1. Copyright © 20051 Ideas on Risk Reporting: Risk Topography and Risk Radar Kanwardeep Ahluwalia Bear, Stearns International Ltd PRMIA / ISDA Seminar 19 July, 2005

2. Copyright © 20052 What does the future hold?

3. Copyright © 20053 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 non- experts

4. Copyright © 20054 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

5. Copyright © 20055 Result: ‘Radar’ for Options Trading

6. Copyright © 20056 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’

7. Copyright © 20057 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-to- day hedging: Sensitivities

8. Copyright © 20058 A Risk Report (figures in millions)

9. Copyright © 20059 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?

10. Copyright © 200510 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

11. Copyright © 200511 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

12. Copyright © 200512 1-D View: Notional by Strike

13. Copyright © 200513 1.5-D view: Notional by Strike

14. Copyright © 200514 2-D version of same data

15. Copyright © 200515 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

16. Copyright © 200516 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

17. Copyright © 200517

18. Copyright © 200518 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

19. Copyright © 200519 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

20. Copyright © 200520 Other examples

21. Copyright © 200521 Heavy Trading