1. Copyright © 2015, SAS Institute Inc. All rights reserved. MEASUREMENT AND OPTIMAL HEDGING OF LIQUIDITY RISK 9TH FINANCIAL RISKS INTERNATIONAL FORUM, PARIS MARCH 21 & 22, 2016 jimmy.skoglund@sas.com

2. Copyright © 2015, SAS Institute Inc. All rights reserved. Background: Liquidity Risk Measuring liquidity risk Hedging liquidity risk Planning Liquidity execution Cash Liquidity at Risk – A Special Case with Cash Hedging Portfolio References

3. Copyright © 2015, SAS Institute Inc. All rights reserved. Background: Liquidity Risk Measuring liquidity risk Hedging liquidity risk Planning Liquidity execution Cash Liquidity at Risk – A Special Case with Cash Hedging Portfolio References

4. Copyright © 2015, SAS Institute Inc. All rights reserved. LIQUIDITY RISK BACKGROUND Issue in banking Treasury manager wants to know the optimal size and composition of hedging portfolio for liability outflow Issue for investment funds The fund manager wants to know what would be the optimized asset selling strategy to cover for withdraws from the fund

5. Copyright © 2015, SAS Institute Inc. All rights reserved. LIQUIDITY RISK BACKGROUND Focus of this talk Dynamic hedging of liquidity shortfalls using optimal strategies 1) Dynamic hedging strategies and the selection of the optimal asset portfolio for liquidity shortfall hedging 2) For a given asset portfolio, the optimal execution strategy using asset sales etc.

6. Copyright © 2015, SAS Institute Inc. All rights reserved. LIQUIDITY RISK BACKGROUND Before the 2007 financial crisis liquidity risk was rarely incorporated into models (or incorporated ad-hoc) Learnings from the 2007 crisis Compounded itself quickly into a major liquidity crisis (or funding problem), leading to insolvency of major financial institutions A key characteristic of the financial crisis was the inaccurate and ineffective management of liquidity risk Many financial institutions [banks] did not have a dedicated liquidity buffer or liquidity portfolio that was managed

7. Copyright © 2015, SAS Institute Inc. All rights reserved. LIQUIDITY RISK BACKGROUND Regulatory response [Banking] The Basel III liquidity risk regulation underscores the importance of managing the liquidity contingency buffer (sufficiency, liquifiability) Focusing on maintaining a high quality liquidity portfolio that can hedge out liquidity outflows under stress scenarios And, integrate the liquidity pricing and hence incentive to raise liquidity as well as price costly liquidity according to the opportunity cost of raising the needed buffer Illiquid holdings may create a need for liquidity buffer

8. Copyright © 2015, SAS Institute Inc. All rights reserved. Background: Liquidity Risk Measuring liquidity risk Hedging liquidity risk Planning Liquidity execution Cash Liquidity at Risk – A Special Case with Cash Hedging Portfolio References

9. Copyright © 2015, SAS Institute Inc. All rights reserved. GENERAL LIQUIDITY EXPOSURE “Liquidity insolvency happens the first time t the firm cannot generate sufficient counterbalancing capacity (CBC) from the liquidity hedging portfolio to cover the funding (withdrawal) gap” The complexity of CBC creation means that liquidity solvency at T > t does not guarantee solvency at t.

10. Copyright © 2015, SAS Institute Inc. All rights reserved. GENERAL LIQUIDITY EXPOSURE Path-dependence of liquidity solvency  The capability of executing the liquidity hedging portfolio (liquid funds) results in a term-structure of liquidity across t=1,…,T and a path-dependency of liquidity risk  Liquid funds generated at t+1 to cover the outflow at t is too late  In contrast, market risk, credit risk required solvency capital is generally monotone (solvency at T implies solvency at t) “A firm is able to satisfy the demand for cash, and hence is liquid, as long as at each point in time outflows of cash are smaller or equal to inflows and the hedging flows that can be generated”

11. Copyright © 2015, SAS Institute Inc. All rights reserved. GENERAL LIQUIDITY EXPOSURE “We will define liquidity risk insolvency in general using a classical insurance ruin theory analogy such that insolvency occurs the first time a risk reserve process, composed of cash inflows and outflows and the hedging capacity, turns non-positive” Projected forward liquidity exposure (fund need) Projected forward liquidity hedging flows

12. Copyright © 2015, SAS Institute Inc. All rights reserved. GENERAL LIQUIDITY EXPOSURE Risk reserve process

13. Copyright © 2015, SAS Institute Inc. All rights reserved. GENERAL LIQUIDITY EXPOSURE

14. Copyright © 2015, SAS Institute Inc. All rights reserved. Background: Liquidity Risk Measuring liquidity risk Hedging liquidity risk Planning Liquidity execution Cash Liquidity at Risk – A Special Case with Cash Hedging Portfolio References

15. Copyright © 2015, SAS Institute Inc. All rights reserved. HEDGING LIQUIDITY RISK Planning vs. Liquidity execution Planning  Plan for reducing structural vulnerability of the balance sheet  Aquire naturally complementing assets/liabilities  Plan for cost-optimal endowment (earmarked) liquidity hedge portfolio » Up-front cost and opportunity cost (return foregone) Liquidity execution  Test and plan for liquidity execution of endowment portfolio

16. Copyright © 2015, SAS Institute Inc. All rights reserved. Background: Liquidity Risk Measuring liquidity risk Hedging liquidity risk Planning Liquidity execution Cash Liquidity at Risk – A Special Case with Cash Hedging Portfolio References

17. Copyright © 2015, SAS Institute Inc. All rights reserved. OPTIMAL HEDGING / PLANNING One of the most challenging aspects of liquidity risk [& Basel III] is that firms need to continuously manage a dedicated liquidity portfolio and that the adequacy of this portfolio in hedging liquidity outflows needs to be frequently tested Two general approaches to liquidity hedging in banking industry  Acquiring more assets that can generate future cash ‡flows that can complement the potential net cash outflows (hedging with contractual cash flows, structural liquidity mismatch)  Dynamic counterbalancing capacity through use of asset sales and repo agreements to generate liquidity at the exact time when net contractual cash flows cannot balance by itself

18. Copyright © 2015, SAS Institute Inc. All rights reserved. CONTRACTUAL HEDGING Tail constraint e.g., CVaR may still allow insolvency in risk reserve process as we have not yet introduced CBC portfolio Chen, W., Skoglund, J, 2012. Cash Flow Replication with Mismatch Constraints. Journal of Risk, vol 14(4).

19. Copyright © 2015, SAS Institute Inc. All rights reserved. CONTRACTUAL HEDGING Assumes that the assets/liabilities in the portfolio generate contractual cash flows that naturally complement the liquidity term structure  No active intervention are required at any future horizons  Leverages classical portfolio immunization techniques  Used at ’normal’ times to optimize the firms strategic liquidity balance sheet  However, …hard to find naturally complementing [asset] cash flows that are efficient under stress such as unexpected fund withdrawals Need dynamic counterbalancing capacity to mitigate such stressed liquidity outflow

20. Copyright © 2015, SAS Institute Inc. All rights reserved. CBC HEDGING Tail constraint e.g., CVaR is >=0 so that solvency is guaranteed at each t Note: Optimization is conditional on current balance sheet  on already performed structural balance sheet optimization Chen, W., Skoglund, J., 2014. “Optimal Hedging of Funding Liquidity Risk“, Journal of Risk, vol 16(3).

21. Copyright © 2015, SAS Institute Inc. All rights reserved. CBC HEDGING Available short-term liquidity Cash Contingent Credit Line Borrowing Assets  Sell  Repo (?)

22. Copyright © 2015, SAS Institute Inc. All rights reserved. CBC HEDGING Example: Optimal Endowment Portfolio  Liquidity gap: Stressed gap from ’negative’ log-normal plus negative Poisson jumps and Gamma jump severity, t=1,…,5 horizons  CBC Portfolio: credit facility, bond and cash » Credit facility usage fee (applied limit) – 0.1%, usage rate – 2% » Bond Price – follows GBM process » Case 1: Expected Stable/Increasing Bond Price – Flight to Quality » Case 2: Expected Decreasing Bond Price – Lower Quality Bond Asset Optimal endowment Case 1: High Quality BondCase 2: Low Quality Bond Credit FacilityApply for offered limit BondBuy bondNo bond CashNo cashAcquire cash

23. Copyright © 2015, SAS Institute Inc. All rights reserved. OPTIMAL MANAGEMENT Asset t=1t=2t=3…. Credit facility10,000-9,0007,000 Bond-200-800200 t=1 t=2 t=3 t=4 Cost optimal to pay back

24. Copyright © 2015, SAS Institute Inc. All rights reserved. OPTIMAL MANAGEMENT Assumes firm can manage liquidity outflow using CBC - without excessive trading costs i.e., no fire sale What happens if there needs to be a fire sale ?  All assets are considered for sale » Remaining CBC assets » Trading positions » … Need a model/approach that can be used to plan for optimal liquidity execution (at execution time and for a priori contingency planning) i.e., a ’best liquidity execution strategy’

25. Copyright © 2015, SAS Institute Inc. All rights reserved. Background: Liquidity Risk Measuring liquidity risk Hedging liquidity risk Planning Liquidity execution Cash Liquidity at Risk – A Special Case with Cash Hedging Portfolio References

26. Copyright © 2015, SAS Institute Inc. All rights reserved. LIQUIDITY EXECUTION All available assets are eligible for execution (fire sale) Liquidity evolves in worsening stages and the stage gap needs to be fulfilled Assume the assets have  Globally available liquidity amounts  Available amounts at 1 tier market depth  Available amounts at 2 tier market depth ….Sample Case  2 stages with duration 3 and 2 days  Gap that needs to be closed in both stages are 2,000,000 units of CCY Chen, W., Skoglund, J., and Cai, L., 2012. “Planning for Optimal Liquidity Execution“, IRAFIE, vol. 4(1).

27. Copyright © 2015, SAS Institute Inc. All rights reserved. LIQUIDITY EXECUTION AssetFirst Tier Cost Second Tier Cost First Tier Depth Day 1Day 2Day 3 Cash 10bp 500,000 Cash 21bp 1,000,00000 Bond 12bp25bp500,000700,000 Bond 210bp40bp300,000800,000 Facility1bp20bp250,0000500,000 Equity 18bp30bp200,000600,000 Equity 218bp55bp150,0000300,000 AssetFirst Tier Cost Second Tier Cost First Tier Depth Day 4Day 5 Cash 10bp 500,000 Cash 21bp 1,000,000 Bond 14bp45bp300,000700,0007000,000 Bond 220bp100bp100,000500,000 Facility2bp40bp50,000150,00050,000 Equity 118bp50bp100,000600,000 Equity 230bp125bp20,000100,000 Duration 3 days Duration 2 days Day 1Day 2Day 3Day 4Day 5 Daily market depths

28. Copyright © 2015, SAS Institute Inc. All rights reserved. LIQUIDITY EXECUTION Optimal Plan:  Optimal to rank liquidity facilities based on their anticipated execution costs and haircuts across the expected stages of a liquidity crisis - execute least quality assets first, saving the liquid assets for later execution as they do not have a significant decrease in value as liquidity distress worsens.  Refrain from using the least quality assets if they are not needed to keep execution costs to a minimum LiquidityAvailable amount Optimal amount, Stage 1Optimal amount, Stage 2 Cash 1500,000000 0 Cash 21,000,0000000 Bond 1700,00000297,189102,811300,000 Bond 2800,000115,763300,000 00 Facility500,0000250,000150,00050,000 Equity 1600,000200,000 00 Equity 2300,00000000 Raised = 2,000,000

29. Copyright © 2015, SAS Institute Inc. All rights reserved. LIQUIDITY EXECUTION What if even the least quality (value) assets have to be executed to fulfill the gap?  Optimal to execute first as their value in the beginning of a crisis is anticipated to be higher than in later more severe stages  A firm that underestimates the severity of the liqudity crisis will end up with the least quality assets …. Beause, under the firms anticipated stress, it was optimal not to execute those assets to keep execution costs to minimum ”Cash first” vs. ”Cash last” execution strategies ?

30. Copyright © 2015, SAS Institute Inc. All rights reserved. Background: Liquidity Risk Measuring liquidity risk Hedging liquidity risk Planning Liquidity execution Cash Liquidity at Risk – A Special Case with Cash Hedging Portfolio References

31. Copyright © 2015, SAS Institute Inc. All rights reserved. CASH LIQUIDITY EXPOSURE Skoglund, J., Chen, W., 2012. “Cash Liquidity at Risk“, IRAFIE, vol. 4(1). Cumulated cash liquidity need ”We are now asking the question: How much initial cash at t=0 is needed to cover for all the projected outflows at t=1,…,T”

32. Copyright © 2015, SAS Institute Inc. All rights reserved. CASH LIQUIDITY AT RISK

33. Copyright © 2015, SAS Institute Inc. All rights reserved. Background: Liquidity Risk Measuring liquidity risk Hedging liquidity risk Planning Liquidity execution Cash Liquidity at Risk – A Special Case with Cash Hedging Portfolio References

34. Copyright © 2015, SAS Institute Inc. All rights reserved.  Skoglund, J., Chen, W., 2015. Financial Risk Management: Applications in Market, Credit, Asset and Liability Management and Firmwide Risk, Wiley Finance Series.  Chen, W., Skoglund, J., 2014. “Optimal Hedging of Funding Liquidity Risk“, Journal of Risk, vol 16(3).  Skoglund, J., 2013. Modern Risk Based Funds Transfer Pricing, Journal of Performance Management, vol 25(1).  Chen, W., Skoglund, J, 2012. Cash Flow Replication with Mismatch Constraints. Journal of Risk, vol 14(4).  Skoglund, J., Chen, W., 2012. “Cash Liquidity at Risk“, IRAFIE, vol. 4(1).  Chen, W., Skoglund, J., and Cai, L., 2012. “Planning for Optimal Liquidity Execution“, IRAFIE, vol. 4(1).  Duffie, D., Ziegler, A., 2003. “Liquidation Risk, Financial Analysts Journal, vol 59(3). REFERENCES FOR THIS PRESENTATION