Ideas on Risk Reporting:
Risk Topography and Risk Radar
Kanwardeep Ahluwalia
Bear, Stearns International Ltd
PRMIA / ISDA Seminar 19 July, 2005
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What does the future hold?
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Starting Point
• A derivatives portfolio, e.g. equity options
on a single underlying stock or index
• A desire to anticipate risk that might be
faced in the future
• A need to make the risk visible to nonexperts
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Mechanics
• Pick a market movement you care about, say equity prices
falling 10%
• Pick a hedging routine that you want to assume, e.g. the
desk stays delta neutral
• Calculate the value and delta of your option portfolio in a
grid with price steps representing all market levels, and
with time steps for all future times
• Use the results of that calculation to infer the profit or loss
impact of a 10% market fall at the times and market levels
you have chosen (stripping out p/l from delta positions)
• Plot the p/l impact in a ‘heat map’ coloured graph, scaled
to your particular p/l tolerance
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Result: ‘Radar’ for Options Trading
Call Spread
280%
220%
160%
100%
10-Nov-11
5-Mar-11
28-Jun-10
21-Oct-09
13-Feb-09
8-Jun-08
2-Oct-07
25-Jan-07
20-May-06
12-Sep-05
5-Jan-05
40%
525 -575
475 -525
425 -475
375 -425
325 -375
275 -325
225 -275
175 -225
125 -175
75 -125
25 -75
(25)-25
(75)-(25)
(125)-(75)
(175)-(125)
(225)-(175)
(275)-(225)
(325)-(275)
(375)-(325)
(425)-(375)
(475)-(425)
(525)-(475)
(575)-(525)
(625)-(575)
(675)-(625)
(725)-(675)
(775)-(725)
40%
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Objectives of Talk
• Primary: Introduce a novel method for
reporting risk for derivatives portfolios
• Secondary: Initiate public recognition about
the importance of practical risk reporting
• Tertiary: Stimulate risk management
discussion about the the art of influence,
since effective reporting is a key component
of ‘influencing skills’
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Risk Reporting Expectations
• A common metric, probably statistical, to
compare different trading risks: VaR
• Market shocks to look at extreme events
considered plausible: Stress
• Detailed risk calculations to assist in day-today hedging: Sensitivities
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A Risk Report (figures in millions)
VaR
Portfolio 7.5
Top 5
Ford
GM
IBM
Microsoft
AIG
4.4
3.3
2.7
2.5
2.4
Mkt -10%
(20 )
(5 )
(8 )
2
(1 )
(12 )
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Delta Gamma Vega
15
3
2
3
(5 )
1
10
2
(4 )
(7 )
5
5
(1 )
(2 )
4
2
(1 )
3
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Considerations
• Is the risk too big (or too small)?
• What is the riskiest position?
• Clearly there is no context for these
numbers
• Can we rely on VaR alone, with all its
flawed assumptions, as an indicator of
absolute risk?
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Here and Now
• All risk measures presented apply to the
portfolio as it appears today (naturally)
• It could be that the risk we might encounter
tomorrow, or a week/month/year later, will
be what we want to address now
• Waiting for the risk to show as too large
could be too late
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More Dimensions of Risk
• Looking at an option portfolio we can:
– investigate where they sit in strike space, for a
one-dimensional graphical view
– plot their positions in strike and maturity space
for a two-dimensional tabular view
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1-D View: Notional by Strike
Where Are Our Options?
40
.
30
Notional (millions)
20
10
0
(10 )
(20 )
(30 )
(40 )
60%
70%
80%
~ Out of the money put options
90%
100%
110%
Strike / Spot
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120%
130%
140%
~ Out of the money call options
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1.5-D view: Notional by Strike
Where Are Our Options?
80
.
60
Notional (millions)
40
20
> 1yr
0
3mths to 1yr
(20 )
< 3mths
(40 )
(60 )
(80 )
(100 )
60%
70%
80%
~ Out of the money put options
90%
100%
110%
Strike / Spot
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120%
130%
140%
~ Out of the money call options
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2-D version of same data
Notional (in millions) plotted by Strike / Spot and Maturity
1 month
3 months
6 months
1 year
2 years
5 years
60%
40
10
(30 )
(30 )
0
(20 )
70%
10
(30 )
30
(20 )
0
0
80%
(10 )
0
0
0
20
0
90%
5
0
(20 )
0
(10 )
20
100%
20
20
(30 )
0
10
10
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110%
20
0
0
0
0
0
120%
15
0
10
(10 )
0
(40 )
130%
0
(10 )
0
0
10
20
140%
(10 )
(20 )
(30 )
30
40
(20 )
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Big Picture vs Trader Detail
• More detail leads to greater specialised
knowledge of the risks
• Increasing information density makes the
message less transparent to a wider
audience, e.g. senior management
• The data presented doesn’t provide a
quantification of risk
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Gamma Graphs
• Gamma, i.e. curvature or non-linear behaviour, is
a key measure of risk
• Gamma risk grows as you approach the strike and
expiry of an option
• Plotting gamma over a variety of spot prices, and
times in the future, is relatively straightforward
method to illustrate troughs (short option risk) and
peaks (long option risk, i.e. time decay)
• Using gamma automatically strips out delta risk
that is likely to be hedged
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Hang Seng Gamma Profile over next 40 days
$15,000,000 -$18,000,000
$12,000,000 -$15,000,000
$9,000,000 -$12,000,000
$6,000,000 -$9,000,000
$3,000,000 -$6,000,000
$0 -$3,000,000
($3,000,000)-$0
($6,000,000)-($3,000,000)
($9,000,000)-($6,000,000)
($12,000,000)-($9,000,000)
($15,000,000)-($12,000,000)
$18,000,000
$15,000,000
$12,000,000
gamma (USD)
$9,000,000
$6,000,000
$3,000,000
$0
($3,000,000)
9000
9400
9800
10200
($6,000,000)
($9,000,000)
($12,000,000)
10600
11000
($15,000,000)
0 3
index level
11400
6 9
12 15
18 21
24 27
days forward
30 33
36 39
11800
12200
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Current level
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Drawbacks with Gamma
• It has singularities at option expiries, where
it can become arbitrarily large
• It needs to be translated into p/l, which is
the key issue that senior management care
about
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Comments on the Radar Report
• It is a quantification of gamma into p/l,
hence easier to interpret
• Can be used to display diversity of market
making books, or relative risk taking across
various underlying shares or indices
• Does not work well for multiple underlying
shares or indices, does not easily aggregate
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Other examples
Down and Out Barrier Call
280%
220%
160%
100%
10-Nov-11
5-Mar-11
28-Jun-10
21-Oct-09
13-Feb-09
8-Jun-08
2-Oct-07
25-Jan-07
20-May-06
12-Sep-05
5-Jan-05
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40%
525 -575
475 -525
425 -475
375 -425
325 -375
275 -325
225 -275
175 -2 25
125 -175
75 -12 5
25 -75
(25)-25
(75)-(2 5)
(125)-(75)
(175)-(125)
(22 5)-(175)
(275)-(225)
(32 5)-(275)
(375)-(325)
(42 5)-(375)
(475)-(425)
(525)-(475)
(575)-(52 5)
(62 5)-(575)
(675)-(625)
(725)-(675)
(775)-(72 5)
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Heavy Trading
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