4. What do you learn from the results? Is the result fundamentally different from
Hansen-Singleton 1982 using the more recent data?

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EEE8099 Physics 11 ECE2238B Biostat 234 ECON30009 INF10025 CHEM252 CCMA4008 CIVE 3007 STAT0031 ELEC ENG 3108 MGMT90140 CHEM 252 STAT3016 MMM095 MMGT6016 Legal STAT 311 ELEC9764 COMP 370 TCS 3053 EECS 1021 FIT1051 C/C++ EE3C COMP2003J COM398 COMP51915 Simulator FIN42330 8PRO102 PGD ELEC5160 XJCO1921 COMP5123M INFS 2042 CHE1148H ECA5313 IN3329 Microsoft Modeling B15 2TT COMP3687 COMP2432 DMS2030 KAN4TSF CFKG CSE 5322 CSE 445 STATS 3DA3 CHC5223 COMP1048 EL3105 EECS 3221 CS231 ME 4434 ITP4510 ITP4501 CSCI 5708 Controller EECE 5699 CPEN 231L CPN programs CSC8016 MATU9D2 ENGN4213 2. SVM. (10 points) Consider an SVM classifier using RBF kernel, and finish the following python code to search for the optimum kernel parameter γ. You are required to calculate the RBF function and search yourself, instead of using functions in Scikit-Learn (sklearn). def parameter search(gamma list ,Xtr,ytr,Xts,yts ,...): """ Parameters gamma list: A list of RBF kernel parameter gamma to search for Xtr: Training data, shape (ntr,nrow,ncol) ytr: Training labels, shape (ntr,) Xts: Test data, shape (nts,nrow,ncol) yts: Test labels, shape (nts,) ... Add other parameters as needed Returns: gamma optimum: The gamma with minimum error on Xts, yts """ ... return gamma optimum

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