8 th November 2012 Willis, 51 Lime Street Brandon Davies Board - - PowerPoint PPT Presentation

Gatehouse Bank plc I 125 Old Broad Street, London EC2N 1AR United Kingdom I Authorised and regulated by the UK Financial Services Authority I www.gatehousebank.com

CISI Major Risk Event – Risk 8th November 2012 – Willis, 51 Lime Street Brandon Davies – Board Director, Gatehouse Bank

• Regulators have recently shown interest in using Expected Shortfall (ES), to replace or to

supplement VaR as a measure of risk.

• But do they understand the different definitions and more importantly the relationship

between the definitions and the measures?

• Is ES a better measure of risk than VaR, or are we in danger of getting confused by

mathematics, and will we simply produce very accurate wrong numbers?

• ES has entered the “frame” because it focuses on the tail risk in a distribution, it has

some advantages but one potentially very big disadvantage, it is inappropriate as a measure for many financial markets in distress.

• We shall look at why this is the case and why “fat tails” can just get fatter and fatter.

Agenda

A health warning – no equations (except one)

OR PUT ANOTHER WAY:

1 + 1 = 2

Basel Committee & Expected Shortfall

Basel Committee – Fundamental Review of the Trading Book, Pub May 2012

• VaR Metrics – a benchmark e.g. one day 95% USD VaR.
• VaR Measure – is an algorithm with which to calculate a portfolio’s VaR.
• VaR Model - is the finance theory, mathematics and logic that motivate a VaR measure

(it is the intellectual justification for the VaR measure)

• VaR is a single, summary, statistical measure of possible portfolio losses.
• The portfolio is measured against Risk Factors not against individual asset values.
• Specifically, VaR is a measure of losses due to “normal” market movements.
• Losses greater than VaR are suffered only with a specified small probability.
• Above we have greatly simplified the measure, complexity arises if the distribution is not

normal or the values are not additive (i.e. we need to consider correlations between individual asset values) .

VaR a simple model of risk

• So problems can arise if we miss-specify the problem but any mean variance measure

has an inherent flaw as it ignores extreme outcomes.

• A simple look at the problem of using VaR:
• By ignoring the tails, Value-at-Risk creates an incentive to take excessive but remote risks.

Consider an investment in a coin-flip. If you bet $100 on tails at even money, your Value- at-Risk to a 99% threshold is $100, as you will lose that amount 50% of the time, which

• bviously is within the threshold. In this case the VaR will equal the maximum loss.
• Compare that to a bet where you offer 127 to 1 odds on $100 that heads won’t come up

seven times in a row. You will win more than 99.2% of the time, which exceeds the 99%

• threshold. As a result, your 99% Value-at-Risk is zero even though you are exposed to a

possible $12,700 loss. In other words, an investment bank wouldn’t have to put up any capital to make this bet.

VaR a simple model of risk

• Expected Shortfall is a measure of risk just as is Value at Risk
• Is it a better measure of risk?
• What is the right test of a measure?
• What are we after in a measure - Accuracy or Appropriateness?
• In the real world:
• Tail risks happen – frequently
• Very extreme events also happen
• Some extreme events initiated by exogenous shock feed upon themselves
• There are incentives to “game” the risk measurement system, extreme contingent risk

(e.g. out of the money options) may create reward and no VaR measured risk.

VaR and Expected Shortfall

Mean-Variance or Extreme Values?

Distribution 1 – Courtesy FinAnalytica

Ukrainian Hryvnia and United States Dollar Exchange Rate

Mean-Variance or Extreme Values?

• 20.00%
• 15.00%
• 10.00%
• 5.00%

0.00% 5.00% 10.00% 15.00% Daily % change in Spot USDUAH

Daily % change in Spot USDUAH rate from 5 July 2002 Distribution 2 – Courtesy Premier European Capital

Tail Risk Measurement a Problem for Banks and Regulators - Limitations of VaR as a measure of risk - Volatility in Real Markets

Top = IBM 1959/96 Mid = from random walk (Normal Distribution) Btm. = $/EUR Benoit Mandelbrot “The Miss-behavior of Markets”

• Note all this would not matter so much if we did not tie capital to risk. It is not the only

way! General provisions, reserve accounting were once part of PRUDENCE based capital

• Risk based capital is a product of Basel I/II/III but possibly not Basel IV (Andy Haldane –

“The Dog and the Frisbee”, paper given at Jackson Hole 2012)

• Economic capital is the amount of capital required to absorb severe unexpected losses
• ver a specified period with a specified confidence level
• Economic capital is often depicted using charts such as the one shown below. The chart

shows the typical distribution of a bank’s losses, with the size of loss indicated on the ‘X’ axis and the frequency of loss indicated on the ‘Y’ axis.

• The shape of the chart indicates that losses will usually be less than the expected (mean)

loss, but that occasionally there will be very large losses.

• Expected loss is the anticipated average loss over a defined period of time. Income to
• ffset these losses would normally be factored into product pricing.
• For example, product margins should cover expected credit losses as well as overhead

costs and the cost of un-hedged risk.

• Unexpected loss is the potential for actual loss to exceed the expected loss, which

reflects the inherent uncertainty in the loss estimate.

• Capital is held to absorb unexpected losses, and the cost of holding such capital should

be factored into pricing decisions

Tying risk to capital – why this matters!

Capital and risk

• The confidence level (or level of certainty) indicates the probability that the economic

capital will be sufficient to absorb unexpected losses over a specified time period.

• It is sometimes interpreted as the risk of insolvency during the specified time period.
• Both the level of certainty and the time period are determined by bank management.
• Tail risk is the potential for actual loss to exceed the unexpected loss.
• Capital is held to absorb these extreme losses (losses beyond unexpected loss), and the

cost of holding such capital should be factored into pricing decisions.

• So how does tail risk behave?

Tail risk

• It is important to recognize that correlations are observations, they do not imply cause

and effect.

• Moreover correlations in financial markets in particular are in general conditional - the

relationships change depending on where the economy is in its cycle.

• Such correlations are also dynamic in that they change as a result of potential drivers

such as technology, which occurs with the development of new products or markets.

• It is important therefore to maintain a certain wariness in relying on observed or

assumed correlations within, let alone across, risk categories.

• It is also important to look at factors that may cause significant changes in correlationsIn

wholesale markets market risk and credit risk are clearly closely correlated through counterparty exposures on derivative contracts – AIG and CDS

• In retail markets the value of security and the credit standing of borrowers are closely

related – House prices and mortgage debt in a recession, through unemployment levels

Tail risk and portfolios

• Banks derive their liquidity from two sources, the liquidity that comes from their funding

structure (Funding Liquidity) and the liquidity that comes from their ability to use markets to turn assets into cash (Market Liquidity).

• A long term stable base of deposits, unsubordinated and subordinated debt and equity,

gives both an ability to fund the holding of assets and the ability to do so even when markets are disrupted.

• Provided the levels of default on the assets does not rise significantly the bank will have

the cash flow to pay returns to all liability holders and provided depositors remain confident of this (where the bank is relying on behavioural rather than contractual stability of the deposits) the bank has long term viability.

• A bank reliant on its ability to raise funds through the sale of assets through a market, or

the pledging of the assets to obtain funding, is entirely reliant upon the ability of markets to absorb the assets and the price it can obtain for those assets in the markets.

• Any market disruption either through a fall in asset values or the lack of available funds in

the market will threaten directly and immediately the viability of the bank.

Tail risk and the liquidity of markets

• So lets go back 30 yrs
• Prices are not normally distributed.
• Empirical studies of financial markets show that asset price distributions exhibit “fat

tails” (leptokurtosis).

• This does not sound alarming but the mathematics of such distributions are complex and

imply far higher capital requirements than normal distributions.

• It also implies that analysis of the tails is more important than that of the variance from

the mean, which means an Expected Shortfall (ES) measure is a more relevant measure

• f risk than is VaR.
• Expected shortfall also invariably produces a far higher capital requirement than VaR.
• This implies capital based on a VaR measure of a normal distribution is, for many

markets, a gross under estimate of risk and capital.

• SEE DIAGRAM BELOW
• But is fat tails sufficient? Or do we need to look at the processes that generate them?

Market prices and fat tails

Tail Risk? - Idiosyncratic

Market prices and fat tails

Diagram 1 GPD = Generalised Pareto Distribution

• Liquidity Black Holes (see Prof. Hyun Song Shin, Princeton University) are not simply

instances of large price changes – release of important economic data are frequently accompanied by such changes, and are arguably a sign of the smooth functioning of the market as it adjusts rapidly to new (exogenous) information.

• Liquidity Black Holes appear as large price changes that appear to gather momentum

from the endogenous response of market participants

• Market distress can feed upon itself.
• When asset prices fall some dealers will suffer losses, at or close to their loss limits, this

cause them to sell assets for fear of exceeding their limits.

• This action causes further rounds of selling as other dealers get close to their limits and

are induced to sell, creating a downward spiral in asset prices “offer no bid”.

• Portfolio insurance based on dynamic hedging rules is one well known example of such

feedback.

• Any widespread sale of an asset class can cause a Liquidity Black Hole.

Fat and fatter tails?

• Whilst the price falls may initially be generated by shocks from outside the price setting

system (exogenous events), they are re enforced by forces that come from within the price setting system itself (endogenous events).

• Endogenous risk appears where there is a conjunction of :-
• Individuals reacting to their environment
• Where these reactions affect the environment
• The taxonomy of LBH models control mechanisms dependent on Funding Liquidity and

Accruals Accounting

• What happens if funding liquidity is not available and all assets are mark to market?
• BOND DEALER EXAMPLE

Market liquidity is endogenous

Market liquidity is endogenous – the role of VaR models

Tail Risk? – Market Wide

Dynamic Conditional Correlation (DCC)

Diagram 2

• So how do we measure DCC?
• We need a model of the correlation within and between asset portfolios.
• Use of Copula maths – essentially a probability distribution of the correlations.
• What copula?
• Random Walk = Drunk in a field = Gaussian = Normal distribution = Moody’s CDO models.
• Only one view of randomness.
• Cauchy = Blind archer = No mean and infinite variance = No copula and no answer

(between zero and infinity with equal probability!)

Dynamic conditional correlation

Dynamic Conditional Correlation & Asset Class Correlations

Source: MPI Stylus, Absolute Return Pertners LLP

• The chart above shows a comparison of correlations during the 2000-03 period (bright

blue) with correlations in the current environment (dark blue).

• As you can see, with one or two exceptions, correlations are generally much higher now.
• In the 2000-03 bear market commodities were an excellent diversifier against equity

market risk with the two asset classes being virtually uncorrelated (+0.05).

• Nowadays, the two are highly correlated (+0.69).
• It follows that we are not only in a low return environment at present, as evidenced by

the low return on equities since the end of the secular bull market in early 2000, but we can’t rely on the ability to diversify risk either.

Asset Class Correlations

Market storm

Hurricane Winds = High Volatility & Extreme Outcomes Eye = Very low volatility & Few transactions Hurricane Winds = High Volatility & Extreme Outcomes

• If quantitative models have inherent shortcomings what role can qualitative assessment

play?

• Qualitative assessment is too often dismissed as lacking rigour but that is not necessarily

correct

• One tool that needs to be used more readily is the simple one of learning from our

mistakes (and near mistakes)

• Essentially this is a rigorous approach to post mortems and near miss incidents
• Regulators need to play a role not simply in ensuring banks fully document such incidents

but that regulators also do so.

• Reaction Functions - Central banks are part of the system, creation of money, role of

commercial banks, central bank intervention, effective or ineffective?

• Academic input also needs to be encouraged
• There is a need for better incident analysis
• Building an enquiry friendly culture

Qualitative approach

• Methods of stress testing can be derived from the VaR computational methodologies
• Main Methods of computing VaR.

Historic Simulation

• A simple a-theoretical approach, it uses historic changes in market rates and prices to

construct a distribution of potential future portfolio profits and losses and then reading

• ff the VaR at the appropriate percentile.

Variance-covariance Approach

• Based on the assumption that the underlying market factors have a multivariate Normal

Distribution. Monte Carlo Simulation

• Involves choosing a statistical distribution that approximates the possible changes in

market factors. Then a pseudo – random number generator is used to generate thousands

• f changes in market factors which are used to generate thousands of hypothetical

portfolio P&L’s. and their distribution from which the VaR is determined. TIP choose the paths that produce problems and can be rationalised (today = stagflation).

Methods of stress testing

• All the stress testing approaches chosen that are consistent with the VaR approach

chosen have limitations

• History does not always repeat itself, correlations are known to be dynamic and

conditional which cannot easily be incorporated into measurement approaches (Gaussian Copulas & CDOs)

• There are real limitations to statistical approaches when trying to model endogenous

processes (see liquidity black holes theory)

Quantitative approaches - limitations

• Scenario basis for stress tests may lack any statistical validity but they do have some

benefits

• Scenarios have a more intuitive meaning to senior executives, boards and regulators
• Scenarios can be developed that are ‘tailored’ to the risk profile and /or business model
• f the individual bank (see ICAAP and ILAA)
• Scenarios can be bank specific and /or system wide (see ICAAP and ILAA)
• Scenarios can be developed to show reaction functions and opportunities

Qualitative approach – scenario analysis

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