Market Risk

Risks Faced by Financial Intermediaries Credit Risk Liquidity Risk Interest Rate Risk Market Risk Off-Balance-Sheet Risk Foreign Exchange Risk Country or Sovereign Risk Technology Risk Operational Risk Insolvency Risk

Market Risk: Market risk is the uncertainty resulting from changes in market prices . It can be measured over periods as short as one day. Usually measured in terms of dollar exposure amount or as a relative amount against some benchmark.

Market Risk Measurement Important in terms of: Management information Setting limits Resource allocation (risk/return tradeoff) Performance evaluation Regulation (internal model)

Calculating Market Risk Exposure Estimate potential loss under adverse circumstances. Three major approaches of measurement JPM RiskMetrics (or variance/covariance approach) Historic or Back Simulation Monte Carlo Simulation

JP Morgan RiskMetrics Model DEAR = ($position)(price sensitivity) (potential adverse move in yield) = ($position)(price volatility) VAR = DEAR

Risk Metrics:Fixed-Income Security Daily Price Volatility = (MD)(adverse daily yield move) MD* = = dR

Risk Metrics:Fixed-Income Security

Risk Metrics:Foreign Exchange DEAR = ($FX position)(price volatility) cx. spot FX=swf 1.6M, spot rate=$0.625/swf of spot rate=56.5 bp

Risk Metrics:Equity σit2=βit2σmt2+σeit2

Risk Metrics:Portfolio Aggregation

Historic or Back Simulation Advantages: Simplicity Does not require normal distribution of returns Does not need correlations or standard deviations of individual asset returns.

Historic or Back Simulation Basic idea: Revalue portfolio based on actual prices (returns) on the assets that existed yesterday, the day before, etc. (usually previous 500 days). Then calculate 5% worst-case (25th lowest value of 500 days) outcomes. Only 5% of the outcomes were lower.

Historic Simulation :Weaknesses 500 observations is not very many from statistical standpoint. Increasing number of observations by going back further in time is not desirable. Could weight recent observations more heavily and go further back.

Monte Carlo Simulation Approach To overcome problem of limited number of observations, synthesize additional observations. Perhaps 10,000 real and synthetic observations. Employ historic covariance matrix and random number generator to synthesize observations. Objective is to replicate the distribution of observed outcomes with synthetic data.

Regulatory Models BIS Standerdized Framework BIS (including Federal Reserve) approach: Market risk may be calculated using standard BIS model. Specific risk charge. General market risk charge. Offsets. Subject to regulatory permission, large banks may be allowed to use their internal models as the basis for determining capital requirements.

BIS:固定收益交易部位

BIS:外匯交易部位 換成本國貨幣後 必要資本 = 8 %  max{|long|, |short|}

股票部位 必要資本 = X Factor + y Factor =

Large Bank:BIS vs.Internal Models Problems of 1993 BIS framework for measuring mkt risk  not accurate teniques  failed to encourage diversification  incompatible with large bank internal systems

Large Banks: BIS versus RiskMetrics In calculating DEAR, adverse change in rates defined as 99th percentile (rather than 95th under RiskMetrics) Minimum holding period is 10 days (means that RiskMetrics’ daily DEAR multiplied by 10. Capital charge will be higher of: Previous day’s VAR (ie. DEAR  10) Average Daily VAR over previous 60 days times a multiplication factor  3.