Portfolio Optimization and Risk Management - PowerPoint by etr19906


									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
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

                       5% of Occurrences   VaR = $8 M       Average return = $2 M




                      -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.
   Advantages
       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







           01-03   03-03    05-03       07-03        09-03          11-03

                           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

To top