2013 Investment Seminar Colloque sur les investissements 2013 Session/Séance: Volatility Management Speaker(s)/Conférencier(s): Nicolas Papageorgiou Associate Professor, HEC Montréal Derivatives Consultant, Montreal Exchange
Agenda Managing equity risk exposure Drawdown (Tail risk) management Understanding volatility and volatility products Volatility Targeting or risk based re-balancing Extensions to Risk Parity Implementation of futures based overlays
MANAGING EQUITY RISK
Risk management and asset allocation Diversification, both geographically and across assets, is neither a sufficient nor a reliable risk control mechanism. During severe market corrections, traditional relationships between assets break down: Volatility of risky assets tend to rise as there is greater uncertainty (and panic) Correlations across assets increase dramatically; In summary, the assumptions underpinning our asset allocation do not always hold, particularly when markets are stressed. Market risk should be actively managed to reduce the impact of market corrections on equity portfolio.
How do we diversify equity risk? 1982 1987 1990 1998 2003 2008 S&P/TSX Drawdown -39.2-14.9-18.4-19 -12.5-32.5 Dex Universe Return 39.7 14.9 24.5 13.2 11.7 10.5 Canada 10-Year Yield 16.4 10.4 11 5 5 3 Source: PIMCO Historically, Fixed Income has been a good hedge against Equity drawdowns However with long-term yields at historical lows, it would be fair to say that the potential hedge that fixed income can provide is greatly reduced
The pitfalls of employing long-term risk/return assumptions A portfolio designed based on the long-term risk/return characteristics 40% Risk/Return Reward High Vol State 30% 20% 10% Low Vol State Medium Vol State 0% -10% 47% 45% 8% -20% -30% -40% Return Volatility -50% Frequency Does not take full advantage of the available risk budget when volatility is low (and risk/return trade-off is most favorable) Is fully exposed to extreme market corrections when these events occur. 6
Dealing with changing market regimes 1. Simply to ignore the bad regime; that is, realize that diversification and allocation benefits will protect an investor most of the time but losses are inevitable. 2. The all-weather approach that seeks to optimize performance over both good and bad regime scenarios. Separate distributional assumptions and correlations in the allocation are used to determine optimal portfolios within each regime, which are then combined together based on probability estimates of the likelihood of each regime. The resulting is actually suboptimal most of the time given that the markets are normally behaved, and investor will outperform during the bad times. 3. Implement a fair-weather asset allocation while integrating tail risk hedging into the portfolio. Set aside a portion of expected return for the purpose of purchasing hedges that will protect the portfolio from the adverse conditions during a tail event.
DOWNSIDE (TAIL) RISK HEDGING
Black Swans? Traditional risk management methods typically underestimate the frequency or severity of tail events. Thus, when tail events occur, the damage to investment portfolios is often devastating. For instance, the decline of U.S. equity markets in October 2008 was a three-standarddeviation event that theoretically should occur once every 745 years. The move in investment-grade spreads was a 20-standard-deviation event that should occur once in the lifetime of the universe. The lasting effects of such events on investment portfolios cannot be understated.
What makes a good hedge? For a tail risk hedge to be effective it should possess two important characteristics: 1. the hedge must be negatively correlated to asset returns 2. The hedge should exhibit convex behavior to the upside during periods of market stress.
How to hedge tail risk How much protection do I need? If I need a lot, I might want to reconsider my asset allocation How much should I spend? How much upside am I willing to give up? OTC vs Exchange traded solutions
Most obvious solutions: Buy a put and truncate the downside The higher the implied volatility the costlier the put option Source: Bloomberg and Poar securities 12
The downside of buying portfolio insurance Purchasing insurance is an effective but potentially expensive risk management strategy. Is a collar a viable solution to reduce the cost of insurance? Volatility skew is time variant and greatly affects the amount of upside that must be foregone to protect the downside. What are the other alternatives? 13
Re-thinking volatility can help better understand risk Cumulative returns with daily annualized volatility 400% 70% Daily cumulative performance 350% 300% 250% 200% 150% 100% 50% 0% 60% 50% 40% 30% 20% 10% Daily annualized volatility -50% 0% 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010 Volatility, or the measure of the variability of returns, is dynamic. Making an asset allocation decision using historical volatility measures ignores the time-varying nature of volatility.
How does volatility fit into the portfolio Volatility and risk Is volatility an asset class? Things we need to know about volatility The tools: volatility products Types of volatility: implied vs. realized Term structure of volatility 15
Product Investor Listed/OTC Charateristics Variance Swaps Volatility products Hedge funds, Insurance companies, pension plans OTC -Exposure to Variance is constant and not path dependent. -Provides exposure to realized variance. -Counterparty and liquidity risk. VIX Hedge funds, Insurance companies, pension plans Exchange traded -Liquidity is good and improving. -Exchange traded with daily mark-tomarket. - Position requires rolling of futures position, cost-of-carry can be significant. -Provides exposure to a forward looking measure of volatility. Forward starting swaps Hedge funds, Insurance companies, pension plans OTC -Exposure is to implied volatility and does not accrue any realized volatility. -There is a cost of carry in maintaining exposure to forward implied volatility.
Historical payoff of vol. and variance swaps Convexity pain Source: Bloomberg, Polar Securities
Market value of Variance swaps The use of variance swaps exposes the trader to realized voiatility. Can be tailored to investors portfolio Variance swaps are convex in volatility whereas VIX products are linear. The mark to market value of a variance swap is a function of realized vol and anticipation about future vol. VarSwap t t T t = Notional * realized vol 0 T T Where T is initial maturity and t is time expired ( t) + [ vol( t) ] ( ) 18
Performance of rolling VIX futures Source: CBOE, Polar Securities 19
Recent performance of VIX ETFs «VIX» est une marque de commerce de la Chicago Board Options Exchange («CBOE»)
Potential solutions using volatility products If you are long risk premium in volatility, you must be selling insurance (receiving implied vol) and therefore are long tail risk In order to hedge tail risk with VIX (implied) volatility, you need to be long volatility and there is a cost to this. A good long volatility strategy will aim to minimize this cost by being dynamic (generating some alpha) Pick and choose: shape of term structure, price of convexity, etc. 21
Dynamic beta and volatility targeting If you have a static exposure your risk is variable and changes with market conditions The most direct way to control risk is to render your exposure conditional to contemporaneous risk environment. There are a number of issues that must be addressed before any dynamic beta model can be implemented: At what level am I modelling and targeting risk? Stock? Industry? Asset Class? Portfolio? How do I model risk? Historical? Implied? Forecast? How do I decide on my volatility target?
The volatility of volatility: A story of two tails Conditions in the markets change over time and, as a consequence, the risk (volatility) profile of a given asset also varies. As market volatility increases: the distribution of returns for the asset flattens; the tails fatten relative to their average historical distribution; and the historical probabilities are no longer representative of actual loss potential.
Targeting a constant volatility There is a systematic and predictable component to volatility that managers/investors should exploit. Exposure should be managed actively so as to keep the portfolio volatility at the target (desired) level. Market exposure is removed if volatilty rises above the target level. Market exposure is increased if volatility falls below the target level. This eliminates fat-tails by ensuring that the drawdowns are consistent with the volatility targets. Eliminating vs. managing tail risk
VOLATILITY TARGETING (OR RISK BASED RE-BALANCING)
Re-balancing approaches Most institutional investors apply some form of optimization to determine portfolio weights. Rebalancing works on the premise that, as time goes by, the weights of each of the portfolio s assets will drift away from their optimum. In theory, investors should rebalance their portfolios when the cost of suboptimality exceeds the cost of restoring the optimal weights. The two most common methods of rebalancing are: Calendar-based rebalancing Rebalances portfolios monthly, quarterly or annually. This approach does not account for the unpredictability of portfolio drift Tolerance-band rebalancing Rebalances portfolios only when they shift away from their optimal targets by a predetermined amount typically 3 to 5 percent.
Calendar rebalancing A calendar rebalancing strategy rebalances the portfolio back to its original weights at predetermined time intervals. The fundamental question is: what is the optimal rebalancing frequency? Although this is the most popular form of re-balancing, it is the most arbitrary and performance is very sensitive to choice of rebalancing frequency. Calendar rebalancing has been shown to outperform buy-andhold Calendar rebalancing is a contrarian strategy based on lunar cycles...
Threshold rebalancing Threshold rebalancing recognizes that it is not always optimal to rebalance at set time intervals, as market conditions might not necessarily push the portfolio s asset mix sufficiently out of balance. Threshold rebalancing only occurs if the portfolio s asset weights drift beyond a predetermined trigger away from the target mix. This trigger is generally set as a percentage of deviation away from the optimal asset mix Several studies (i.e. Cao, 2009) shows that threshold rebalancing in the traditional rebalancing context outperforms buy-and-hold and calendar rebalancing in most situations.
Rebalancing based on risk Although re-balancing has been shown to add value over the long term, it does not necessarily guarantee that the plan/portfolio is respecting its risk budget as the volatility of the different assets also changes over time. Rather than target an asset mix, the plan should target a level of volatility that is constant and consistent with the assumptions underpinning your asset mix. This approach requires a little more effort: Risk targets need to be established A dynamic measure of risk for each asset class needs to be estimated A re-balancing rule needs to be established This approach should eliminate fat-tails by ensuring that the drawdowns are consistent with the volatility targets.
Rebalancing based on risk 30
Measuring volatility There are a number of volatility measures: Historical standard deviation (Moving average, Exponential Moving Average, etc ) Econometric models (GARCH, NGARCH etc.) Implied Volatility measures (VIX, VIXC, VSTOXX etc ) VaR, CVaR, EVT Volatility is a mathematical construct and there are an unlimited number of volatility models/measures. We need to be aware of the implications regarding our choice of risk (volatility) parameter.
Translating volatility into exposure Having established the volatility measure and volatility target, we still need to calculate the required exposure. Again, there are a number of possibilities: Ratio of actual to target volatility Ratio of actual to target variance Distributional targeting
Payoff Distribution Model
Simple numerical illustration Target Volatility selected to be 10% (Variance = 0.01) Actual volatility (according to chosen measure) is 20% (Variance = 0.04) Ratio of vols would indicate 50% exposure required Ratio of variance would indicate 25% exposure required. Distributional targeting? Exposure will depend not only on the volatility estimate but also on mtd returns and convexity of payoff grid.
Quarterly Rebalancing on GARCH - 15% Target Volatility Beta Realized Volatility Beta 2 1,8 1,6 1,4 1,2 1 0,8 0,6 0,4 0,2 0 1-3-01 1-3-02 1-3-03 1-3-04 1-3-05 1-3-06 1-3-07 1-3-08 1-3-09 1-3-10 1-3-11 1-3-12 0,9 0,8 0,7 0,6 0,5 0,4 0,3 0,2 0,1 0 Realized Volatility
S&P 500 risk control indices
Efficient rebalancing Rebalancing by adjusting the physical allocations in the portfolio would be cumbersome and expensive. Most plans that rebalance in a systematic manner use futures contracts to adjust their asset allocation. Futures provide a liquid, cost effect vehicle through which adjustments to the portfolio can be made.
Implementation: Target Volatility Index Fund or Overlay Asset allocation Implementation Asset/Liability Modelling Risk Tolerance MPT/Efficient Frontier Tactical 25% 25% S&P 500 50% S&P/TSX MSCI EAFE Short Long Overlay Equity Index Futures contracts are managed on top of an existing equity portfolio to maintain the portfolio volatility at the targeted level The result is that manager Alpha is preserved while market volatility remains constant
Conclusion The balanced portfolio (60/40) no longer provides the required level of tail risk protection We need to find new and better adapted tools to protect our investment portfolios Volatility (in its various forms) offers an interesting option for managing risk. Since volatility is a mathematical construct and cannot be purchased directly, we have two choices: 1. Obtain exposure to changes in volatility through derivatives. It is important to understand the payoff and carry cost of these instruments. 2. Use volatility as a conditionning tool (dynamic beta)
Appendices
RISK PARITY
Evolution of asset allocation MPT The next generation Risk Parity? Model Asset Classes Geography Liquidity Allocation Weighting Classic Equity Bonds Home bias High Static Capital Equal Weight Equity Bonds Commodities Hedge Funds Private Equity Global Partly low Static Capital
Yale Model successful up to financial 225 crisis 200 175 150 125-18% Yale Model -38% 100 75-26% Classic Balanced -28% 99 00 01 02 03 04 05 06 07 08 09 10
Evolution of asset allocation MPT The next generation Risk Parity Model Classic Yale Risk Weighted Asset Classes Equity Bonds Equity Bonds Commodities Hedge Funds Private Equity Equity Bonds Commodities Alpha- Strategies Geography Home bias Global Global Liquidity High Partly low High Allocation Static Static Dynamic Weighting Capital Capital Risk
The risk parity concept Universe Risk parity Tail risk Risk parity: the portfolio view point Measure risk of each asset class. Use leverage to normalize risks across assets No return forecasts or tactical asset allocation considerations Risk parity (risk weighted investing) Evaluated signal: Symmetric risk measures Asymmetric risk measure Risk weights Capital weights Equity Bond STIR Commodity
Risk Parity Solution No leverage constraint: You will end up reallocating a substantial part of the equity exposure to bonds Assuming a 8% vol for LTB and 16% vol for equity you need to hold 2 times more LTB for risk parity portfolio. Not necessarily inefficient, but level of risk much lower than 60/40 and therefore lower expected returns. Better Sharpe at the cost of lower returns is not necessarily a good thing unless We can leverage the entire portfolio
Risk Parity needs derivatives An effective risk parity portfolio requires the extensive use of derivatives in order for the strategy to produce an acceptable return. The type of derivatives will depend on the assets in the portfolio and the re-balancing frequency of the risk parity strategy.
The evolution of risk parity Given the dynamic nature of volatility and correlations a static risk parity portfolio does not guarantee a specific level of risk Risk parity portfolios need to be rebalanced to account for the time varying nature of risk.
Conclusion Risk (and volatility) is dynamic process and a robust risk management procedure is required to account for the time-varying nature of risk Overlays offer an effective tool for managing market risk at the plan level. Volatility targeting (a.k.a.risk-based rebalancing) provides a robust framework that ensures actual market exposure is consistent with risk assumptions underlying the asset allocation.
IMPLEMENTATION OF AN OVERLAY STRATEGY
Key issues in implementing an overlay strategies with futures Selecting a method to post initial margin Selecting a method for financing the variation margin Selecting a Futures Clearer (if needed) Managing currency exposure
Posting initial margin Since the overlay strategies use futures contracts to manage portfolio exposures, the client will be required to post an initial margin ( collateral ) to initiate a long or short futures position. Initial margin requirements are defined by the clearing house and are specific to each futures contract. Initial margins are expressed as a fixed amount per contract in the local currency of the selected futures contract.
Typical haircuts on collateral
Financing the variation margin Futures contracts are marked to market on a daily basis and the client is required to deliver cash to cover any losses on outstanding positions. There are several options at the client s disposal to effectively manage the daily cash flows relative to the variation margin. Four possible options are detailed below Actively manage daily cash transactions Synthetic cash equitization Direct financing (credit line) Repo agreement on collateral
Selecting a broker/clearer To trade futures contracts, the client (not the asset manager) must open a futures brokerage account with a futures clearer/broker. Futures brokers not only execute transactions but also take care of settlement with the futures clearing house and can also provide financing for margin requirements. There are two distinct activities performed in a futures transaction: Execution and clearing. For a given futures account, there can be a number of brokers used to transact on behalf of the client, however there will be only one futures broker that is delegated to clear and settle all the transactions. The delegated futures broker becomes the custodian of the margin that needs to be sent to the clearing house. Technically speaking, the asset manager can trade with any futures broker but will need to give-up the settlement with the client s futures clearer. This can be done through a give-up agreement.
Typical setup of accounts
Implementation costs Bid/ask spread Brokerage/clearing fee Custodian fee