2008 implementation of va r in financial institutions
- 1. EF5603 Implementation Of Value-at-Risk In Financial Institutions Dr. LAM Yat-fai (林日辉博士) Doctor of Business Administration (Finance) CFA, CAIA, FRM, PRM, MCSE, MCNE PRMIA Award of Merit 2005 E-mail: quanrisk@gmail.com 2:00 pm to 3:15 pm Saturday 1 November 2008 Big question How to implement a real Value-at-Risk system in my bank? Expected return vs risk What is the expected return of my portfolio? The single most important number for investments What is the risk of my portfolio? Does the expected return justify the risk to be taken? Historical return vs expected return Historical return Value Value turn Today Re 100% Expected return Adjusted historical return CAPM Discounted future cash flows P/E multiples 0 0 × − = Value
- 2. Risk measures Equities – volatility, Beta Debts – duration, convexity Options – Delta, Gamma, Vega Different financial instruments have different risk measures How many risk measures you can read in one day? Single universal risk measure What is the risk of a bank’s entire trading portfolio over the next 24 hours? Want a single universal measure which can incorporate the risks of all financial instruments, taking into account netting, correlation, margining and hedging Worst scenario Long position lose all you have on hand Short position unlimited loss Accumulator half of a company the life Value-at-risk 1-day value-at-risk at 95% confidence level The maximum loss that will occur tomorrow, if the worst 5% situations are not considered The minimum loss that will occur tomorrow, if the only worst 5% situations are considered
- 3. Value-at-Risk 1-day 95% confidence level 5% VaR 95% VaR Average(S )-Percentile(S , %) % 5 95 1 1 = Variance-covariance method =Σ= V m S m S = = w 1 1 w 2 2 w 3 2 = ⋅ ⋅ Q Correl Q σ σ σ ρ ρ ρ ... 12 13 1 2 1 ρ σ 2 21 2 . ... . ρ σ . ... . : : : ... : n ρ σ σ σ σ σ 2 95% 0 2 1 2 31 3 2 0 1 1 0 1.65 . . ... : 1,2,3,... VaR V Correl w Q k n V w T n n n k k n k k k ≈ = = Historical simulation k , j = = ⋅ Σ= − = ⋅ ⋅ ,0 i , j S i j , 1 For j to S S i j i S Portfolio Share S i k k S S − ( ) ( ,5%) 1 500 , ,0 95% 1 , 1 = − i i n k k j VaR Average Portfolio Percentile Portfolio Monte Carlo simulation Parameters 1,000 simulations , ( ) ( ) S k i S = μ μ Average = k , day k , i σ μ k , day k , i ρ ρ ρ 11 12 13 ρ ρ ρ 21 22 23 ρ ρ ρ 31 32 33 = = − k k day k day k k day k i k i Mean SD Stdev , 2 , , , 1 , 2 Correl ln σ σ μ μ = = − = For i 1 to 1000 = x MultNormal(n,Mean,SD,CorrMatrix) ( ) ( ) = S S x i j i j Σ= = ⋅ Portfolio Share S i j i j ( ) ( ,5%) exp 99% 1 , , 0 , = − i i n j i,j VaR Average Portfolio Percentile Portfolio
- 4. Components of industry VaR system Market data provider Pricing engine VaR computation Market data Latest market quotes Statistics and financial time series Equity – volatility, beta, correlation Interest rate – Hibor, Libor Interpolation Volatility surface Interpolated interest rate Pricing engine To calculate tomorrow’s price of stocks, derivatives, fixed income and credit instruments Stock prices with CAPM and Beta Derivative prices with Delta-Gamma-Vega approximation Fixed income prices with cash flow mapping duration and convexity approximation Major industry VaR solutions VaR system Market data Pricing 1. RiskMetrics Reuters RiskMetrics 2. Algorithmics Bloomberg NumeriX 3. Konto Reuters NumeriX
- 5. Use of VaR in banks - internal risk management Single VaR number provides little information comparison – by day, trader, desk Component VaR who, what contribute the most/least VaR Limit setting a limit to be violated once a month on average Risk adjusted return return attributed to skill vs risk Rouge trader detection difficult to manipulate both return and risk Regulatory requirement 10-day 99% VaR x 3 CA-G-3 “Use of internal models approach to calculate market risk” http://www.info.gov.hk/hkma/eng/bank/spma/ attach/CA-G-3.pdf Capital reporting General market risk Interest rates – treasury yield curves Equities – equity indices FX – exchange rates Commodities – commodity prices Specific risk Credit quality – bond prices Profit and loss – equity prices Incremental risk – being proposed by BIS Limitations of VaR VaR makes a lot of approximations as good as its model assumptions VaR gives an order of magnitude, not an accurate number VaR does not tell anything beyond the confidence level to be complemented with stress test No single VaR system can cover all financial instruments VaR system costs from HKD 0 to HKD million http://www.riskgrades.com VaR does not work well with credit derivatives sub-additively expected short fall – a even better risk measure
- 6. A low cost VaR solution - Bloomberg portfolio manager Bloomberg portfolio uploader Bloomberg portfolio analytics Equities, fixed income, warrants Bloomberg VaR Bloomberg stress test Bloomberg scenario analysis Bloomberg portfolio manager Bloomberg portfolio analytics Bloomberg VaR
- 7. Black-Scholes formulas = − − c S N d K rT N d ( ) exp( ) ( ) 0 1 2 = − − − − p K rT N d S N d ∫−∞ 2 r T 2 r T S S 1 = − = − + − = + + = x dt t N x d T T K d T K d ) 2 exp( 2 ( ) ) 2 ln( ) ( ) 2 ln( ) ( where exp( ) ( ) ( ) 2 1 0 2 0 1 2 0 1 π σ σ σ σ σ Questions and Answers