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

Introduction

Page 4
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?

Page 6
How is s actually measured in practice?
VOLATILITY

Page 7
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)

Page 8
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)

Page 9
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%

Page 10
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.)

Page 11
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”

Page 12
S&P500 volatility of weekly returns
0.00%
5.00%
10.00%
15.00%
20.00%
25.00%
30.00%
4
5
6
7

Page 13
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

Page 14
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

Page 15
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

Page 17
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)

Page 18
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 푡,훼=훿∗훼∗√푡
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)

Page 19
Empirical distribution of S&P 500 returns
0
200
400
600
800
1000
1200
1400
1600
-6.78%
-6.28%
-5.78%
-5.28%
-4.78%
-4.28%
-3.78%
-3.28%
-2.78%
-2.28%
-1.78%
-1.28%
-0.78%
-0.28%
0.22%
0.72%
1.22%
1.72%
2.22%
2.72%
3.22%
3.72%
4.22%
4.72%
5.22%
5.72%
6.22%
6.72%
7.22%
7.72%
8.22%
8.72%
9.22%
9.72%
10.22%
10.72%
►Parametric VaR 0.95 20d = 1.08%* 1.654 *√20 = 8.00%
►Non-Parametric VaR 0.95 20d ≈ 7.23 %

Page 20
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).

Page 21
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%?

Page 22
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)

Page 23
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?

Page 24
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

Page 26
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

Page 27
Liquidity Risk I
►Various concepts to assess asset liquidity:
Days of traded volume held (SEC rule5d 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.

Page 28
Liquidity Risk II – Mutual Funds
Liabilities
Asset liquidity

Page 29
Model Risk
Delta Neutral Portfolio (High Optionality)

Page 30
VIX in May 2010
0
5
10
15
20
25
30
35
40
45
50

Page 31
Derivatives (Non-linear) I

Page 32
Derivatives (Non-linear) II
-0.60%
-0.50%
-0.40%
-0.30%
-0.20%
-0.10%
0.00%
0.10%
2412
2422
2432
2442
2452
2462
2472
2482
2492
2502
2512
2522
2532
2542
2552
2562
2572
2582
2592
2602
2612
2622
2632
2642
2652
2662
2672
2682
2692
2702
2712
2722
2732
2742
2752
2762
2772
EuroStoxx Options Payoff

Page 33
Derivatives (Non-linear) III
04/12/2012 -VaR20d 0.99
►MC (non-parametric): 0.68%
►Linear (parametric): 0.56%

Page 34
Derivatives (Non-linear) IV
-1.00%
0.00%
1.00%
2.00%
3.00%
4.00%
5.00%
6.00%
2412
2422
2432
2442
2452
2462
2472
2482
2492
2502
2512
2522
2532
2542
2552
2562
2572
2582
2592
2602
2612
2622
2632
2642
2652
2662
2672
2682
2692
2702
2712
2722
2732
2742
2752
2762
2772
EuroStoxx Options Payoff

Page 35
Derivatives (Non-linear) V
05/12/2012 -VaR20d 0.99
►MC (non-parametric): 0.57%
►Linear (parametric): 3.79%

Page 36
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)

Page 37
Example: Counterparty Risk

Risk Monitoring & Governance

Page 39
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

Page 40
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
✔
11.00
12.00
13.00
14.00
Value
X
0.50
2.00
Value
✔
Tracking Error (% change)
-5.00%
5.00%
% Change
✔
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
12.00
13.00
14.00
15.00
Value
?
1.80
2.00
Value
✔
Portfolio Weight Of Index Stocks
80.00
90.00
101.00
110.00
Value
?
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
✔

Page 41
Risk Scorecard I

Page 42
Risk Scorecard II

Page 43
Risk Scorecard III

Summary

Page 45
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

Page 46
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

Page 47
Questions?

Page 48
Contact

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