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STAT 4261/5261 Department of Statistics

创建日期：2024-06-08 14:57:51

所属分类：统计学statistics

标签： STAT 4261

Department of Statistics

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STAT 4261/5261
Department of Statistics
The project requires you to synthesize all the material from the course. This is not a
regular Homework and it should be treated differently. The goal here is for you to solidify
your understanding of the financial statistics methods that you have learned in this course.
You will present your findings in a written report. You should explain what you did using
simple words. You do not need to explain the terminology in details. No formulas and
no cut and paste from R. The final report should be clear and readable. The maximum
number of pages allowed for the report is five 8x11 sheets of paper (both sides). All figures
and tables that are included should be readable, relevant and well labeled. Figures can
relegated to an Appendix (not part of the 5 sheets). Make sure to only include relevant
plots. What follows are some suggestions for your final project. You need to find your own
data and a good source for it is yahoofinance.com. You will need to use exactly 20 assets
and you should look for at least 5 years of monthly returns from 2017 to 2022. You are
required to hand in your report no later than Monday, December 15th at 1pm. You
are required to email me your data and your R programs by the same day.
1 Grading of the project:
• Write-up: your project should be well written. clear with concise sentences. It should
be easy to read with no formulas.The tables and the graphs should be clearly labeled.
You will also be graded on the organization of the results (20% of the grade)
• Coverage: the project should cover at a minimum 85% of the material covered in
class. (20 % of the grade)
• Correctness of the results. 60% of the grade will be based on the correctness and the
accuracy of your results.
Your project should consist of at least the following items:
1. An executive summary, in which you give a brief summary of the main
results using bullet points
2. Descriptive Statistics
3. Sections that summarize the results of your statistical analysis by topic
(see below)
4. A conclusion
1
2 Summary
This section should be short description of the assets you use and a brief summary of your
main results using bullet points
3 Descriptive Statistics
In this section you report sample statistics (Means, standard deviations, Skewness Coef-
ficients, Kurtosis Coefficients and beta of each asset) and comment of your results. You
should also provide an equity curve for each asset (that is, a curve that shows the growth of
a $1 in each of the asset over the time period you chose) and comment of your results. You
should do the same for S&P 500 and compare it with the assets. Run a test for stationarity.
Do the returns look normally distributed ? Are there any outliers in the data? Fit different
distributions to your data, which ones fits better? Compute Sharpe’s slope for each asset.
Which asset has the highest slope? Make sure to convert the monthly sample means and
standard deviations into annual estimates by multiplying by 12. Comment on the values of
these annual numbers. Results should be displayed in tables as follows.
asset. mean stand. dev. Sharp ratio. VaR0.05 ES0.05 β distribution
A. 8% 15% 1.5 13500 17550 0.90 t5
B. 10% 20% 1.75 15500 20550 1.10 Normal
4 Portfolio Theory:
In this part of the project, you construct some of the portfolios that we covered in class.
Compute the minimum variance portfolio (MVP) and estimate its mean return, its standard
deviation, its value at risk and expected shortfall. Comment on the weights of this portfolio
and annualize the monthly mean and risk by multiplying the mean and the risk by 12.
Comment on these values relative to those of each asset. Assume that you have $100,000
to invest. For the MVP, determine the 5% value-at-risk of the $100,000 investment over a
one month investment horizon. Compare this value to the VaR values for the individual
assets. Repeat this with the added restriction that short-sales are allowed, and calculate
the expected return and risk of this portfolio. Using the estimated means, variances and
covariances computed earlier, compute the efficient portfolio frontier, with and without
short sales allowed, for the risky assets using the Markowitz approach Compare the Sharpe
ratios of each asset with that of the tangency portfolio. Compute the tangency portfolio
when short-sales are not allowed and compute its expected return and standard deviation.
Obtain the Sharpe ratios and comment on your results.
Show the weights and the statistics of each portfolio in tables.
2
5 Asset Allocation:
Suppose you wanted to achieve a target expected return of 6% per year (which corresponds
to an expected return of 0.5% per month) using only the risky assets and no short sales
allowed, what is the efficient portfolio that achieves this target return? How much is invested
in each of the assets in this efficient portfolio? Compute the monthly risk on this efficient
portfolio, as well as the monthly 5% value-at-risk and expected shortfall based on an initial
$100,000 investment. Now suppose you wanted to achieve a target expected return of 6%
per year (which corresponds to an expected return of 0.5% per month) using a combination
of T-Bills and the tangency portfolio (that does not allow for short sales). In this allocation,
how much is invested in each of the assets and how much is invested in the risk free asset?
Compute the monthly risk on this efficient portfolio, as well as the monthly and 5% value-
at-risk and expected shortfall based on an initial $100,000 investment. Compare this with
the VaR computed from the allocation of risky assets without short sales.
6 Principal Component Analysis:
Compute the sample correlation matrix of the returns on your assets. Which assets are
most highly correlated? Which are least correlated? Based on the estimated correlation
values do you think diversification will reduce risk with these assets? Run the PCA analysis
and comment on your results. Run factor analysis and report the number and the loadings
of each factors. Do they have any meaningful interpretation?
7 Risk Management:
Assume that you have $100,000 to invest. For each asset, estimate the 5% value-at-risk of
the and expected shortfall on $100,000 investment over a one month investment horizon
based on the normal distribution using the estimated means and variances of your assets.
Do the same using the nonparametric method we discussed in class. Which assets have the
highest and lowest VaR at a one month horizon? Which assets have the highest and lowest
expected shortfall at a one month horizon? Do the same for all your portfolios. Use the
bootstrap to compute estimated standard errors and 95% confidence intervals for your 5%
VaR and expected short fall. .
8 Copulas:
Use copulas to to model the joint distribution of the returns. Which copula fits better the
data? What are the implications?
9 Conclusion
In this section you give your conclusion

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关键词一关键词二关键词三关键词四关键词五和法规和的发更好的风格和 ECON 615 FINC 612 CSC148 COMP 639 ACCT 203 ACCT 211 PSYC 101 MTH2009 COMP52315 PSYCO 432 statistics MATH4063 11 xxx 1 MA1MSP MAST30028 MATH3888 CS341 EEE30002 ES2F5 MCD4160 CC0933 ECON 1101 MCHM3001 CHEM3118 COMMGMT 2511 COMP41280 STAT 631 24T1 IRE379 SENG365 ECON433 FIT3139 MATH4602 LING5621M FINS5516 ECON3208 MN2177 L2 SM EEET1415 Finance DS4023 COMP3004 7CCSMRTS K1S5B6 Stat230 CSCI4211 CSI2132 ECON30130 MAS6100 ENVS222 COM2107 INFO1112 STAT 4004 FIT2100 comp2022 COMP4691 Physics 307 Econ 659 probability CSCI316 fir29 CSCI203 COMP3160 COMP6714 INFO1113 Physics 7B Physics Photonics S203031 STAT2005 COMP90015 CSCI 2110 CSCC46 Information CSC477 COMP4650 Statistical COMP 346 COMP1017 ELEC340 MATH1007 Programming function STAT 244 CS 134 Java cse13s Math 108A FW20 ECON3389 CSE 130 Science 331 COMP9020 engineering COSC 445 CSE 5523 GAME2012 visualization MATH 235 Math 370 CSC343 COGS 108 EE524 COMP10200 STAT 416 3FK4 MSCI 311 ECON6113 ACC40700 EMESTER1 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FE 825 IERG 5130 STAT 8178 EE161 ADS2 G54FUZ CS326 113B ECN 226 QBUS6860 ELEC3202 COMP9334 MGT11B MET CS 777 STA238 00099F Python SMM306 CMT206 EC116 SP MAST90084 CS480/680 BCPM0091 CMPT 300 ECON2209 FY20 STAT 432 CVEN9625 MATH1712 CMP9771M CMP3750M CIS 325 AI506 MAT344H1S MGT7180 PSTAT 160B CSYS5010 1D STAT 453/558 ME152B STA304H1F CSCI-128 ME428 CO3002 FINE 7640 COMP3234 ECSE 223 EE497 – 3D MATH5905 ECS648U ENG5009 MATH10242 EC665 A CPI221 ISOM5220 MACE40402 MGT B456F COMP9315 AFM 113 STAT 778 CS 564 MA231 CS 230 CS 124 COMP5511 CSC317 ITEC1010 ELEC207 INFT 3019 7CCMFM06 EE 161 5G ECLT5810 MATH 7349 CS526 O2 COMP90054 ELE00063M ACCT5034 ARC1015 CSCI 40 CSCI E40 FIN 524B CS 462 389COM CMT309 MFIN703 COMP4250 STA304 STA304H1S STA 1003 FIN 448 BUFN 732 CS520 CVEN3701 ECMT6006 PHAS0100 CSIT314 MDIA 5028 CSCI 2134 MAT 451 CMPT 459 STAT 457 INFO20003 COMP4141 IELE8066 F540 ECM9 CSE 6321 FIN 430 MATH3911 BFC5916 COMP1011 EEE 6209 STATS 240 CW3 COMP206 COMP1003 4331W ISE 530 CMPT 295 MATH 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