RISK VALUATION

RISK VALUATION

Risk can be valued using :

• Derivatives Valuation– Using valuation method– Value the gain

• Risk Management Valuation– Using statistical parameters– Value the loss

RISK VALUAT ION

DERIVATIVES VALUATION

RISK MANAGEMENT

VALUATION

PRINCIPLEExpected discounted value

Distribution of future values

FOCUSCenter of distribution

Tails of distribution

PRECISIONHigh precision needed for pricing purposes

Less precision needed, simply approximate tails

DISTRIBUTIONRisk-neutral distributions and discounting

Actual, objective distributions

RISK MANAGEMENT VALUATION

RISK MANAGEMENT VALUATION

VALUE AT RISK

The expected maximum loss ( or worst loss )

over a target horizon within a given confidence interval

Models to estimate VaR• Historical Market Data

– assumption is that historical market data is our best estimator for future changes and that

– asset returns in the future will have the same distribution as they had in the past

• Variance – Covariance (VCV)– assuming that risk factor returns are always (jointly)

normally distributed and that the change in portfolio value is linearly dependent on all risk factor returns

• Monte Carlo Simulation– future asset returns are more or less randomly simulated

Historical Market Data• involves running the current portfolio across a set of

historical price changes to yield a distribution of changes in portfolio value, and computing a percentile (the VaR).

• Benefits – Simple to implement– does not assume a normal distribution of asset returns

• Drawbacks – requires a large market database– computationally intensive calculation.

VALUE AT RISK (VAR)

Market Value

x

Risk Variability

x

x

Confidence Level

=

Worst Loss

yearin horizontime

DEFINITION :

• Market Value :– Current market value of the respective transaction to be

managed– Mark to market at the end of time horizon

• Risk variability :– Usually the standard deviation of the risk to be managed – The higher the variability the higher is VAR

DEFINITION :

• Time Horizon :– Time period to be considered correspond to time required for

corrective actions as losses starts to develop– Annualized– The longer the time horizon the higher is VAR

• Confidence Level :– Confidence level of loss occurring– The higher the confidence level the higher is VAR

Example :• Current market value of transaction USD 100,000 paid by 3

months usance L/C

• Standard deviation of Rp/USD is 10%

• Time horizon is 3 months

• Confidence level is 95%

• VAR = 100,000 X 0.10 X X 0.95

= USD 4,750.00 Maximum expected loss

123

Variance – Covariance (VCV)• i = individual asset

• p = portfolio • all returns are returns over the holding period • there are N assets • μ = expected value; i.e., mean • σ = standard deviation • V = initial value (in currency units)

Vi / Vp

• = vector of all ωi (T means transposed) • (i)

• (ii) • The normality assumption allows us to z-scale the calculated portfolio standard

deviation to the appropriate confidence level. So for the 95% confidence level VaR we get:

• (iii)

i

n

iip

1

Tp

PPPVVaR 645.1

Variance – Covariance (VCV)

VAR formula for VCV :

for 95% confidence level is 1.645 for 99% confidence level is 2.33

)(1

Ti

N

iipVVaR

Monte Carlo Simulation• Decide on N, the number of iterations to perform. • For each iteration:

– Generate a random scenario of market moves using some market model.

– Revalue the portfolio under the simulated market scenario. – Compute the portfolio profit or loss (PnL) under the simulated

scenario. (i.e., subtract the current market value of the portfolio from the market value of the portfolio computed in the previous step).

• Sort the resulting PnLs to give us the simulated PnL distribution for the portfolio.

• VaR at a particular confidence level is calculated using the percentile function.

• For example, if we computed 5000 simulations, our estimate of the 95% percentile would correspond to the 250th largest loss; i.e., (1 - 0.95) * 5000.

Indications on method to use• For Value at Risk for portfolios, that do not include options,

over very short time periods (a day or a week) and normality can be assumed, the variance-covariance approach does a reasonably good job.

• If the risk source is stable and there is substantial historical data (commodity prices, for instance), historical simulations provide good estimates.

• In the most general case of computing VaR for nonlinear portfolios (which include options) over longer time periods, where the historical data is volatile and non-stationary and the normality assumption is questionable, Monte Carlo simulations do best.

DERIVATIVES VALUATION

DERIVATIVES VALUATION• Define all risks that might have an impact on the cy’s cash flow

• Do several cash flow projections with the assumptions of each respective occurring use MONTE CARLO simulation

• Use valuation method for every projected cash flow Cash Flow at Risk (CFaR)

• Cash flow before risk management vs cash flow after risk management

• Difference of value is the gain from risk management

• Value the gain

DERIVATIVES VALUATION

PV ( of company’s cash flow with hedge plus hedging cost )

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PV ( of company’s cash flow without hedge plus bankruptcy cost)

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Benefit of risk management

Requirements :

• Use EBITDA or operational cash flow excluding interest

• Calculate projected Cashflow/EBITDA considering probabilities of occurrence

• Use WACC as discount rate

• Include risk premium in cost of equity

• Include transaction cost of hedging

• Include bankruptcy cost

NO RISK MANAGEMENT RESULTS IN :

• Bear more bankruptcy costs and financial distress than it should

• Pay more taxes than they should

• Have less leverage than they should

More bankruptcy costs & financial distress than it should

• Debt does not reduce company’s value since it only has to distribute its cash flow to different claimants

• Bankruptcy costs are costs as result of a bankruptcy filing

• Probability of bankruptcy is probability of no cash flow to repay the debt

• Full hedge means reducing the risk of bankruptcy to zero

• Trade off between hedging cost and bankruptcy cost

Pay more taxes• Depending on the distribution of probability of

occurrence of every event, can result in higher expected income, hence higher expected taxes to be paid

• Hedged cash flow provides stability and definite value of taxes to be paid

Have less leverage• Debt provides tax shield for interest payment

• Cash flow based on EBITDA or Operational cash flow excl interest

• Tax payment is considered after interest payment

• Risk management provides opportunities for the company to issue risk free debt (no bankruptcy risk)

QUALITATIVE ASPECTS

Fail to retain valuable large shareholders

• Small diversified shareholders are not sensitive to company’s risk management

• Large undiversified shareholders are interested in company’s risk management

• Large shareholder’s might have some expertise in managing the company

• Manager’s might not be keen to embark on risky projects

Have managers provided with poor incentives

• No risk management reduces company’s value

• If manager’s incentive are tied to firm’s value, managers are provided with poor incentive

Fail to get stakeholders make firm-specific investments

• No risk management is a risk factor affecting company’s health

• If company’s health is affected stakeholder’s won’t be willing to invest in company e.g. long term employees learning skills required by company

Prone to invest in probable negative NPV projects

• No risk management increases the company’s risk of default

• If no risk management, the company is affected to get into a debt overhang, projects will be financed by debt than equity

• Since shareholders equity not at stake, more prone to invest in projects who have high probability of gain but also probably results in negative NPV

Does not invest in positive NPV projects

• If debt overhang and projects financed by debt

• Benefits of project goes to debt holders

• No incentive to invest in positive projects for shareholders/professionals

Does not give an overview of management capabilities

• Information asymmetry on agency cost is always present in professional managed companies

• No risk management can result in shareholders distrust management capabilities

• Risk management clears aspects of uncontrollable risks

• Shareholder’s can form a better judgement on management’s capabilities