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E&Y AdvisoryFinancial Services RiskVakpresentatie Caleidoscoop

Pagina 2

Contacts

► Diederik Fokkema► [email protected]► (088) 407 08 36

► Hans Hellemons► [email protected]► (088) 407 21 80

mailto:[email protected]






Pagina 3

Agenda

► Introductie► Wie zijn wij?► Wat doen wij?► Wie zoeken wij?► Wat bieden wij?

► Terugblik vorige week► Theorie portfolio optimalisatie► Opdracht uitwerken

► Bank balans optimalisatie

Wie zijn wij? – Ernst & Young

► Aantal medewerkers in NL: 4.600

► 56% man, 44% vrouw

► Gemiddelde leeftijd 34 jaar

► Aantal locaties: 15

► Hoofdkantoor: Rotterdam Boompjes

► Assurance, Advisory, Tax, Transactions

Pagina 4

Sub-service lines

Service Lines

Geographical Area EMEIA

Assurance Tax Advisory

Performance

ImprovementITRA Actuarial

Services

Transaction

Advisory Services

Wie zijn wij? – Advisory

Pagina 5

Financial Clients

Risk BeNe

FS Risk

Pagina 6

Wie zijn wij? – FSRisk

► FSRisk bestaat uit ± 55 collega’s► Standplaats kantoor Amsterdam► Lokaal team met een internationale oriëntatie► Jong, ambitieus en snel groeiend team

► Staat bekend om:► Kennisgericht► Kwaliteitsgericht► No-nonsense► … en een grote verscheidenheid aan competenties

Wie zijn wij? – FSRisk - quant

Achtergrond► Econometrie, wiskunde, statistiek, BWI, natuurkunde,

scheikunde en (bedrijfs)economie► Gezonde affiniteit met de financiële wereld

Uitdagingen► Je kennis gebruiken op nieuwe terreinen► Een schakel zijn bij grote projecten► Commerciële en communicatieve vaardigheden

ontwikkelen

Pagina 8

Wat doen wij? - Klanten

RetailBanking

Pensioenfondsen

WholesaleBanking

Vastgoed investeerders

Treasury bij Corporates en

Non-profit

Overige financials

Energie bedrijven

Market Makers

(Commodity) Traders

Verzekeraars

Vermogensbeheerders

FSRiskKLANTEN

Pagina 9

Wie zoeken wij? – ‘de beste mensen’

De FSRisk’er is:

► Ondernemend► Ambitieus► Innovatief & creatief► Communicatief sterk► Team speler► Vaktechnisch sterk

Pagina 10

Programma

► Terugblik naar vorige week► Terminologie rondom portfolio optimalisatie► Excel demo

► Bank balans optimalisatie► Probleemstelling► Wiskundige problemen

► CVaR optimalisatie

Pagina 11

Terugblik vorige week

► Portfolio optimalisatie► “Het toewijzen van kapitaal aan een portfolio van activa (e.g.,

aandelen) om zo de winst te maximaliseren en/of het risico te minimaliseren.”

► Terminologie► Mean-variance portfolio optimization► Efficient frontier

Pagina 12

Terugblik vorige week: terminologie

► Consider a portfolio consisting of n assets. The weights to each asset is given by a decision vector , ,

with being the position in asset i and

► The returns on the assets are denoted by a random vector , such that represents the return on asset i. Consequently, the expected rates of returns are defined as and the expected portfolio

return equals

x = 1

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► The variance of the return on asset i (i.e., the variance of a random variable) is given by

► And the covariance between asset i and j is defined as

x = 1

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► Subsequently, the variance of a portfolio consisting of n assets is given by

► Or in matrix notation as , with representing the covariance matrix

x = 1

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► An efficient portfolio is defined as an allocation of assets that maximizes the returns for a certain level of risk

► Here represents the maximum level of risk. Additionally an extra constraint on the bounds can be added

here and respectively represent the lower and upper bound

x = 1

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► Alternatively, a combination of assets that minimizes the risk for a certain level of return is given by

► Here denotes the minimum level of required return

x = 1

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► The efficient frontier is defined as a curve that shows all efficient portfolios in a risk-return framework.► First calculate the solution to the optimization where the return is

maximized, while ignoring the risk constraint. This gives an upper bound on the expected return,

► Secondly, calculate the solution to the optimization where the risk is minimized, while ignoring the return constraint. This gives a lower bound on the expected return,

► Finally, the efficient is obtained by solving the last optimization problem (including the risk constraint) for a certain number of required returns on the interval

x = 1

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Terugblik vorige week: opdracht

► Excel demo

Pagina 19

Bank balans optimalisatie

► Portfolio approach for bank balance sheet optimization► Balance sheet is a summary of the financial balances as of a

specific date (e.g., end of financial year)► Financial balances include

► Assets► Liabilities ► Shareholder’s equity

► The following should hold:► Total value assets = total value liabilities + shareholder’s equity

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► A stylized bank’s balance sheet looks as follows

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► Assets on the balance sheet produce a positive return, whereas liabilities produce a negative return

► This is respectively translated to interest income and interest expenses

► Shareholder’s equity does not make any return► Now consider the stylized balance sheet as a portfolio

consisting of 7 asset instruments and 4 liability instruments (n=11)

► Here the decision vector denotes the positions in the optimal portfolio

► And each instrument has a certain return, which is denoted by the return vector

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► Ultimately led to thefollowing non-linear optimization problem

► Conditional Value-at-Risk (CVaR) minimization function

► Given a confidence level , the conditional expectation of the portfolio losses above the -percentile are minimized (worst-case scenarios)

► J is the number of scenarios

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► Mean retained earnings ( ) should be higher than expected retained earnings

► This constraint is comparable to

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► Constraints needed for CVaR optimization objective function, such that only the worst-case scenarios are taken into account

► is a complex loss function (explained later)

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► The weights to all assets instruments should add up to 1

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► The weights to all liability instruments and equity instruments should also add up to 1, such that the balance sheet is in “balance” ► Total value assets = total value

liabilities + shareholder’s equity

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► Constraints on the maximum weight shift per portfolio instrument.

► Here denotes the initial portfolio weight for asset i

► The lower and upper bounds for the maximum shift are given by

► and respectively

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► Constraint on the lower and upper bounds for the portfolio weights

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► Lower bound is greater than 0

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► Banks are subjected to strict regulation, prescribed by the BIS (Bank of International Settlements), such that a bank resistant to several types of risk

► Recently the BIS released new regulation, called Basel III

► Constraints to comply to Basel III

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► Most important risk types for banks► Credit risk: the risk of loss arising from the default by a creditor or

a counterparty► Market risk: the risk of losses in on and off-balance-sheet

positions arising from movements in market prices► Operational risk: the risk of direct or indirect loss resulting from

inadequate or failed internal processes, people and systems, or from external events

► Liquidity risk: the risk that the bank is unable to meet expected and unexpected current and future cash flows without affecting either daily operations or the financial condition of the firm

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► Banks are required by regulation (Basel III) to► Keep a certain amount of capital available for credit, market and

operational risk► Have a liquidity buffer (consisting of assets that are considered

easily converted into cash) available for liquidity risk

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► Mathematical techniques/difficulties► Creating the scenario set

► From January 2003 to December 2012► Monthly returns (120 scenarios)

► Conditional Value-at-Risk optimization for trading portfolio► Dynamic Conditional Correlation (DCC) GARCH model for trading

portfolio► Non-linear optimization problem was implemented using in R,

software for statistical computing, and optimized using a sequential quadratic programming (SQP) algorithm from NLOPT (a free/open-source library for nonlinear optimization)

Pagina 34

Bank balans optimalisatie: CVaR optimization

► The model includes daily returns of 10 equity indices (e.g., AEX, NASDAQ, S&P 500) and 5 commodity indices (energy, industrial metals, precious metals, livestock and agriculture)

► Each month the trading portfolio had to be optimized► Trading portfolio is subjected to market risk

► The risk of losses in positions arising from movements in market prices

► Regulation requires banks to hold capital against this market risk► Capital consists of the 10-day 99% Value-at-Risk (VaR) of the

trading portfolio

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► 99%-VaR is minimum amount of capital such that, with probability 99%, the loss will not exceed this amount.

► VaR measure lacks convexity when calculated using scenarios

► 99%-CVaR is the conditional expectation of the losses exceeding the 99%-VaR

► CVaR can be optimized by optimization algorithms► By definition: CVaR ≥ VaR

Pagina 36


► CVaR optimization problem

Minimize the conditional expectation of the losses above the threshold (i.e., α-VaR level)

For each of the J scenarios, the portfolio weights ( ) are multiplied by the returns for a scenario j ( ). The negative of this value is the loss function:

This leads to J losses. Where the conditional expectation of the losses greater than threshold are minimized

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► Loss function explained

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► The efficient frontier of an optimization for the trading portfolio looks like:

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► The loss function in the final problem is the negative of the following

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Bank balans optimalisatie: DCC GARCH model

► CVaR optimization was performed for 120 scenarios► Correlation however is not constant over time ► DCC GARCH model is capable of measuring correlations over

time ► First estimate the univariate volatility for each asset► Secondly, construct standardized residuals (i.e., returns divided by

conditional standard residuals)► Finally, estimate the correlations between the standardized residuals

e&y advisory financial services risk vakpresentatie caleidoscoop texpoint fonts used in emf....

Documents

advisory pagina

interval slide

aa slide

transactions pagina

upper bound slide

shareholders equity

covariance matrix slide

expected return