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Statistics C183/C283: Statistical Models in Finance

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Announcements

First lecture is on Monday, 28 March 2022

Location: Fowler A139

Day/time: MWF 12:00 - 12:50

See you then!

For the course syllabus click
here.
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Useful links:

Statistics Online Computational Resource (SOCR):
http://www.socr.ucla.edu

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SOCR Educational Materials:

http://wiki.stat.ucla.edu/socr/index.php/SOCR_EduMaterials.

Probability and Statistics EBook.

Download R and packages.
Download RStudio.
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Handouts

1. Historical note
(from "Against the Gods, the Remarkable Story of Risk", by Peter Berstein, Wiley 1998).

2. Introduction.

3. Diversification - a simple example.

4. Basics.

5. Correlation coefficient and portfolio risk.

6. Why diversification works.

7. Matrix and vector
differentiation.

8. An Analytic Derivation of the
Efficient Portfolio Frontier (JFQA, Robert Merton, 1972).

9. Short sales.

10. Hyperbola.

11. Efficient frontier with risk free lending and borrowing.

12. How to find the point of
tangency (see also handout 11).

13. Point of tangency - example.

14. Review questions.

15. Single index model - summary.

16. Distribution of R square.

17. Adjusting the betas using Blume's technique.

18. Adjusting
the betas using Blume's technique (summary).

19. Adjusting the betas using Vasicek's technique.

20. Adjusting the betas - summary.

21. Are betas best?

22. On the Short-Term Stationarity of Beta Coeffcients.

23. Adjusting betas -
sources of prediction errors.

24. Adjusting betas -
sources of prediction errors - summary.

25. Simple criteria for optimal portfolio selection.

26. Single index model steps.

27. Single index model -
Kuhn-Tucker conditions when short sales are not allowed.

28. Single index model - example with short sales allowed.

29. Single index model - example with short sales not allowed.

30. Single index model and optimization procedure give the same answer.

31. Constant correlation model steps.

32. Constant correlation - example with
short sales allowed.

33. Constant correlation - example with short sales
not allowed.

34. Simple criteria for optimal portfolio selection: The multi
group case.

35. Multigroup model.

36. Multi-index model.

37. Components of
Investement Performance (paper by Eugene Fama).

38. Plot of the decomposition
of overall performance.

39. Options - basics.

40. Lower and upper bounds for call and put options and put call parity.

41. Trading strategies using
options.

42. Butterfly example using R.

43. Options - general notes.

44. Binomial option pricing model.

45. Binomial option pricing model - Cox, Ross, Rubinstein (1979).

46. Binomial option pricing model for put option.

47. A model for stock prices.

48. Ito process and Black-Scholes-Merton
model.

49. Options - summary.

50. The Greeks.

51. Exercise.

52. Implied volatility.

53. Exam 2.

54. Exam 2 solutions.

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Labs

1. Example with two and three
stocks- R script: Compute the the composition of the miniumum risk portfolio, draw the frontier (two stocks).

2. Parabola example - R script.

3. Hyperbola
and mutual fund theoremexample - R script.

4. Mutual
fund theorem - R script.

5. Mutual
fund theorem - R script: Find the minimum risk portfolio using m stocks or using two portfolios on the frontier.

6. Risk free asset - R script.

7. R code for point of tangency.

8. Trace out the efficient frontier - example.

9. Trace out the
efficient frontier - R code.

10. R code with several results
from previous notes.

11. Adjusting the betas using
Blume's and Vasicek's technique - example in R.

11a. csv file stockData48.csv.

11b. csv file stockData49.csv.

11c. csv file stockData50.csv.

12. Decomposition of PRESS -
example in R (see handout #23).

13. Single index model -
example in R.

14. Single index model:
Trace out the efficient frontier when short sales not allowed - example in R.

15. Constant correlation
model - R example.

16. Time plots of S&P 500 and equal
allocation portfolio using 5 stocks.

16a. Data used for handout 16.

16b. Data used for handout 16.

17. Portfolio performance: Plots and
arithmetic and geometric mean of the portfolio growth rate.

17a. Data used for handout 17.

17b. Data used for handout 17.

18. Investing
strategies using options - R examples.

19. Butterfly example using R.

20. Monte Carlo simulation of a
stock's path.

21. Pricing of a call option using simulations, the binomial model and the Black-Scholes-Merton
model.

22. Options lab - example.

23. Value at Risk - examples.

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Project

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Project 1: Updated on 03/29:
Due by 22:00 on Monday, 04/04.

Project 2: Updated on 04/03:
Due by 22:00 on Sunday, 04/10.

Project 3: Updated on 04/11:
Due by 22:00 on Sunday, 04/17.

Project 4: Updated on 04/17:
Due by 22:00 on Sunday, 04/24.

Project 5: Updated on 04/25:
Due by 22:00 on Monday, 05/02.

Project 6: Updated on 05/03:
Due by 22:00 on Thursday, 05/12.

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Practice exams and problems

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Homework

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Homework 1: Due by 22:00
on Monday, 04 April.

Homework 1 - solutions.

Homework 2: Due by 22:00
on Tuesday, 12 April.

Homework 2 - solutions.

Homework 3: Due by 22:00
on Monday, 18 April.

Homework 3 - solutions.

Homework 4: Due by 22:00
on Sunday, 24 April.

Homework 4 - solutions.

Homework 5: Due by 22:00
on Monday, 02 May.

Homework 5 - solutions.

Homework 6: Due by 22:00
on Wednesday, 11 May.

Homework 6 - solutions.

Homework 7: Due by 22:00
on Tuesday, 17 May.

Homework 7 - solutions.

Homework 8: Due by 22:00
on Tuesday, 24 May.

Homework 8 - solutions.

Homework 9: Due by 22:00
on Tuesday, 31 May.

Homework 9 - solutions.

Homework 10: Due by 22:00
on Saturday, 04 June.

Homework 10 - solutions.

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Back to the Statistics Department
Home page.

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