Dr. Sanjiv Das has held positions as at Citibank, Harvard University Professor and Program Director at the FDIC’s Center for Financial Research. His research relies heavily on R for analysis and decision-making. In this webinar, Dr. Das will present a mix of some of his more current and topical research that uses R-based models, and some pedagogical applications of R. He will present: * An R-based model for optimizing loan modifications on distressed home loans, and the economics of these modifications. * A goal-based portfolio optimization model for investors who use derivatives. *Using network modeling tools in R to detect systemically risky financial institutions. *Using R for web delivery of financial models and random generation of pedagogical problems. Promising to be entertaining and enlightening, this webinar will emphasize the interplay of mathematical models, economic problems, and R.

1. Using R in Academic Finance
Sanjiv R. Das
Professor, Santa Clara University
Department of Finance
h?p://algo.scu.edu/~sanjivdas/

2. Outline
• High‐performance compuGng for Finance
• Modeling the opGmal modificaGon of home
loans using R
• IdenGfying systemically risky financial
insGtuGons using R network models.
• Goal‐based porOolio opGmizaGon with R
• Using R to deliver funcGons/models on the
web, and for pedagogical purposes.
R works well with Python and C.

3. h?p://www.rinfinance.com/RinFinance2010/agenda/
h?p://cran.r‐project.org/web/views/Finance.html

5. Calling C from R: An Example of Tax‐opGmized PorOolio Rebalancing

6. Calling C from R: An Example of Tax‐opGmized PorOolio Rebalancing

7. R CMD SHLIB tax.c

8. Topic 1
MODIFYING HOME LOANS
WITH R MODELS
THE PRINCIPAL PRINCIPLE: OpGmal ModificaGon of Distressed Home Loans
(Why Lenders should Forgive, not Foresake Mortgages)
STRATEGIC LOAN MODIFICATION: An OpGons based response to strategic
default
(joint work with Ray Meadows)

13. Game theoreGc problem:
Lender determines the loan
modificaGon that maximizes
value of loan given that the
borrower will act strategically in
his best interest.

14. Model
Home value
HJM
CorrelaGon
h?p://algo.scu.edu/~sanjivdas/ 14

15. “Iso‐Service” Surface
choose
Loan balance = $300,000
Home value = $250,000
Remaining maturity = 25 years
A = $1,933 per month
Amax = $20,000 per year
($1,667 per month)
2/27/12 h?p://algo.scu.edu/~sanjivdas/ 15

16. Some R

17. Values of Iso‐Service Loans
h?p://algo.scu.edu/~sanjivdas/ 17

18. Default Put Exercise Region
L=225,000
L=250,000
h?p://algo.scu.edu/~sanjivdas/ 18

19. Cure risk and Re‐default Risk
The risk of unnecessary relief, i.e., the Providing fuGle relief, leading to
borrower would not have ulGmately ulGmate default anyway.
defaulted.
Value of loan accounGng A: borrower income available for housing
for willingness to pay service, with mean μ and std. dev σ.
h?p://algo.scu.edu/~sanjivdas/ 19

20. h?p://algo.scu.edu/~sanjivdas/ 20

21. Logit: Explaining Re‐default
h?p://algo.scu.edu/~sanjivdas/

22. Reduced‐Form Analysis of SAMs
Home values
Normalize iniGal home value to 1. The opGon to default is ITM when (H > L).
There is a home value D at which the borrower will default. D is a “default level”
or default exercise barrier.
D is a funcGon of the lender share θ, we write it as D(L, θ).
D increases in L and in θ.
Foreclosure recovery as a fracGon of H is ϕ.
22 h?p://algo.scu.edu/~sanjivdas/

23. Default Barrier and Lender Share
23 h?p://algo.scu.edu/~sanjivdas/

24. Barrier Model IntuiGon
No default
Payoff=L
Region of
no default
H0 = 1 and gains
to SAM
Default
Payoff=фD
D=L exp[‐γ(1‐θ)]
Region of default
24 h?p://algo.scu.edu/~sanjivdas/

25. A Barrier OpGon DecomposiGon
Non‐default
component
Default component
Shared AppreciaGon
component
25 PDE h?p://algo.scu.edu/~sanjivdas/

26. The Closed‐Form SoluGon
26
h?p://algo.scu.edu/~sanjivdas/

27. SAM or not?
27
h?p://algo.scu.edu/~sanjivdas/

28. Topic 2
MANAGING SYSTEMIC RISK BY ANALYZING
NETWORKS USING R
THE MIDAS PROJECT @IBM
Paper: “Unleashing the Power of Public Data for
Financial Risk Measurement, RegulaGon, and
Governance” (with Mauricio A. Hernandez, Howard Ho, Georgia
Koutrika, Rajasekar Krishnamurthy, Lucian Popa, Ioana R. Stanoi, Shivakumar
Vaithyanathan) IBM Almaden)

29. Midas Financial Insights
Proxy Statement Insider Transaction
Annual Report
Loan Agreement
Raw Unstructured Data Raw Unstructured Data
Extract Integrate
Related Companies
Data for Analysis Exposure by subsidiary
Loan Exposure
…
…
29

30. Systemic Analysis
Systemic Analysis
• DefiniGon: the measurement and analysis of relaGonships across enGGes
with a view to understanding the impact of these relaGonships on the
system as a whole.
• Challenge: requires most or all of the data in the system; therefore, high‐
quality informaGon extracGon and integraGon is criGcal.
Systemic Risk
• Current approaches: use stock return correlaGons (indirect). [Acharya, et
al 2010; Adrian and Brunnermeier 2009; Billio, Getmansky, Lo 2010;
Kritzman, Li, Page, Rigobon 2010]
• Midas: uses semi‐structured archival data from SEC and FDIC to construct
a co‐lending network; network analysis is then used to determine which
banks pose the greatest risk to the system.
30

31. Co‐lending Network
• DefiniGon: a network based on links between banks that lend
together.
• Loans used are not overnight loans. We look at longer‐term
lending relaGonships.
• Lending adjacency matrix:
• Undirected graph, i.e., symmetric
• Total lending impact for each bank:
31

32. Centrality
• Influence relaGons are circular:
• Pre‐mulGply by scalar to get an eigensystem:
• Principal eigenvector of this system gives the centrality score for a
bank.
• This score is a measure of the systemic risk of a bank.
32

33. Data
• Five years: 2005—2009.
• Loans between FIs only.
• Filings made with the SEC.
• No overnight loans.
• Example: 364‐day bridge loans, longer‐term credit arrangement,
Libor notes, etc.
• Remove all edge weights < 2 to remove banks that are minimally
acGve. Remove all nodes with no edges. (This is a choice for the
regulator.)
33

36. 2005
CiGgroup Inc.
J.P. Morgan Chase
Bank of America Corp.

37. 2006 2007
2008 2009
37

38. Network Fragility
• DefiniGon: how quickly will the failure of any one bank
trigger failures across the network?
• Metric: expected degree of neighboring nodes R!2
averaged across all nodes.
• Neighborhoods are expected to expand when
• Metric: diameter of the network.
38

39. Top 25 banks by systemic risk
39

40. Topic 3
PORTFOLIO OPTIMIZATION USING R
The research papers for this work are on my web page – just google it.
h?p://algo.scu.edu/~sanjivdas/research.htm/
1. Das, Markowitz, Scheid, and Statman (JFQA 2010), “PorOolio OpGmizaGon with
Mental Accounts”
2. Das & Statman (2008), “Beyond Mean‐Variance: PorOolio with
Structured Products and non‐Gaussian returns.”

41. Standard OpGmizaGon Problem
Risk aversion
Mean
Covariance matrix
Portfolio weights
SOLUTION:
See D, Markowitz, Scheid, Statman (JFQA 2010)
Sanjiv Das 41

42. SoluGon Math
Sanjiv Das 42

43. Final soluGon
Sanjiv Das 43

44. Example: ConstrucGon of PorOolios: Available securiGes
Expected returns Standard
deviations
Bond 5% 5%
Low-risk stock 10% 20%
High-risk stock 25% 50%
The correlation between the two stocks is 0.2.
Other correlations are zero.
Sanjiv Das 44

45. Investor goals (sub‐porOolios)
45

46. Sub‐porOolios and overall porOolio
The expected return of the overall porOolio is the weighted
average of the expected returns of the sub‐porOolios.
The risk of the overall porOolio is not the weighted average of
the risk of the sub‐porOolios.
Sanjiv Das 46

47. Mean‐variance efficient fronGer
Sanjiv Das 47

48. Real porOolios versus virtual porOolios
Sanjiv Das 48

49. An alternate problem
For normal returns
Solve for γ
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52. Risk as probability of losses
Mean-variance problem: Minimize Risk
(variance) subject to minimum level of
Expected Return.
Behavioral portfolio theory: Maximize
Return subject to a maximum probability
of falling below a threshold.
Sanjiv Das 52

53. Efficient FronGers in the BPT
(Mental Account) World
Sanjiv Das 53

54. Short‐Selling Constraints
Linear program with non‐linear constraints. This is not a standard quadraGc
programming problem (QP) like the Markowitz model.
MVT uses a standard QP: quadra6c objecGve funcGon with linear constraints.
54

55. Modified Problem
Standard QP
Standard QP problem
with linear constraints
Amenable to industrial opGmizers; we use the R system with the quadprog
package and minpack.lm library.
San Diego, 12‐Nov‐2007 55

56. MV FronGer with Short‐selling
Sanjiv Das 56

57. DeviaGng from Normality with Copulas
Sanjiv Das 57

58. Gaussian Copula
Sanjiv Das 58

59. Extended OpGmizaGon Problem
Sanjiv Das 59

61. SoluGon
Sanjiv Das 61

62. Non‐Linear Products
U is a set of states over r(u) is a n-vector of random returns
n assets
Sanjiv Das 62
Compute p[r(u)]

63. Restatement of the problem
This is a quadratic optimization with linear constraints.
Not a quadratic optimization with non-linear constraints.
Sanjiv Das 63

64. Introducing Structured Products
Can we improve the risk-adjusted returns in a
portfolio by using puts and calls?
Derivatives are very risky.
Sanjiv Das And so ….
64

65. Are puts opGmal?
No, they add very little value to the portfolio.
But …
Sanjiv Das 65

66. Puts are needed when the threshold return is high
For high thresholds the investor cannot get an acceptable portfolio without puts.
Sanjiv Das 66

67. Should investors use calls?
Calls are risky too.
But have attractive and high mean returns!
Sanjiv Das 67

68. Calls give be?er porOolios
Improvement is greater
than 60 bps !
Sanjiv Das 68

69. Structured Product:
The Barrier‐M‐note
Sanjiv Das 69

70. Barrier‐M Note
Sanjiv Das 70

71. Truncated Straddle
Barrier-M-note
Return pick-up greater than 250 bps!
Sanjiv Das 71

72. Equity‐Indexed Product
Sanjiv Das 72

73. Conclusion
• Investors find it easier to think in terms of mental accounts or sub‐porOolios
when trying to reach their separate financial goals.
• Behavioral porOolio theory deals with maximizing return subject to managing
the risk of loss. This problem has a mathemaGcal mapping into mean‐variance
opGmizaGon, yet is much more general.
• Even with short‐selling prohibited, the loss from sub‐porOolio opGmizaGon is
smaller than the loss from misesGmaGng investor preferences.
• ReporGng performance by sub‐porOolio enables investors to track their goals
be?er.
• Goal‐based opGmizaGon enables choosing porOolios even when normality is
not assumed.
• Goal‐based opGmizaGon provides a framework for including structured
products in investor porOolios.
The research papers for this work are on my web page – just google it.
h?p://algo.scu.edu/~sanjivdas/research.htm/
1. Das, Markowitz, Scheid, and Statman (JFQA 2010), “PorOolio OpGmizaGon with
Mental Accounts”
2. Das & Statman (2008), “Beyond Mean‐Variance: PorOolio with
Sanjiv Das 73
Structured Products and non‐Gaussian returns.”

74. Topic 4
PEDAGOGICAL USES FOR R USING THE WEB
h?p://sanjivdas.wordpress.com/

75. Use the Rcgi package from David Firth: h?p://www.omegahat.org/CGIwithR/
You need two program files to get everything working.
(a) The html file that is the web form for input data.
(b) The R file, with special tags for use with the CGIwithR package.

76. R Code called from CGI

77. h?p://algo.scu.edu/~sanjivdas/Rcgi/
mortgage_calc.html

78. High-performance
computing (parallelR)
Network modeling
Q?
Optimization
Web functions
Calling C from R
Lattice dynamic
optimization
High-dimensional
distributions with
copulas