Statistics C183/C283: Statistical Models in Finance

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.

Useful links:

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


    SOCR Educational Materials:
  • http://wiki.stat.ucla.edu/socr/index.php/SOCR_EduMaterials.
  • Probability and Statistics EBook.
  • Download R and packages.
  • Download RStudio.

    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.

    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.

    Project

  • 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.

    Practice exams and problems

    Homework

  • 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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