CISI Major Risk Event – Risk 8 th November 2012 – Willis, 51 Lime Street Brandon Davies – Board Director, Gatehouse Bank 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
Agenda • 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.
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 a simple model of risk • 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 obviously 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 and Expected Shortfall • 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.
Mean-Variance or Extreme Values? Distribution 1 – Courtesy FinAnalytica
Mean-Variance or Extreme Values? Ukrainian Hryvnia and United States Dollar Exchange Rate Daily % change in Spot USDUAH rate from 5 July 2002 15.00% 10.00% Daily % change in Spot USDUAH 5.00% 0.00% -5.00% -10.00% -15.00% -20.00% 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”
Tying risk to capital – why this matters! • 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 over 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 offset 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
Capital and risk
Tail 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 and portfolios • 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 the liquidity of markets • 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.
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