Risk Measurement in practice

RISK MEASUREMENT IN PRACTICE

Martin Ewen

15/07/2014

Copyright © Arkus Financial Services - 2014 Risk Measurement in Practice Page 2

Outline

► Introduction

► How is s actually measured in practice?

► Value at Risk

► Other types of risk

► Risk monitoring & Governance

► Summary

Copyright © Arkus Financial Services - 2014 Risk Measurement in Practice

Introduction


Introduction

PRACTITIONERS

ACADEMICS

REGULATORS

INVESTORS

► Widely used concept in Financial Economics: Risk = s

► (Standard deviation of returns of an asset or portfolio)

► Used to be mainly concerned in a systemic context (Bank Regulation)

► Recently started to care about risk a little more

► How to measure s with real world data?

► What else is needed to monitor risk?

Sigma?

s s


How is s actually measured in practice?


How is s actually measured in practice?

VOLATILITY


Sigma I

► Intraday vs. daily vs. weekly vs. monthly

► Availability constraint for illiquid assets (e.g. Real Estate Funds, Private Equity Funds)

► How long is the time series of returns to be chosen?

► Moving fixed window vs. increasing window

► Length of window (smoothing)


S&P 500 Standard deviations

0.00%

1.00%

2.00%

3.00%

4.00%

5.00%

6.00%

7.00%

8.00%

9.00%

10.00%

Weekly Std. (3m) Daily Std. (3m)


Fixed vs. increasing window

Daily Std. (3m fixed) Daily Std. (increasing)

0.00%

0.50%

1.00%

1.50%

2.00%

2.50%

3.00%

3.50%

4.00%

4.50%

5.00%


Sigma II

► Factor models (will the CAPM do the job?)

► Time series models (EWMA,GARCH etc.) Forecast models

► Measuring volatility using information from derivative markets (implied volatility)

► Particularly important when calculating volatility for portfolios with a large number of assets

► Availability constraint for illiquid assets (e.g. Real Estate Funds, Private Equity Funds)

► Treatment of OTC instruments (no published market prices)

► Newly launched assets or products (IPO, Certificates etc.)


Observed Facts

Observed facts concerning the calculation of sigma in practice ► Volatility usually refers to the annualized standard deviation of returns;

► In documents published to investors most commonly realized returns (daily/weekly) are used to calculate volatility and performance measures (Sharpe Ratio etc.);

► Portfolios investing extensively in derivatives tend to use shorter time horizons;

► Idem for traders;

► European Regulators oblige investment funds to be categorized into one of seven risk classes according to the so called Synthetic Risk Reward Indicator (SRRI), which is based on the volatility of weekly returns over the last five years.

“Set-up depends on purpose of calculation and nature of the underlying assets/portfolios”


S&P500 volatility of weekly returns

0.00%

5.00%

10.00%

15.00%

20.00%

25.00%

30.00%

4

5

6

7


Hang Seng volatility of weekly returns

0.00%

5.00%

10.00%

15.00%

20.00%

25.00%

30.00%

35.00%

4

5

6

7


0.00%

1.00%

2.00%

3.00%

4.00%

5.00%

6.00%

ML Global Corporate Bonds Volatility of weekly returns

2

3

4


Critics

► Sigma treats positive and negative variations equally ( semi-standard deviation);

► No clear interpretation with regard to investment decisions;

► Does not necessarily capture all risks that need to be monitored;

► Potentially confusing due to different calculation set-ups (opportunistic disclosure of performance measures);

► Problems dealing with derivatives (e.g. may be gamed by using derivatives).


Value at Risk


Value at Risk

VaR

VaR is the worst loss over a target horizon such that there is a low, pre-specified probability that the actual loss will be larger.

P(L<VaR) ≤ 1-α (α=confidence interval)

Source: Jorion (2007)

► VaR is used to measure capital requirements for banks (Basle II and III)

► Regulatory VaR limit for mutual funds (either absolute or relative to a Benchmark)

► Used to determine position limits for traders

► Concept is as well applied by non-financial institutions (e.g. scenarios for business lines)


VaR Methods I

Parametric VaR

If distribution of returns can be assumed to belong to a parametric family. Estimate parameters of the distribution and compute VaR. E.g. for a normal distribution:

VaR 𝑡, 𝛼 = 𝛿 ∗ 𝛼 ∗ √𝑡

Non-Parametric VaR

Read VaR from the corresponding percentile of empirical or simulated distribution of returns of asset or portfolio. (No assumption about return distribution is made)

Estimated from realized returns of risk factor (e.g. single stock, interest rates)

Corresponding percentile of normal distribution, e.g.

1,645 at 95% CI

Scaling factor depending on time horizon used, e.g. t=20d when VaR 20d is calculated and

sigma is based on 1d returns. (iid assumption)


Empirical distribution of S&P 500 returns

0

200

400

600

800

1000

1200

1400

1600

-6.7

8%

-6.2

8%

-5.7

8%

-5.2

8%

-4.7

8%

-4.2

8%

-3.7

8%

-3.2

8%

-2.7

8%

-2.2

8%

-1.7

8%

-1.2

8%

-0.7

8%

-0.2

8%

0.2

2%

0.7

2%

1.2

2%

1.7

2%

2.2

2%

2.7

2%

3.2

2%

3.7

2%

4.2

2%

4.7

2%

5.2

2%

5.7

2%

6.2

2%

6.7

2%

7.2

2%

7.7

2%

8.2

2%

8.7

2%

9.2

2%

9.7

2%

10

.22

%

10

.72

%

► Parametric VaR 0.95 20d = 1.08%* 1.654 *√20 = 8.00%

► Non-Parametric VaR 0.95 20d ≈ 7.23 %


VaR Methods II

Delta-Normal Method

Use Delta exposures of positions to risk factors and estimated covariance matrix of risk factors to compute VaR.

Historical Simulation

Simulate changes in portfolio value using historical changes in risk factors applied to todays‘ levels.

Monte Carlo Simulation

Random shocks used to generate return distribution (several distributions for risk factors may be used, sophisticated models use Copulas to model joint distributions).

Efficient method for large portfolios with plain vanilla assets.

Requires high computing power, but adequate method for portfolios with high optionality (Full Valuation).


Backtesting VaR

Idea

Monitor VaR results by comparing actual portfolio return between t and t+1 to VaR calculated in t (dirty and clean method)

Question

How many failures would you expect for a daily VaR in one year on a confidence level of 99%?


VaR Analysis

Important for Practitioner: What drives risk? ► Incremental VaR: Difference in VaR of the portfolio with and without the position (esp.

used for MC/HS )

► Marginal VaR: Change in VaR if an additional dollar was invested in a given component (dVaR/dx)

► Component VaR: Partition of the portfolio that shows how much VaR would change if position was sold, CVaRi = VaR

Source: Jorion (2007)


Example Incremental VaR Extraction from comparison report for an equity portfolio

POSITION COMPARISON

PortfolioID SecurityID SecurityName Date1 NoOfShares1 Value1 UnderlyingPrice1 Date2 NoOfShares2 Value2 UnderlyingPrice2 RelatiVeQuantityChange

1234 180207 DAX FUTURE ######## -250.00 -1,838,375.00 7,358.23 20/05/2011 250.00 1,817,875.00 7,266.82 -200.00%

1234 94478 Surgutneftegaz-Sp ADR ######## 16,000.00 108,002.74 20/05/2011 -100.00%

INCREMENTAL VAR

PortfolioID SecurityID SecurityName CodeISIN EMACode APTCode SecurityType Date_1 IncrementalVaR_1 Date_2 IncrementalVaR_2 IncrementalVaR_Change

1234 180206 DAX INDEX DAX INDEX 187653 DAXINDX Index (/Tracker) 19/05/2011 -1.96% 20/05/2011 2.24% 4.20%

1234 94478 Surgutneftegaz-Sp ADR US8688612048 281014 US8688612048 Equity 19/05/2011 0.20% 20/05/2011 -0.20%

Incremental VaR in t

VaR 0.95 20d goes from 10.2% to 15.1% between the two dates

► Interpretation?


Critics

► VaR does not consider what happens when it is surpassed Tail Risk (expected shortfall)

► Focus on VaR can lead to neglecting other sources of risk

► Introduces substantial Model Risk

► Nassim Taleb: Black Swans, “Fooled by Randomness“

► Non coherent in the sense of Artzner et al. (1999)

► VaR needs to be supplemented by other metrics (Tail Risk measures, Stress Testing, Scenario Analysis, Derivative measures, etc.)

► Notional Leverage obligatory for UCITS funds (convert Derivatives into exposure in the Underlying).


Types of risk


Types of Risk

Market Risk

Sigma, Value at Risk (VaR), Expected Shortfall

Credit Risk

Ratings, Concentration Ratios, Probability Models, VaR

Liquidity Risk

Bid/Ask Spread, LVaR, Turnover Ratios, Cash Flow Simulations

Operational Risk

Qualitative (SLA, Certification), Model Risk


Liquidity Risk I

► Various concepts to assess asset liquidity:

Days of traded volume held (SEC rule5d to liquidate position without market impact)

Rating of asset or issuer (assuming relation between quality and ability to sell asset)

Bid-Ask Spread (Tends to be a little late!)

► Overall Portfolio Liquidity assessed by liquidity grid (liquidity classes). Assets are put into liquidity buckets according to pre-specified rules. (Rules specific to system – heuristic vs scientific)

► Also: LVaR=VaR + L (L being and add up based on the spread e.g. 0.5*(ms+a*ss ))

(Assumes that worst market loss and the spread widening occurs simultaneously. Generally high correlation between volatility and spreads, but not true for all assets.)

Liability side ► What are the obligations (payments) I have to

meet?

► Recurring/One-Off

Asset side ► How liquid are assets?

► What is the discount in case of immediate sale?

vs.

► Liability side assessed on the basis of Redemptions or Net Redemptions. UCITS funds are obliged to stress test their redemptions.


Liquidity Risk II – Mutual Funds

Liabilities Asset liquidity


Model Risk Delta Neutral Portfolio (High Optionality)


VIX in May 2010

0

5

10

15

20

25

30

35

40

45

50


Derivatives (Non-linear) I


Derivatives (Non-linear) II

-0.60%

-0.50%

-0.40%

-0.30%

-0.20%

-0.10%

0.00%

0.10%

24

12

24

22

24

32

24

42

24

52

24

62

24

72

24

82

24

92

25

02

25

12

25

22

25

32

25

42

25

52

25

62

25

72

25

82

25

92

26

02

26

12

26

22

26

32

26

42

26

52

26

62

26

72

26

82

26

92

27

02

27

12

27

22

27

32

27

42

27

52

27

62

27

72

EuroStoxx Options Payoff


Derivatives (Non-linear) III

04/12/2012 -VaR20d 0.99

►MC (non-parametric): 0.68%

► Linear (parametric): 0.56%


Derivatives (Non-linear) IV

-1.00%

0.00%

1.00%

2.00%

3.00%

4.00%

5.00%

6.00%

24

12

24

22

24

32

24

42

24

52

24

62

24

72

24

82

24

92

25

02

25

12

25

22

25

32

25

42

25

52

25

62

25

72

25

82

25

92

26

02

26

12

26

22

26

32

26

42

26

52

26

62

26

72

26

82

26

92

27

02

27

12

27

22

27

32

27

42

27

52

27

62

27

72

EuroStoxx Options Payoff


Derivatives (Non-linear) V

05/12/2012 -VaR20d 0.99

►MC (non-parametric): 0.57%

► Linear (parametric): 3.79%


Counterparty Risk

Counterparty Risk

Risk of a Counterparty defaulting on its payment obligation.

► OTC Derivatives: Risk stems from the P&L of the trade (<> Market Risk). Only positive MTM has to be considered

► Margins have to be considered as well (if not specially protected).

► Cash account with Banks. Netting Arrangements may be applied.

Mitigation of Counterparty Risk:

► Diversification across Counterparties (multiple Brokers/Banks)

► Legal limit for UCITS: 5% per Counterparty (10% Banks)

► Due diligence/ Counterparty committee (Ratings)

► Collateral to reduce Counterparty risk. (High requirements)

Note: Usually not applicable to traded Futures. (Central Counterparty)


Example: Counterparty Risk


Risk Monitoring & Governance


Risk Monitoring & Governance

► No single measure capturing all aspects of risk A set of risk measures is used to monitor portfolio risk. Measures depend on assets in the portfolio. (e.g. equity vs. bonds)

► Level of details depends on the addressee (e.g. Head of Risk vs. Portfolio manager)

► Risk Management Process needs to be institutionalized (responsibilities, escalation, etc.) conflict of interests!

► Risk Monitoring oriented at regulatory limits and internal guidelines


Exceptions report

Guideline Min Lower Warn Upper Warn Max Type Current Value Result Notes

IRM Demo: European Equity + Global FoF

Portfolio Total Risk (range) 15.00 16.00 17.00 18.00 Value ?

Portfolio Total Risk / Benchmark Total Risk 0.80 0.90 1.80 2.00 Value ✔

Tracking Error (% change) -5.00% 5.00% % Change ✔

Tracking Error (range) 7.00 7.50 9.50 10.00 Value ✔

VaR % limit 15.00% 20.00% Value ✔

IRM Demo: Global EMB

Portfolio Total Risk (% change) -5.00% 5.00% % Change ✔

Portfolio Total Risk (range) 11.00 12.00 13.00 14.00 Value X

Portfolio Total Risk / Benchmark Total Risk 0.50 2.00 Value ✔

Tracking Error (% change) -5.00% 5.00% % Change ✔

Tracking Error (range) 5.00 6.00 7.00 8.00 Value X

Unrecognised Securities: number (max) 0.00 Value ✔

VaR % limit 8.00% 10.00% Value ✔

IRM Demo: Pan Europe Long Equity

UCITS: Weight of securities greater than 5% not to exceed 40%

0.00% 35.00% 40.00% Value ✔

# securities where active weight > 2% 0.00 2.00 Value ✔

Illiquid stocks (max weight %) 0.00% 5.00% Value ✔

Number of Countries with Active Weight > 10% 0.00 0.00 Value X

Portfolio Total Risk (range) 12.00 13.00 14.00 15.00 Value ?

Portfolio Total Risk / Benchmark Total Risk 1.80 2.00 Value ✔

Portfolio Weight Of Index Stocks 80.00 90.00 101.00 110.00 Value ?

Tracking Error (range) 6.00 7.00 8.00 9.00 Value X

Unrecognised Securities: number (max) 0.00 0.00 Value X

VaR % limit 15.00% 20.00% Value ✔


Risk Scorecard I


Risk Scorecard II


Risk Scorecard III


Summary


Summary

► s usually refers to the annualized standard deviation of returns

► VaR used extensively, easy interpretation introduces substantial other shortfalls

► VaR needs supplementary information to overcome these (model validation, stress tests etc.)

► Other types of risk need to be monitored as well

► Risk Management Process

► Attention: Risk of creating Data Dump


Further Reading

► Jorion, Phillipe (2007), Value at Risk: The Benchmark for Managing Financial Risk, 3rd ed. McGraw-Hill.

► Hull, John C. (2009), Option, Futures and other Derivatives, Pearson International Edition.

► Artzner et al. (1999), Coherent measures of risk, Mathematical Finance , Vol. 9., No. 3; p.223 -228.

Regulatory information:

► http://www.esma.europa.eu/system/files/10_788.pdf

► http://www.irml.net/documentation.php


Questions?


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Risk Measurement in practice