Portfolio Optimization and Risk Management - PowerPoint by etr19906

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```									Portfolio Optimization and
Risk Management

Professor W.K. Li
Department of Statistics and Actuarial Science
The University of Hong Kong
Portfolio Optimization and
Risk Management
   The financial world has always been risky.

   How should we invest our wealth?

   How should we manage the risk of our
investment?
Portfolio Optimization
   Portfolio theory is developed by Markowitz
(1952), the Nobel Prize winner in
Economic Sciences in 1990, for his work
in financial economics

   Markowitz’s portfolio theory is based upon
two principles:
   To maximize the expected return of a portfolio
   To minimize the risk of portfolio

   Markowitz model has long been used in
solving many asset allocation problems.
Drawbacks of Markowitz Model

   Estimates of input parameters including
expected asset returns and covariance matrix
could be fairly unstable and inaccurate.

   The optimized portfolio of Markowitz Method is
in fact not the optimal one as it is only an
estimate of the ‘best’ portfolio based on the
estimated input parameters.
New Model:
Robust Monte Carlo Method
   Estimation of input parameters
   Use robust estimates of input parameters

   Uncertainty of the optimized portfolio
   Adopt a Monte Carlo method to gauge the sampling
variation of optimized portfolio
Why HPC in
Portfolio Optimization
   Performing Monte Carlo simulations
increases the computational time

   HPC can assign the simulation processes to
different nodes. Thus, front-end users can get
the asset allocations and simulated efficient
portfolios in a timely manner.
Risk Management

   During the late 1980’s, JP Morgan developed its
own firm-wide value-at-risk system to measure
market risk.
   VaR summarizes the worst loss over a target
horizon with a given level of confidence such as
95% confidence.
   RiskMetrics was a free service offered by JP
Morgan in 1994 to promote value at risk (VaR)
as a risk management tool.
An Example of Value at Risk

Distribution of portfolio returns

0.25
5% of Occurrences   VaR = \$8 M       Average return = \$2 M
0.20
Probability

0.15

0.10

0.05

0.00
-16    -12     -8     -4     0         4      8      12       16   20
\$ Millions
Models of Value at Risk

   We can apply financial time series model to
simulate the volatility of the assets
   GARCH models have become mainstay of time
series analysis of financial markets, which
systematically display volatility clustering.
   There are literally hundreds of papers applying
GARCH models to stock return data, to interest
rate data, and to foreign exchange data.
Estimation of Value at Risk

   Monte Carlo Simulation Method is widely used in
this area.
   The accuracy of VaR is high
   It can mimic the extreme events in the market
   Drawback
   However, the computational time of this method could be
extremely long.
   HPC can speed up the simulation of the VaR.
.NET Web Services and HPC

Client Side   Middle Tier    HPC Cluster

Node 01

Node 02
Excel          .NET
Web Services
Node 03

Node 04
Case Study

   Michael visits his bank and would like to
invest in a portfolio that suits his need.

   After answering a series of questions, the
financial planner realizes that his risk
tolerance level is 20%.

   How to recommend a portfolio to Michael
based on his risk tolerance?
Case Study

   Training period: Jan 99 – Dec 02
   Testing period: Jan 03 – Dec 03
   9 stocks under study are
   Cheung Kong, Bank of East Asia, HSBC, Hang
Seng Bank, Cathay Pacific, China Merchants,
Citic Pacific, CLP, Hong Kong Electric.
   Two portfolio construction methods:
   Markowitz Method
   Robust Monte Carlo method
Performance in Testing Period

140

130

120
Index

110

100

90

80
01-03   03-03    05-03       07-03        09-03          11-03
Date

Markow itz   Robust Monte Carlo Method
Performance in Testing Period
HPC Applications in other areas
   Clearly a HPC would also be useful to projects that
require a large amount of computing power.
   Examples:
   bioinformatics
   quantum computation
   nanotechnology
   theoretical condensed matter physics
   Advances in these areas will certainly have
important impacts on the society.
Online Demonstration
Q&A

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