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Convex Risk Parity,
Fat-tails Management, and practical CVA/XVA
Mihail Turlakov
Global Derivatives conference
Budapest, May 2016

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Convex Risk Parity,
Fat-tails Management, and practical CVA/XVA
CVA/XVA portfolio management – part 1
XVA desks are portfolio managers, not perfect hedgers - what is the reality of
CVA/XVA management?
 The major tension at the heart of CVA management
 CVA/XVA are tail-risks
Convex Risk Parity and Tail Management – part 2
Cross-asset and ‘systemic carry’ portfolios – what are the practical and “efficient
frontier” strategies to manage these portfolios?
 The modern portfolio theory and the drawdown/loss aversion
 Tail management
 Convex Risk Parity

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Why not to hedge perfectly?
 Single-name protection is not available for large part of the portfolio
 CDS market has limited coverage and liquidity. CDS market became less liquid (a side effect of
regulations), three times less volume from 2008 to 2015
 Many names (i.e. project finance, etc.) never had publicly traded credit instruments
 Shorting bonds is also a precarious effort
 Systemic hedges by indices (ITRX, etc.) or sovereign CDSs is a proxy/model hedge
 Jump-to-Default and recovery are not hedged
 MtM model volatility is hedged, but basis risk (between index and single-name) is increased
 Although CVA was intended by regulators to be hedged fully, and the banks obeyed as
best as they can. But the direct hedging of the credit risk of CVA cannot be done in
practice - the major tension at the heart of CVA reality.
Reality is quite different than it actually is
-Antoine de Saint-Exupery-

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 XVAs (CVA, FVA, MVA and KVA) are systemic risks of corporate and sovereign
hedging which explode in the market crises
 Systemic concentration risks transform into counterparty and funding crises, although rarely yet
quite abruptly
 XVAs (CVA, FVA, MVA and KVA) are illiquidity risks
 Not easily tradable/novated OTC, not repo-able and only CCP-convertible at full cost
CVA/XVAs are a measure of Tail-Risks (1)
Tail risk is a very rare but strong-impact event

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 Coupled shocks in credit, FX, and IR/funding markets cause even more non-linear
changes of CVA and FVA
 “Good, bad, and ugly” feedback loops and liquidity
 Wrong-way risk is important
 Defaults (jump-to-default in CVA) and liquidity squeezes (jump to insolvency in FVA)
are “last stage” tail-risk events
CVA/XVAs are a measure of Tail-Risks (2)

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Bank’s credit risk – a complex picture
 Credit risk on a loan – accrual accounting in the banking book
 Credit risk on a loan is not hedged typically, because credit risk is a main business of a
bank
 Credit risk on a derivative – CVA MtM (mark-to-market) in the trading book
 Credit risk is expected to be hedged (Tier-1s approach), because the management and
shareholders do not like revenue volatility
 The exposure is in principle unlimited
 CVA and Loan management on the bank’s level - mixed accrual and MtM risks
 Credit exposures of the loans are determined by longer economic cycles and “rebalanced
by real economy”
 Derivatives exposures are determined by shorter market cycles and ”hedged”/transformed
 Different capital treatment and costs in the Trading and Banking books - FRTB
 Credit risks on derivatives and loans are better managed on a portfolio basis, but
the reality and practice are complicated.

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XVA management – the part 1 – key points
 CVA/FVA/KVA models can vary somewhat, but CVA/XVA management is very
different in different banks due to multiple (organisational, top-management, different
markets, and business models) reasons
 CVA/XVAs are tail-risks with non-hedgeable jump-to-default and recovery risks
 Significant model risks – “basis risks by design”, wrong-way risk, forward-rating risk, ... appreciated
only over economic cycle (2-5 years)
 CVA/XVA management is better to have some pro-active elements
 Tier-1s and some Tier-2s banks have to hedge CVA PL volatility to manageable levels
 Tier-2s and Tier-3s can, very sensibly, keep the credit risk and not hedge, yet “management-
sensitivity threshold” is likely to be breached under some stressed conditions

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Motivational questions and other talks at Global Derivatives 2016
 XVA desks are portfolio managers, not perfect hedgers - what is the reality of
CVA/XVA management? Quantitative understanding and proposals
Good example – FVA debate - FVA can be hedged in theory but not in practice (Kjaer, Burgard), the
reality of the markets and internal banks operations are the main issues
 Andrey Chirikhin – junior quant seminar – the overview of XVA and its capital requirements
 Andrew Green – some real world problems of XVA risk managing
 Mihail Turlakov – part 1 – brief review of the practice of CVA/XVA management
 Chris Kenyon – the trade-off between MVA and KVA
 Massimo Morini – innovating XVAs (including “perfecting imperfect hedging”)
 Leif Andresen – bank’s balance sheet and FVA – the FVA debate continued
 Cross-asset and ‘systemic carry’ portfolios – what are the practical and “efficient
frontier” strategies to manage these portfolios? Portfolio and Risk management
understanding and proposals
 Buy-side Summit: QUANTITATIVE INVESTMENT & PORTFOLIO STRATEGIES
 Nick Baltas – exploiting cross-asset carry
 Kartik Sivaramakrishnan, Robert Stamicar - Optimising Multi-Aset Portfolios To Minimise
Downside Risk: A CVaR Based Approach
 Emanuel Derman – the review of “good and not so good ideas”
 Mihail Turlakov – part 2 – Tail risk management and Convex Risk Parity

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part 2 - Convex Risk Parity, Fat-tails Management,
and practical CVA/XVA
Convex Risk Parity and Tail Management – part 2
 A brief review of Risk Parity
 The portfolio theory and a drawdown/loss aversion
 Kelly portfolio leverage and fat tails
 Fat-tails management
 Convex Risk Parity

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Risk Parity (1) – a brief review
 Risk Parity (RP) is a risk-adjusted portfolio management approach
 The assets in the portfolio are risk-balanced, i.e. weighted by the inverse of the risk, here volatility
 The leverage is used for low-volatility, positive return, assets (G10 government bonds, typically).
 More successful approach than the classic 60/40 mix of stocks/bonds throughout the long history
 Avoid unintended skews and risks of the mean-variance portfolio theory
 RP assumes equal risk-adjusted expected returns
 Returns are not predictable, no input of “exact expected” returns and correlations
 Correlations can regime-change and are not stable
 Exploiting the leverage by using derivatives - the drawdowns have to be controlled
 A connection to part 1 - RP is well suited for carry portfolios (i.e. CVA portfolio)
 In practice, a combination of model hedging (the standard approach according to the internal
model) and Risk Parity can be applied in order to keep PL volatility within desired threshold.

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Risk Parity (2) – criticisms and developments
 Risk Parity criticisms
 “Lucky” success due to the era of trending lower rates and the bonds leverage
 Returns (risk premiums) have to be considered
 Correlations between stocks and govt bonds has been consistently negative. What happens if
that's no longer the case?
 Negative skew of positive return assets and tail/drawdown risks
 Risk Parity family – the variety of approaches and performances
 “All Weather” (Bridgewater Associates), Tail Risk Parity (AllianceBernstein, GAM), “Two regimes”
Risk Parity (First Quadrant), Active Risk Parity (AQR), Risk Parity with the inclusion of momentum
(Salient), Factor-based Risk Parity (JP Morgan AM), Invesco, PIMCO, etc.

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Risk Parity (3) – addressing the drawdown/tail risk
 The markets and the world are fat-tailed, therefore we have to deal with tail events
 Tail-Risk Parity (TRP) adopts Risk Parity approach with the focus on the drawdown
protection
 The drawdown (tail loss), rather than volatility, is considered as more important measure of risk
 Risk Parity focuses on volatility, Tail-Risk Parity [Alankar] defines risk as expected tail loss (ETL)
 Markets can sustain the notion of risk as drawdown risk (permanent loss)
 Empirical results - “Risk premium is strongly correlated with tail-risk skewness but very little
with volatility” (a clear exception is trend following) [Lemperiere]
 Trade-off between skewness and excess returns – basic reasons and mechanisms
 Crowding into carry trades – decreasing returns and increasing downside (“unwind tail risk”)
 Liquidity shocks and “super-shocks” - fast market snap reactions and re-pricing
 Behavioural balance (prospect theory) of the “skew value” for buyers(hedgers)and sellers

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Portfolio theory and the drawdown aversion (1)
 Drawdown/loss[Kahneman]/leverage[Asness]/ETL/VaR aversion
 “What the investors fear is the possibility of permanent loss”… not the volatility
 More important risk measure
 Drawdown aversion is essentially a more general and quantitative version of the
leverage aversion
 Leverage aversion changes the predictions of the portfolio theory [Asness]
 Leverage is a tool and a capability, not a danger by itself, while a permanent loss is
 The different costs and types of the leverage/drawdown aversion
 The cost of OTM insurance - “hard drawdown” aversion - overall portfolio leverage
 Liquidity and rebalancing costs – margin cash and leverage of some particular assets
 Gap (il)liquidity costs – unwinding of the portfolio
 Outflows risk

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Portfolio theory and the drawdown aversion (2)
 Concave and lower efficient frontier due to the drawdown aversion
 Different Capital Lines for different levels of drawdown aversion
 Differentiation between investors due to their different drawdown aversion

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Portfolio theory and the drawdown aversion (3)
 The investors are sensitive to mark-to-market and price of liquidity– [Illinski]
 The stop-loss cost makes efficient frontier strongly concave and even downward sloping
 Unstable leveraged returns due to “selling of tails "and optionality
 Superiority of option portfolios in “Extremistan” (world with fat tails) – [Thorp]
 Option portfolios can reach beyond geometric efficient frontier of the underlying – buy
attractively priced “lottery tickets”
 Options, being on the efficient frontier, can have better MDD (Maximum Drawdown Distribution),
even in “Mediocristan” (Gaussian world)
return
risk
𝑅𝑓𝑟𝑒𝑒
CAPM
Reality

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Kelly allocation for the long run – the stinging tail
 The effect of the drawdown on Kelly ratio [Kelly]
 Kelly allocation is very sensitive to vol skew and tail drawdowns
 Kelly skew – asymmetric affect of left and right fat tails*
 Sharpe ratio is not a good guide in the presence of the tails
The growth becomes negative
* from extended Kelly calculations Sharpe= Kelly * volatility

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Kelly Risk Parity and skew – open questions
 Kelly Risk Parity (KRP)
 If the unknown excess returns are the same, RP is equivalent to Sharpe maximization (i.e. MVA).
Under the same condition, maximizing long-run growth is 1/variance parity – KRP, the
general leveraged risk parity, is the variance parity (VP) therefore.
 Positive skew of KRP due to 1/variance weighting versus negative volatility and Kelly skews
 The dynamics and conditional probabilities are very important
 Volatility skew is similar to wrong-way risk (WWR)
 Vol skew - left-tail risk-off spot move is accompanied by higher vol
 WWR - left-tail credit widening is accompanied by risk-off moves in spots/rates
 See a scenario model of wrong-way risk [Turlakov] in CVA/XVA context
We need to free ourselves from “average” thinking
-P. W. Anderson (Nobel laureate in Physics)-

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Fat-tails management – general aspects
 Tail dangers-opportunities[Brown] is much more about risk management than
about the core strategy
 Be prepared not to make stupid mistakes under stress conditions
 (All) Tail events cannot be hedged by definition
 Risk Management is about human decisions
 Market takes a single path unlike Monte Carlo simulations
 A strong behavioural uncertainty about the consequences and the level of the drawdown
 Portfolio management – a mix of active and passive elements
 Diversification is a risk reduction, not risk management
 Actively managed fat left and right tails
 To protect against major drawdowns and be flat during “normal periods”.
 Left-Tail-Risk options hedging with monetisation rules and momentum[Bhansali]
 Right-Tail (risk-on) options (beyond base efficient frontier [Thorp])

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Tail Dangers-Opportunities (1a) – the insights
 Volatility is the only real asset class [Artemis]… for liquid financial assets
 Carry strategies, risk parity, etc. are effectively volatility strategies

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Tail Dangers-Opportunities (1b) – the insights
 Inconvenient truth about stocks-bonds anti-correlation
 Shadow Convexity of major Central Banks [Artemis] - exploit or protect against?

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Convex Risk Parity – portfolio management framework
 Convex Risk Parity
 A strategic approach/portfolio is Risk Parity – passive core (in the sense of conventional core-
satellite approach of the portfolio management). Naturally, short volatility and convexity. Risk Parity
creates a systemic framework with low turnover and liquidity costs
 A positive convexity (long volatility) for selected drawdown risks – active satellite. Active
management is about major tensions/tail risks – buying insurance-lottery tickets
 Convex Risk Parity – positive carry, negative convexity, core
 Risk Parity diversification – a portfolio of pairs of (possibly illiquid) anti-correlated assets
 Kelly Risk Parity - optimal leverage and positive skew
 Macroeconomics with the view on major structural imbalances a) carry and major trends b) risk-
off/safe-heaven assets (currently, G10 govy bonds)
 Convex Risk Parity – active, positive tail convexity, satellite
 Actively managed fat left and right tails. These strategies aim to protect against major drawdowns
(the main objective) and at a flat return during “normal periods”.
 Avoid illiquid (usually credit/counterparty related?) and model-dependent risks and assets

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Summary
 CVA/XVA management is the portfolio management
 “Going the full circle” – from introducing the illiquidity adjustments (CVA/XVA), enforced by
regulators, to realising the limits of CVA/XVA hedging
 Practical CVA/XVA management must have some pro-active elements
 Convex Risk Parity and Tail Management
 Convex Risk Parity is an attractive portfolio approach for ‘systemic carry’ portfolios
 combine dynamic Positive Convexity and Kelly Risk Parity
 The modern portfolio theory must consider the drawdown aversion
 Risk Management of tail events is better to be dynamic (option-based, momentum, etc.)

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References
1. [Asness] C. Asness, A. Frazzini, L. H. Pedersen, “Leverage aversion and Risk Parity” (2012)
2. [Illinski] K. Illinski, A. Pokrovski, “Lies of Capital Lines” (2010)
3. [Thorp] E. Thorp, S. Misuzawa, “Maximising capital growth with Black-Swan protection” (2013)
4. [Alankar] A. Alankar, M. DePalma, M. Scholes, “The introduction to Tail Risk Parity” (2012)
5. [Lemperiere] Y. Lemperiere,… J-P. Bouchard, “Tail risk premiums versus pure alpha” (2015)
6. [Bridgewater] Bridgewater Associates, Daily Observations (August 18, 2004)
7. [Kelly] J. L. Kelly, “A new interpretation of information rate” (1956)
8. [Artemis] Vega Fund, C. Cole, “Shadow Convexity and Prisoners Dilemma” (2015)
9. [Kahneman] D. Kahneman, A. Tversky, “Advances in prospect theory……” (1992)
10. [Brown] A. Brown, “Red Blooded Risk” (2012)
11. [Bhansali] V. Bhansali, “Tail Risk Hedging” (2014)
12. [Booth] J. Booth, “Emerging markets in an Upside Down World” (2014)
13. [Turlakov] M. Turlakov, “Wrong-way risk, credit and funding” (2013)

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The opinions presented here is a personal opinion of the author. They
do not represent the opinions of Sberbank CIB. Neither author nor his
employer are responsible for any use of the presented material. None
of the ideas in this presentation are claimed to be used or will be used.
Disclaimer