Managing equity risk in a low-rate environment. AN EXPERTISE OF

Transcription

1 Managing equity risk in a low-rate environment AN EXPERTISE OF

2 Quantitative Research White Papers # 2 2

3 # 2 Quantitative Research White Papers CONTENTS Introduction 5 Endogenous protection: dynamic portfolio insurance 5 Endogenous protection: low-volatility stocks 8 Exogenous protection: volatility futures 1 Conclusion: Which solution should be employed? 14 Glossary 15 3

4 Quantitative Research White Papers # 2 SUMMARY Investors operating in a low-rate environment, in which equities still enjoy an attractive risk premium, are faced with a major dilemma: how best capitalise on the high-risk premium while limiting drawdown risk. This publication provides an in-depth study of ways an investor can look to durably manage equity risk over time. We showcase different investment solutions that aim to mitigate equity risk while providing an objective view, presenting both the advantages and drawbacks for each solution from the perspective of a practitioner. 4

5 # 2 Quantitative Research White Papers INTRODUCTION The low levels of financing represent a real constraint in terms of implementing portfolio insurance. Low interest rates only allow for marginal participation in a put option, thereby effectively limiting portfolio hedging efficiency. Since the downward trend in rates that began in the US in 29, the 3-month Libor rate only funds a hedging level that represents less than 1 of the face value of an S&P 5 portfolio over a 3-month horizon (see Figure 1). FIGURE 1 I PROTECTION LEVEL RELATIVE TO SHORT-TERM RATES 3 225% % 5% 4% 15 75% nov-5 may-7 nov-8 may-1 % of portfolio hedged 1 3% 2% 5 1% nov-11 nov-5 may-7 nov-8 may-1 nov-11 nov-5 may-7 nov-8 may-1 nov-11 Put premium 3-month Libor Source: Bloomberg, daily figures, Contribution ratio (i.e. % of assets hedged) for a 95% 3-month put on the S&P 5 financed by an upfront coupon equal to the discounted 3M Libor. Put premiums were determined using the Black & Scholes model, based on 3-month implied volatility. Despite the low rates currently prevailing, long-term liabilities still remain retrospectively tied to relatively higher rates. In order to hedge them, it is thus necessary to find investment avenues that offer returns in excess of the current levels. The demand for yield represents the main catalyst behind the development of strategies involving selling out-of-the-money puts, in other words being short volatility. The change in supply and demand dynamics has structural implications for equity market volatility. This is something we have learnt from the Japanese market which, since the crisis that hit it in early 199s, has experienced the structural consequences of a lowrate environment. Combined with changes in the behaviour of volatility, a low-rate environment poses something of a challenge to equity hedging strategies. We first explored two solutions endogenous to portfolio construction, the first based on a dynamic portfolio insurance approach with recourse to a risk-free asset, while the second consists of taking advantage of the bias of low-beta or low-volatility stocks within the equity portfolio itself. Finally, we looked at a third category of solutions that tackles the problem from an exogenous standpoint, namely protecting a portfolio by means of applying a flexible approach to volatility futures. The second section of this paper provides a comparative analysis of these various solutions. ENDOGENOUS PROTECTION: DYNAMIC PORTFOLIO INSURANCE There is a category of solutions offering endogenous portfolio protection, in other words, protection through the continuous adjustment of equity exposure. This involves dynamic portfolio insurance techniques, the simplest of which is CPPI (Constant Proportion Portfolio Insurance 1 ). Unlike passive approaches based on option strategies, these techniques are intended to be more flexible in that they consist of limiting drawdown risk by dynamically allocating to socalled safe assets as the value of the equity portfolio declines. In the opposite scenario, the weighting of risk-free assets is reduced and offset by an increase in equity exposure. The charts in Figure 2 show a comparative analysis of historical return profiles for a long put passive insurance strategy and a CPPI strategy, both achieving 95% capital protection over 1 See Glossary. 5

6 Quantitative Research White Papers # 2 a 3-month horizon. The CPPI shows a convex profile that tends to outperform the passive approach in negative return scenarios at maturity or extreme upswing scenarios. It proves less effective in other circumstances. This can also be confirmed by looking at the return distribution. This convex profile is not achieved without a number of major drawbacks that can be summarised in two points: (1) CPPI faces a rebalancing cost that increases with portfolio volatility, and this cost (referred to as the Gamma cost) stems from upside/ downside buy/sell movements; (2) it is particularly exposed to cash lock-in in the case of a V market scenario (major downturn followed by an upswing), resulting in the portfolio cushion being prematurely used up, and an opportunity cost by virtue of having missed out on the upswing at maturity. FIGURE 2 I RETURN PROFILE OF A CPPI STRATEGY (CONSTANT INVESTMENT MULTIPLE) 3-month performance of the strategy 55% 45% 35% 25% 15% 5% -5% -15% -25% month performance of the underlying Passive stategy CPPI strategy m=5 Probability 3 25% 2 15% 1 5% month performance Underlying Static strategy CPPI strategy m=5 Source: Bloomberg. Daily figures, simulation period Return profile (left) and distribution (right) of a CPPI constant investment multiple strategy, with as its underlying, the MSCI World ($) NDR, compared with those of a MSCI World ($) NDR portfolio hedged by means of a 95% 3-month put on the S&P 5 (static strategy). The put premiums were determined using the Black & Scholes model (see glossary), based on 3-month implied volatility as well as prevailing market parameters on the dates the strategy was initiated. Both strategies are implemented daily for a duration of 3 months, throughout the simulation period. The lower the interest rates are when the strategy is initiated, the greater these flaws become. Indeed, as a general rule, all portfolio insurance strategies turn out to be not very accommodating in a low-rate environment. Specifically in the case of CPPI, the cushion size is determined by the rate level. Low rates imply a small cushion and accordingly require a larger investment multiple to achieve the target equity exposure. This means greater risktaking and tends to exacerbate the cash lock-in issue. It thus becomes critical to tailor the CPPI to this environment. One of the most commonly used solutions involves making the cushion management dynamic in order to reduce the likelihood of the strategy being stopped. This dynamic aspect generally involves an investment multiple, which changes in response to signals or risk measures, such as volatility. The associated approaches are referred to as target volatility. This consists of changing the multiple on a linear basis in line with the ratio of a target volatility threshold to the volatility of the equity portfolio. The equity weighting will thus tend to fall ahead of a downward movement as volatility increases. Figure 3 shows the results of an analysis of the historical return profile of this approach. These results show that making the investment multiple dynamic on the basis of implied volatility makes it possible to significantly improve the performance of the strategy during downturns. However, it performs poorly in market upswings. This is mainly due to the non-linear relationship between volatility and stock price dynamics: following a shock, implied volatility tends to fall slower than prices increase, meaning that the target volatility mechanism tends to slow the upward adjustment of the equity weighting in the portfolio. 6

7 # 2 Quantitative Research White Papers FIGURE 3 I RETURN PROFILE OF A DYNAMIC PORTFOLIO INSURANCE STRATEGY (MULTIPLE BASED ON IMPLIED VOLATILITY) 3-month performance of the strategy month performance of the underlying CPPI strategy m=5 CPPI strategy m=f(vol) probability 45% 4 35% 3 25% 2 15% 1 5% Underlying 3-month performance CPPI strategy m=5 CPPI strategy m=f(vol) Source: Bloomberg. Daily figures, simulation period Return profile (left) and distribution (right) of a portfolio insurance strategy with a dynamic investment multiple compared with those of a CPPI strategy with a constant multiple (m = 5). The underlying is the MSCI World ($) NDR. The investment multiple is based on the VIX such that m = f(vix) = m x min(1; max(; 1/ VIX)), where m is a constant set such that the average value of the multiple is 5 over the whole simulation period (m = 6.6). Both strategies are implemented daily for a duration of 3 months, throughout the simulation period. FIGURE 4 I RETURN PROFILE OF A DYNAMIC PORTFOLIO INSURANCE STRATEGY (MULTIPLE BASED ON MTI). 3-month performance of the strategy month performance of the underlying CPPI stategy m=5 CPPI strategy m=f(mti) Probability 35% 3 25% 2 15% 1 5% month performance Underlying CPPI stategy m=5 CPPI strategy m=f(mti) Source : Bloomberg. Daily figures, simulation period Return profile (left) and distribution (right) of a portfolio insurance strategy with a dynamic investment multiple compared with those of a CPPI strategy with a constant multiple (m = 5). The underlying is the MSCI World ($) NDR. The investment multiple is based on the MTI such that m = f(mti) = m x (1-MTI), where m is a constant set such that the average value of the multiple is 5 over the whole simulation period (m = 9.7). Both strategies are implemented daily for a duration of 3 months, throughout the simulation period. The performance linked to the use of a dynamic investment multiple is wholly dependent on the relevance of the indicator used. The analysis in Figure 4 provides an example of an indicator that is more effective than mere implied volatility. This indicator, known as the MTI 2 (Market Tension Indicator), adds additional information in that it takes account, not only of risk factors endogenous to the equity market, but also exogenous factors. A marked increase in the convexity of the strategy can thus be observed. This results in generally outperforming the CPPI both on the upside and downside, although a number of exceptions do exist. These stem from divergences between the signals provided by the MTI and equity price movements. These examples thus show that making the portfolio insurance strategy dynamic can sometimes lead to poor results in the case where an ineffective indicator is used. It would thus accentuate the Gamma cost as a result of the mistaken adjustment of the investment multiple due to false signals. 2 The definition can be found in the Glossary. 7

8 Quantitative Research White Papers # 2 FIGURE 5 I DISTRIBUTION OF AVERAGE RETURNS OF DYNAMIC PORTFOLIO INSURANCE STRATEGIES DEPENDING ON SHORT-TERM RATES 5 4 frequency ]-8%;-5%] ]-5%;-3%] ]-3%;] Low-rate regime (3-month Libor) ];3%] ]3%;5%] 3-month strategy performance ranges Dynamics of portfolio insurance Source : Bloomberg. Daily figures, simulation period ]5%;8%] ]8%;1] ]1;6] High-rate regime (3-month Libor) Distribution of average returns of the three portfolio insurance strategies discussed above (CPPI with constant multiple and dynamic multiples) depending on the level of the 3-month Libor, this level being defined using historical terciles. The underlying of the strategies is the MSCI World ($) NDR. They are implemented daily for a duration of 3 months, throughout the simulation period. Despite the positives of making the cushion management dynamic, the performance of dynamic portfolio insurance approaches nevertheless remains structurally dependent on the interest rate environment. Figure 5 shows the effect of short-term rates on the distribution of the average historical returns of the three strategies analysed above. It can be seen that low rates result in the return distribution of portfolio insurance strategies being concentrated around a level close to the risk-free rate, and hence around low-return expectations. ENDOGENOUS PROTECTION: LOW-VOLATILITY STOCKS Another category of solutions consists of protecting an equity portfolio by means of appropriate stock picking and portfolio construction. In this respect, it is now well established that low-volatility stocks tend to outperform the market over the medium term, the latter being represented by capitalisation-weighted indices. It is clear that this phenomenon, which can be termed an anomaly, runs completely contrary to financial theory. It must nevertheless be recognised that this low-volatility anomaly represents a factor and thus a risk premium in its own right 3. Low-volatility stocks have specific properties. Firstly, they tend to markedly outperform the market during downturns, in other words during regimes in which volatility increases. Thus, their short-term relative performance is increasingly correlated with market volatility during such regimes, as can be seen from the results of the analysis shown in Table 1. Furthermore, on average they outperform the market over the long term. These characteristics therefore give them a relatively asymmetric return profile, not unlike that of volatility, as can be seen from the historical analysis presented in the left-hand chart in Figure 6. The analysis presented in the right-hand figure shows, on the other hand, that the risk/ return profile of such stocks, measured relative to the performance of the global equity market, is not particularly sensitive to the interest rate environment. In fact, the volatility and relative return spreads between the two rate regimes are not statistically significant 4. 3 See our last issue on this topic: Integrating a New Risk Factor into Equity Investment. 4 Significance measured using the statistical test of equality of averages at a level of 1%. 8

9 # 2 Quantitative Research White Papers TABLE 1 I RELATIVE RETURN PROFILE OF LOW-VOLATILITY STOCKS BY VOLATILITY REGIME VOLATILITY REGIME LOW HIGH CORRELATION VS. 12-MONTH HISTORICAL VOLATILITY 13% 3 BETA VS 12-MONTH HISTORICAL VOLATILITY.22.76* AVERAGE 1-MONTH RETURN SPREAD VS MSCI WORLD AC ($) NDR RETURN MSCI WORLD AC ($) NDR RETURN PERIOD AND PERIODICITY 2.2% 11.83% 18.36% % Source: Bloomberg. Figures from (*) 5% significance threshold. Low-volatility stocks are selected from the MSCI World AC ($) universe and correspond to the 1st quintile in terms of realised volatility over a 3-year rolling period. The ranking is updated monthly. The implied volatility (VIX) regimes are identified using a Hidden Markov chain model (see glossary). The high regime is characterised by an average 12-month volatility of 17% with a standard deviation of 9%. The low regime has an average of 11% and a standard deviation of 3.2. FIGURE 6 I HISTORICAL RELATIVE RETURNS OF LOW-VOLATILITY STOCKS 4 35% 3 25% 2 15% 1 5% jan- jul-1 oct-2 feb-4 jul-5 oct-6 feb-8 1 Y Rolling Global Equity Volatility (LHS) 1 Y Rolling Outperformance (RHS) (Global low volatility stocks - global stocks) jul-9 oct-1 feb Fed rate Sources: Bloomberg. Figures from These patterns thus point to exploiting this risk factor in a manner endogenous to equity portfolios so as to reduce drawdown risks, regardless of interest rate levels. The analysis summarised in Table 2, below, shows that increasing the weighting of low-volatility stocks within a portfolio of global equities results in a marked improvement in its returns. Thus, over the period, a 4 adjustment in the weighting of low-volatility stocks would have doubled the risk/return ratio while reducing the maximum 12-month drawdown risk by 1. This would also double the return / maximum drawdown risk ratio (Calmar ratio see glossary). The chart in Figure 7 also shows that the portfolio thereby adjusted inherits the return asymmetry of low-volatility stocks. In fact, the latter achieves an annual return that is significantly above the broad market throughout shock phases, while also generating a positive average relative return (around 27 bps). This protection solution, which we have classified as endogenous, clearly makes it possible to reduce the drawdown risk, but does not necessarily offer explicit portfolio insurance. It also remains dependent on the persistence of the low-volatility bias. + Volatility - - Annualised outperformance (low volatility equities vs global equities) 14.6% 8.9% (13.3%) (13.2%) 1.4% 2.8% (4.7%) (2.9%) + Left: 1-year rolling historical return spread between the portfolio of low-volatility stocks and the MSCI World AC ($) index. The stocks are selected from the MSCI World AC ($) universe and correspond to the 1st quintile in terms of realised volatility over a 3-year rolling period. The ranking is updated monthly. Right: Relative risk/reward profile of lowvolatility stocks having regard to rate and volatility regimes. The figures in bold represent the annualised average return spreads relative to the MSCI World AC ($) index. The figures in brackets represent the annualised volatility of these return spreads (i.e. tracking error). The implied volatility (VIX) and rate (Fed Rate) regimes are identified using a Hidden Markov chain model (see glossary). 9

10 Quantitative Research White Papers # 2 FIGURE 7 I HISTORICAL RETURNS FROM ALLOCATIONS BASED ON LOW-VOLATILITY STOCKS Absolute performance, 1 yr. rolling jan- apr-1 jul-2 oct-3 jan-5 apr-6 jul-7 oct-8 jan-1 Global equities (LHS) 6 Global equities 4 Low-volatility global equities (RHS) 8 Global equities 2 Low-volatility global equities (RHS) Source: Bloomberg, monthly figures from apr-11 jul-12 15% 1 5% -5% -1-15% Relative performance, 1 yr. rolling Low-volatility stocks are selected from the MSCI World AC ($) universe and correspond to the 1st quintile in terms of realised volatility over a 3-year rolling period. The ranking is updated monthly. TABLE 2 I DESCRIPTIVE STATISTICS OF ALLOCATIONS BASED ON LOW-VOLATILITY STOCKS 8 GLOBAL EQUITIES 2 LOW- VOLATILITY GLOBAL EQUITIES 6 GLOBAL EQUITIES 4 LOW- VOLATILITY GLOBAL EQUITIES GLOBAL EQUITIES LOW- VOLATILITY GLOBAL EQUITIES ANNUALISED RETURN 5.61% 7.6% 4.17% 11.56% MAX. 12-MONTH DRAWDOWN % % MAX. 24-MONTH DRAWDOWN % % % KURTOSIS SKEWNESS ANNUALISED VOLATILITY 14.97% 13.77% 16.26% 11.18% AVERAGE 12-MONTH VOLATILITY 13.92% 12.83% % RISK-REWARD RATIO CALMAR RATIO* PAIN RATIO* Source: Bloomberg, monthly figures from (*) See glossary Low-volatility stocks are selected from the MSCI World AC ($) universe and correspond to the 1st quintile in terms of realised volatility over a 3-year rolling period. The ranking is updated monthly. The definitions of the return ratios used can be found in the glossary. EXOGENOUS PROTECTION: VOLATILITY FUTURES Thanks in particular to the increased development of volatility derivative markets over the past 1 years, equity volatility has become an asset class in its own right. VIX and VSTOXX futures and options offer direct indexation to implied volatility. These derivatives are also unusual in how their liquidity evolves. In fact, unlike CDSs (credit default swaps) for instance, the liquidity of such instruments tends to increase during market shocks (see Figure 8), which in turn provides a major advantage. 1

11 # 2 Quantitative Research White Papers FIGURE 8 I LIQUIDITY OF VIX VOLATILITY DERIVATIVES VS. CDS LIQUIDITY. Volume handled feb Closing price feb-7 feb-8 feb-9 feb-1 feb-11 feb-12 feb-13 jan-6 dec-6 dec-7 nov-8 nov-9 oct-1 oct-11 sep-12 Liquidity Volume of derivatives listed on VIX (LHS) CDS US Liquidity (LHS) S&P 5 (RHS) S&P 5 (RHS) Source: daily figures from Bloomberg, Closing price Historical changes in trading volumes of options and futures listed on the VIX (left) compared with changes in CDS US liquidity (MarkIt CDX IG North America 5Y index universe). Liquidity is measured by the inverse of the average bid-ask spread on index constituents. Furthermore, the dynamics of equity volatility as an asset class are also contingent on the interest rate environment. Thus, in a low-rate environment, volatility tends to contract and to remain contained generally at relatively low levels. It should be remembered that this phenomenon is triggered by low returns which, in turn, leads investors to sell options in order to receive premiums and thereby improve the returns of their portfolios. The analysis shown in Figure 9 (left-hand chart) confirms this relationship between historical rate movements (US real rates) and volatility dynamics (VIX index), with a typical time delay of between 18 and 36 months. In addition to the average risk represented by volatility, the analysis (right-hand chart) also makes it possible to establish a priori a causal link between rate levels and changes in extreme risk in equity markets. The reduction in market shocks following a short-term rate cut can be construed as the positive effect of accommodating monetary policies which generates an influx of liquidity into the markets and ultimately forces investors to first reinvest in credit instruments and then in equities over the following 24 months, thereby helping to reduce their volatility. FIGURE 9 I EQUITY MARKET UNCERTAINTY AND CHANGES IN SHORT-TERM RATES , mar-88 jan-91 dec-93 oct-96 sep-99 VIX in 24 months in % (LHS) jul-2 jun-5 apr-8 mar-11 US rates in % (RHS) -3 mar-88 jan-91 dec-93 Source: weekly figures from Bloomberg, oct-96 sep-99 jul-2 jun-5 apr-8 mar-11 No of 3 Y rolling equity market shocks in 24 months (LHS) Fed rate in % (RHS) Historical changes in FED rates (right) adjusted for inflation (left) compared with the number of shocks over 24 months in excess of 5% in absolute terms (right) as well as the VIX level over 24 months (left). The dynamics of volatility futures prices are also impacted by the interest rate environment. In fact, these prices have, on average, an increasing and steeper term structure (i.e. futures for maturities further out in time are more expensive, reflecting the expectation of higher volatility over time). This therefore means higher cost of carry and has a considerable adverse impact on the performance of passive long futures strategies (e.g. strategies of rolling futures linked to the SPVXSTR index). For example, in an environment in which short-term rates are under 1.5%, the average cost of carry for futures with a constant maturity of one month (i.e. the SPVXSTR index) over a 3-month horizon is 26% assuming the VIX index remains contained in a low regime 5 (see Figure 1). This average cost falls to 2 in an intermediate rate regime. 5 The implied volatility regimes (VIX) are identified using a Hidden Markov chain model (see Glossary). The high regime is characterised by an average VIX of 3.87 and a standard deviation of The low regime has an average of and a standard deviation of The VIX average in the median regime is 2. and its standard deviation is

12 Quantitative Research White Papers # 2 FIGURE 1 I VOLATILITY COST OF CARRY 3-month performance gaps: SPVXSTR - VIX 9% 3% 5.5% VIX %.7% -26% -2-17% - 1.5% % > 4.5% Fed rate Source: daily figures from Bloomberg, Change in 1-month cost of carry based on VIX levels and shortterm rates. This cost is considered as being the 3-month return difference between the SPVXSTR index and the VIX. These specific characteristics of volatility associated to the dependence on the interest rate environment advocate a flexible approach to this asset class. This flexibility would thus make it possible to exploit all features of volatility, with particular consideration given to a low-rate environment. These features can be summarised in three points. (1) Momentum: this is the volatility trend, which is also considerably impacted by the cost of carry, more particularly when short-term rates are low. (2) Mean reversion: volatility tends to recover after major upward or downward moves. (3) Regime-switching: volatility dynamics are characterised by regimes, or breakout phases, during which its attributes can change (e.g. volatility of volatility, speed of mean reversion, etc.). These three characteristics can be exploited in order to implement a volatility indexation strategy with minimal cost of carry. Figure 11 shows the historical changes in a model portfolio built from two blocks with the SPVXSTR index as an underlying. The first is a combination of two strategies: firstly, a trendfollowing strategy and, secondly, a mean-reversion strategy. The second block consists of passive volatility indexing via the SPVXSTR index. The portfolio is then allocated between these two blocks in such a way as to minimise the ex post cost of carry. As can be seen, the behaviour of the resulting strategy is much closer to that of the VIX than the SPVXSTR index. It thus offers very attractive characteristics for hedging equity risk. The two last columns in Table 3 compare the performance of a dynamic hedging approach for a global equities portfolio, based on the minimal cost of carry strategy, with that of a long SPVXSTR index passive approach representing 2 of the overall portfolio. A dynamic approach offers outperformance over a passive approach in that there is a significant return spread (circa +6% over the period reviewed) for an equivalent drawdown risk. This results in a substantial improvement in the risk/return profile. This performance is mainly due to the effect of the reduction in the cost of carry. FIGURE 11 I MAKING VOLATILITY MANAGEMENT DYNAMIC 9 75 Cumulated performance dec-5 oct-6 jul-7 may-8 feb-9 dec-9 sep-1 jul-11 apr-12 feb-13 VIX (base 1) SPVXSTR (base 1) Carry neutral (base 1) Historical changes in a strategy combining both the momentum and mean reversion approaches and making it possible to minimise the cost of carry of the SPVXSTR index. 12 Source: daily figures from Bloomberg,

13 # 2 Quantitative Research White Papers FIGURE 12 I PROTECTION STRATEGIES BASED ON VOLATILITY FUTURES. 1-year rolling performance dec-6 sep-7 jul-8 apr-9 jan-1 oct-1 jul-11 may-12 feb-13 Global equities Passive protection Dynamic protection Source: daily figures from Bloomberg, Historical performance of a portfolio of global equities (MSCI World ($)) partially hedged by means of two protection approaches based on VIX futures. The first is passive. It consists of carrying a notional amount of the SPVXSTR index equal to 2 of the portfolio value. The second approach employs a flexible strategy that minimises the cost of carry of the SPVXSTR index. The same amount is allocated (2). TABLE 3 I DESCRIPTIVE STATISTICS OF PROTECTION STRATEGIES BASED ON VOLATILITY FUTURES MSCI WORLD SPVXSTR CARRY NEUTRAL PASSIVE PROTECTION DYNAMIC PROTECTION ANNUALISED RETURN 4.38% -4.72% -1.18% -1.52% 4.95% MAX. 12-MONTH DRAWDOWN -55.1% -84.9% -67.2% -38.9% -39.2% MAX. 24-MONTH DRAWDOWN -57.8% -94.1% -83.2% -43.7% -44.1% KURTOSIS SKEWNESS ANNUALISED VOLATILITY 19.6% 63.8% 44.7% 13.9% 16. AVERAGE 12-MONTH VOLATILITY 19.1% 63.7% 44.6% 13.2% 15.6% RISK-REWARD RATIO CALMAR RATIO PAIN RATIO Source: daily figures from Bloomberg, Descriptive statistics of two protection approaches employing VIX futures. The first is passive. It consists of carrying a notional amount of the SPVXSTR index equal to 2 of the portfolio value made up of components of the MSCI World ($) index. The second approach employs a flexible strategy that minimises the cost of carry of the SPVXSTR index. The same amount is allocated (2). 13

14 Quantitative Research White Papers # 2 CONCLUSION WHICH SOLUTION SHOULD BE EMPLOYED? By their very nature, the various equity hedging solutions referred to above offer both advantages and drawbacks that are worth noting. In light of the analyses we have just presented, we picked three comparison criteria, to which we added a fourth criterion to reflect the statutory and regulatory constraints associated with using derivatives. The table below highlights a comparison based on these four criteria. It turns out that the flexible approach based on volatility futures has a considerable advantage with respect to the first three criteria. However, the presence of constraints limiting (or prohibiting) the use of derivatives represents a major limitation for such an approach. Conversely, these constraints represent a major advantage for the endogenous protection approach based on low-volatility stocks, the major drawback nevertheless being the level of implied protection it achieves. TABLE 4 I ADVANTAGES AND DRAWBACKS OF THE VARIOUS PROTECTION APPROACHES. COMPARISON CRITERIA PURCHASE OF PUTS DYNAMIC PORTFOLIO INSURANCE LOW- VOLATILITY STOCKS FLEXIBLE APPROACH BASED ON VOLATILITY FUTURES LEVEL OF PROTECTION COST OF PROTECTION SENSITIVITY TO THE INTEREST RATE ENVIRONMENT CONSTRAINTS ASSOCIATED WITH THE USE OF DERIVATIVES - + Source: Quantitative Research White Papers, Natixis AM. The scope of this study, which highlights the dependence of equity risk management on the interest rate environment in which one navigates, goes well beyond the issue of how to simply hedge equity risk in a low-rate environment. In fact, these results raise questions as to the ability of equity volatility, as an asset class, to meet the challenge of insuring the returns of a global equity portfolio. This growing issue stems from the secular decline in yields for bonds. The question is thus how to take advantage of the unique characteristics of volatility and its behaviour, depending on the interest rate environment, in order to protect the returns of a diversified global fixed income/equity portfolio. We will endeavour to answer this question in future research publications. 14

15 # 2 Quantitative Research White Papers REFERENCES L apport d un nouveau facteur de risque dans une allocation action, [Integrating a New Risk Factor into Equity Investment.], Quantitative Research White Papers, No. 1, November 212, Seeyond. Guobuzaite R. and Martellini L. (212), The Benefits of Volatility Derivatives in Equity Portfolio Management, EDHEC-Risk Institute Publication. Stoyanov S. (211), Structured Equity Investment Strategies for Long-Term Asian Investors, EDHEC Risk Institute Publication. GLOSSARY Calmar ratio Hidden Markov chains An asset s Calmar ratio is the ratio of its annualised return and the absolute value of its maximum drawdown over the same period. This is a discrete time random process with no memory (i.e. prediction of the future does not depend on what happened in the past) with a finite number of states and where the probability of switching from one state to another does not vary over time. Markov chain states are not directly observable (they are hidden ) but may be detected by means of signal probability. We use this model to determine the regime (state) of the MTI momentum (the signal) and the probability that the signal switches regimes. CPPI CPPI (Constant Proportion Portfolio Insurance) is a form of dynamic portfolio management that makes it possible to guarantee investors a protection level at maturity or during the life of the portfolio. The latter is invested in a risky segment (e.g. equities, indices, funds or funds of funds) and in a non-risky segment (e.g. bonds, money-market funds). The allocation between these two segments is determined at each rebalancing such that the value of the portfolio is always above the protection level, while seeking to take advantage of the upswing in the risky segment. A number of parameters are relevant: The Floor is the minimum portfolio value that must be invested in the non-risky segment in order to guarantee the protection level. The Cushion is the difference between the portfolio value and the Floor. We also talk about a multiplier or Multiple. The amount invested in risky assets is determined by multiplying this Multiple by the Cushion. Portfolio Value = Risky Assets + Non-Risky Assets. Cushion = Portfolio Value Floor. Risky Assets Exposure = Multiple Cushion. 12-month drawdown Future front month The 12-month drawdown of an underlying is the ratio of the difference between its highest recorded value over a 12-month period and its value at 12 months. Front month future refers to the future with the closest expiry date out of all futures considered. 15

16 Quantitative Research White Papers # 2 Market Tension Indicator (MTI) is a bounded metric that evaluates the degree of risk/uncertainty in the financial markets. It combines 4 risk factors: implied volatility, liquidity premiums, sovereign bond convexity and credit spreads. It ranges between and 1, and transitions through 3 regimes (Safe, Neutral, Risky). Regime switches are identified using a Hidden Markov chain model. Maximum drawdown Black & Scholes model Pain ratio SPVXSTR index The maximum drawdown of an underlying S over a period p is the ratio of the difference between the highest and lowest values of S over its lowest value, recorded over period p. It measures the historical maximum drawdown over p. This is a standard model for valuing European-style options. It determines the value of an option given the following assumptions: no transaction cost, short-selling of the underlying asset is permitted, volatility and interest rates are constant (or deterministic). With just two variables (valuation date t and the price of the underlying S) and the following parameters: exercise price K, interest rate r, dividend yield q, expiry date T and implied volatility s, it is possible to determine the value of a call with a maturity of t =T-t using this formula : C = exp ( - q.t ). S. N( d1 ) - exp ( - r.t ). K. N( d2 ) with d1 = [ Ln( S /K ) + ( ( r - q +.5s² ).t)] / ( s t ), d2 = [ Ln( S / K ) + ( ( r - q -.5s² ).t)] / ( s τt ) = d1 - ( s τt ) et N(.) and N(.) is the cumulative normal distribution density. The pain ratio of an underlying S is the ratio of the annualised return of S over the absolute value of the average of its 12-month drawdowns. A VIX indexation index developed by the CBOE. Its methodology is based on daily rolls of the first into the second futures contracts on the VIX, to maintain a constant maturity of 1 month. 16

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