Risk Management

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Risk Management

1. Financial Risk Management: process by which financial risks are identified, assessed, measured, and managed in order to create economic value.

1.1 Risk Measurement

-1st Step in RM

-Using distribution of potential P&L to measure risk

-Probability Density Function

-Value at Risk (VaR): how many % the loss is over a certain percentage, e.g. 99% confidence level, VaR = 15%

(i.e. there is 1% the loss is over 15%)

1.1.2 Absolute vs. Relative Risk

- absolute risk: measured in terms of shortfall relative to init. val of investment

- relative risk: measured to benchmark index

1.2 Evaluation of Risk Management Process

1.2.1 Known Knowns: risk properly identified and measured

1.2.2 Known Unknowns: risk are known/should be known but are not properly measured by risk mgr

a) risk mgr ignored important known risk

b) distribution of risk factors, incl. vol. & corr., could be measured inaccurately

c) mapping process, replacing positions w/ exposures on the risk factors, could be incorrect

1.2.3 Unknown Unknowns: represent events totally outside the scope of most scenarios

1.2.4 Risk Mgt Failures

a) Some risks unrecognized

b) Mismeasurement of risk / distribution not adequately measured

c) Risk limit could not have been enforced

d) Miscommunication of risk

1.3 Portfolio Construction

1.3.1 Comparing multiple assets

- choose btw. two alternatives (less risk vs. risker assets)

- higher leverage: high risk ==> high exp. return (trade-off btw. higher risk & return)

1.3.2 Risk-adjusted Performance Measurement

SR = [u(Rp)-Rp]/s(Rp) -excess return over risk-free rate

IR = [u(Rp)-u(Rb)/s(Rp-Rb) -excess return over the benchmark

track error vol.:

w^2 = Corr(Ra,Rb) = s(a)^2 -2p*s(a)*s(b) +s(b)^2

1.3.3 Mixing Assets

Analysis: consideration a discrete choice to invest in either asset

1.3.4 Efficient portfolios

- For a large no. of data, e.g. N = 500, it follows a jointly normal distribution; only consider mean & var

- Identification of efficient set

- Given no short-sale restriction on portfolio weights, a closed-form solution exists for the efficient set.

- 1st: Minimum-variance portfolio: lowest volat. across all fully invested portfolios

- 2nd: Portfolio w/ highest Sharpe ratio

1.4 Asset Pricing Theories

CAPM (Capital Asset Pricing Model)

R(i,t) - R(F,t) = alpha + beta[R(m,t) - R(F,t)] + residual error

beta = market factor (systematic risk)

alpha = actively management skill

residual = uncorrelated to R(m,t) (idiosyncratic)