2. Agenda
The Need for VaR
Definition of VaR
Uses of VaR
VaR Methods
VaR - Historical Simulation
Changes since the Financial Crises of 2008
Strengths and Weakness
Summary
3. The Need for VaR
Different Asset Classes use their own measures
Fixed Income – Duration
Interest Rates – DV01
FX – Currency position
Commodity – Number of contracts
Equities – Number of shares
Using these to compare risk in these portfolios is like
comparing apples and oranges
An investor or owner needs a simple measure that can be
used in a consistent way to compare risk between these
portfolios
And with the ability to aggregate risk appropriately
Value at Risk is that risk measure
4. Definition of VaR
How much could we lose over a specified holding period
with a defined probability
So if a portfolio has a VaR of $20 million
We need to know the confidence level used to calculate
We need to know the holding period (time horizon)
Say confidence level is 99% and holding period is 5 days
This then means “We would expect to lose $20 million
or more over a 5 day period, in 1 out of 100 business
days”
Note it does not tell us whether on that 1 day we could
lose $21 million or $200 million!
So if we are relying only on VaR for the answer to that
then we are going to be in trouble
For that we need Tail Measures or Stress Testing
5. Uses of VaR
Made public by JP Morgan in 1994 with RiskMetrics
Widely adopted in the industry very quickly after that
Particularly for Derivatives where measures such as gross
notional or position in contracts units, are not that
insightful
Basel II Capital Accord for Market Risk – 1995
Internal Model Capital is VaR times a multiplier set for each
bank by its regulator as between 3 & 4
Banks report VaR in Annual Financial Statements – 1997
Internal 1d VaR and Regulatory 10d VaR
Clearing Houses for Initial Margin – 1999 (LCH SwapClear)
Margin from defaulting member used to cover the market risk
loss for the period it takes to close-out the portfolio
6. VaR Methods
Three main methods
Parametric (aka Variance-Covariance or Delta-Gamma)
Historical Simulation
Monte-Carlo Simulation
Different assumptions, calculation steps, compute
efficiency but similar numbers for standard portfolios
The most common is Historical Simulation
As easiest to understand
Simple assumptions on distributions of returns
So if for our $20 million VaR portfolio, we also said that we
had used 5 Years of history as well as 99% and 5d
We would say that “given how the market has performed
in the past 5 years” our VaR estimate is $20 million
7. VaR - Historical Simulation
It relies on choosing
A historical period, e.g. 4 Years
A holding period e.g. 5 days
Generating daily holding period returns in this period
Calculating the P&L impact on a portfolio by applying
these returns to today
Ordering the P&L outcomes by decreasing loss
Interpolating for a chosen confidence level e.g. 99%
9. VaR - Historical Simulation
Assume our portfolio has a PV01 of $1million
Assume for simplicity that USD 5Y Swap is the only risk factor
For a 1 bps rise in the 5Y Swap rate, our Profit will be $1m
For a 1 bps fall in the 5Y Swap rate, our Loss will be $1m
We can calculate the PL Series for our portfolio by multiplying the
bps returns on each day by $1 million, which is shown below
-80.00
-60.00
-40.00
-20.00
0.00
20.00
40.00
60.00
80.00
Profit Loss
Sep08 to Sep12
20Nov08 > $60m
10. VaR - Historical Simulation
This PL Series
Has a PL value for each business day from 5 Sep 08 to 4 Sep 12
A total count of 1043 values
Each corresponds to a specific scenario date, starting on 5 Sep 08
The first element represents the PL outcome of applying the 5-day
return shift between 1 Sep 08 and 5 Sep 08 to todays market data
and todays portfolio
We call this the PL vector of the portfolio
The first few elements of which are shown below
-26.51
-5.97
-12.75
-6.47
-3.29
-15.83
-14.76
-37.08
-9.98
-16.55
22.76
71.55
09/05/2008
09/08/2008
09/09/2008
09/10/2008
09/11/2008
09/12/2008
09/15/2008
09/16/2008
09/17/2008
09/18/2008
09/19/2008
09/22/2008
For these dates
11. VaR - Historical Simulation
The PL vector can then be re-ordered by decreasing loss
Keeping a note of the scenario date and PL of each
The first part of this is shown below
1
2
3
4
5
6
7
8
9
10
11
11/20/2008
12/17/2008
10/21/2008
10/22/2008
11/21/2008
06/17/2009
08/14/2009
12/18/2008
10/06/2008
10/07/2008
09/16/2008
-62.58
-56.16
-47.79
-46.24
-44.95
-42.47
-41.29
-39.73
-39.62
-37.45
-37.08
For these datesRe-order by PL
Now we can determine the VaR
Which we will define as 99% or the loss of the 11th worst PL
(We could define as 10th worst or interpolate between 10th and 11th)
So VaR is $37.08m
Occurs on the scenario date of 16-Sep-08, we call this the VaR Date
This is the week of Lehman’s bankruptcy filing
VaR Date
12. VaR - Historical Simulation
0
50
100
150
200
250
-70 -65 -60 -55 -50 -45 -40 -35 -30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80
Frequency
5d PLs
Sep08 to Sep12
Mean -1.21
Standard Deviation 13.03
Kurtosis 2.63
Skewness 0.17
Range 134.13
Minimum -62.58
Maximum 71.55
VaR 99% -37.08
Count 1043
A Histogram is a good way to view the PL vector
Allocate each PL to a bin range
Frequency is high for small PLs, giving the distribution below
13. VaR - Historical Simulation
Zooming in to the largest losses
Mean -1.21
Standard Deviation 13.03
Kurtosis 2.63
Skewness 0.17
Range 134.13
Minimum -62.58
Maximum 71.55
VaR 99% -37.08
Count 1043
11th largest loss
Largest loss
Expected Shortfall
14. Changes since the Financial Crises of 2008
Basell Capital Accord, introduced Stressed VaR
So Trading Book Capital is the higher of Firm’s Multiplier *
VaR or Multiplier * Stressed VaR
Where Stressed VaR covers a period of Market Stress
The Financial Crises of 2008 qualifies as a period of stress
for most major markets
Wider use of Tail measures
Expected Shortfall (ES) or Worst Case Loss (WCL)
Renewed focus that Stress testing must be performed and
the definition and results of these discussed within the firm
and with regulators
Hence US & European Regulatory Stress Tests
15. Strengths and Weaknesses
Strengths
Reduces risk to a single $ amount
Mark to market based measure (not original notional)
Compare risk of different asset class portfolios
Aggregate risk across portfolios
Widely used since 1994
Weaknesses
Reduces risk to a single $ amount
Assumptions may be complex
Depends on market prices being observable and similar
behaviour to that observed in the past
Long-tailed properties of financial markets
Portfolio diversification is not there in a Crisis
So correlation goes to 1
16. Summary
It is crucial to understand any assumptions
For VaR, these are
Method e.g. Historical Simulation
Confidence level e.g. 99.7%
Holding Period e.g. 5 days
Historical Period Used e.g. 5 Years
And not use just a single VaR measure
Or indeed discard VaR (and replace with what?)
So, in addition to VaR
Use Tail Measures e.g. ES or WCL
Stress Tests – Historical and Hypothetical
Independent price verification
Gross measures
17. Contact Details
Our LinkedIn Page: Clarus Financial Technology
Our Website: www.clarusft.com
My contact details: amir@clarusft.com