"Portfolio Optimization and Risk Management - PowerPoint"
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. 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 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