Foundations of portfolio management The risk management revolution Smart beta & factor investing Alternative risk premia Other topics New Trends in Asset Management Thierry Roncalli Professor of Finance, University of Evry, France 7 th JIAO-JI Afterwork Shanghai Jiao Tong University Alumni / Tongji University Shanghai Alumni Skema Business School, October 13, 2016 Thierry Roncalli New Trends in Asset Management 1 / 67
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Foundations of portfolio managementThe risk management revolution
Markowitz (1952)Tobin (1958)Sharpe (1964)Jensen (1969)Portfolio optimization and active management
The efficient frontier
“the investor does (or should)consider expected return adesirable thing and variance ofreturn an undesirablething”(Markowitz, 1952).We consider a universe of nassets. Let µ and Σ be thevector of expected returns andthe covariance matrix of returns.We have:
maxµ(x) = µ>xu.c. σ (x) =
√x>Σx = σ?
There isn’t one optimal portfolio, but a set of optimal portfolios!
Thierry Roncalli New Trends in Asset Management 4 / 67
Foundations of portfolio managementThe risk management revolution
Markowitz (1952)Tobin (1958)Sharpe (1964)Jensen (1969)Portfolio optimization and active management
Passive management vs active management
How to measure the performance of active management?
RF (t) = α+βRM (t) +ε(t)
The rise of cap-weighted indexationJensen (1969): no alpha in mutual equity fundsJohn McQuown (Wells Fargo Bank, 1971)Rex Sinquefield (American National Bank, 1973)
Thierry Roncalli New Trends in Asset Management 7 / 67
Foundations of portfolio managementThe risk management revolution
Markowitz (1952)Tobin (1958)Sharpe (1964)Jensen (1969)Portfolio optimization and active management
Portfolio optimization and active managementFor active management, portfolio optimization continues to make sense.
However...“The indifference of many investment practitioners tomean-variance optimization technology, despite its theoreticalappeal, is understandable in many cases. The major problemwith MV optimization is its tendency to maximize the effects oferrors in the input assumptions. Unconstrained MV optimizationcan yield results that are inferior to those of simpleequal-weighting schemes” (Michaud, 1989).�� ��Are optimized portfolios optimal?
⇒ The mean-variance approach is certainly the most aggressiveactive management model.
Thierry Roncalli New Trends in Asset Management 8 / 67
Foundations of portfolio managementThe risk management revolution
MotivationsWhich risk factors?Risk parity portfoliosWhat is the original risk parity strategy
Risk allocationLet x = (x1, . . . ,xn) be the weights of n assets in the portfolio. LetR(x1, . . . ,xn) be a coherent and convex risk measure. We have:
R(x1, . . . ,xn) =n∑
i=1xi ·
∂R(x1, . . . ,xn)∂ xi
=n∑
i=1RCi (x1, . . . ,xn)
Let b = (b1, . . . ,bn) be a vector of budgets such that bi ≥ 0 and∑ni=1 bi = 1. We consider two allocation schemes:1 Weight budgeting (WB)
xi = bi2 Risk budgeting (RB)
RCi = bi ·R(x1, . . . ,xn)
Thierry Roncalli New Trends in Asset Management 12 / 67
Foundations of portfolio managementThe risk management revolution
MotivationsWhich risk factors?Risk parity portfoliosWhat is the original risk parity strategy
Original risk parity with the volatility risk measureLet Σ be the covariance matrix of the assets returns. We assume that therisk measure R(x) is the volatility of the portfolio σ (x) =
√x>Σx . We
have:∂R(x)∂ x = Σx√
x>Σx
RCi (x1, . . . ,xn) = xi ·(Σx)i√x>Σx
n∑i=1
RCi (x1, . . . ,xn) =n∑
i=1xi ·
(Σx)i√x>Σx
= x> Σx√x>Σx
= σ (x)
The risk budgeting portfolio is defined by this system of equations:
RCi (x) = xi ·(Σx)iσ (x) = bi ·σ (x)
Thierry Roncalli New Trends in Asset Management 13 / 67
Foundations of portfolio managementThe risk management revolution
MotivationsWhich risk factors?Risk parity portfoliosWhat is the original risk parity strategy
An example
Illustration3 assetsVolatilities are respectively 30%,20% and 15%Correlations are set to 80% betweenthe 1st asset and the 2nd asset,50% between the 1st asset and the3rd asset and 30% between the 2nd
asset and the 3rd assetBudgets are set to 50%, 20% and30%For the ERC (Equal RiskContribution) portfolio, all theassets have the same risk budget
Absolute Relative
1 50.00% 29.40% 14.70% 70.43%
2 20.00% 16.63% 3.33% 15.93%
3 30.00% 9.49% 2.85% 13.64%
Volatility 20.87%
Absolute Relative
1 31.15% 28.08% 8.74% 50.00%
2 21.90% 15.97% 3.50% 20.00%
3 46.96% 11.17% 5.25% 30.00%
Volatility 17.49%
Absolute Relative
1 19.69% 27.31% 5.38% 33.33%
2 32.44% 16.57% 5.38% 33.33%
3 47.87% 11.23% 5.38% 33.33%
Volatility 16.13%
ERC approach
Asset WeightMarginal
Risk
Risk Contribution
Asset WeightMarginal
Risk
Risk Contribution
Weight budgeting (or traditional) approach
Asset WeightMarginal
Risk
Risk Contribution
Risk budgeting approach
Thierry Roncalli New Trends in Asset Management 14 / 67
Foundations of portfolio managementThe risk management revolution
MotivationsWhich risk factors?Risk parity portfoliosWhat is the original risk parity strategy
The case of diversified fundsFigure: Equity (MSCI World) and bond (WGBI) riskcontributions Contrarian constant-mix
strategyDeleverage of an equityexposureLow risk diversificationNo mapping betweenfund profiles and investorprofilesStatic weightsDynamic riskcontributions
Diversified funds=
Marketing idea?
Thierry Roncalli New Trends in Asset Management 15 / 67
Foundations of portfolio managementThe risk management revolution
⇒ The original risk parity strategy is a portfolio allocation approach toharvest risk premia across or within asset classes in the most efficient way.�� ��Risk parity = risk premium parity = diversification
Thierry Roncalli New Trends in Asset Management 17 / 67
Foundations of portfolio managementThe risk management revolution
The rationale for factor investingA subset of smart betaFact and fantasiesNew paradigms for the equity active management
What is the rationale for factor investing?
How to define risk factors?Risk factors are common factors that explain the variance of expectedreturns
1964: Market or MKT (or BETA) factor1972: Low beta or BAB factor1981: Size or SMB factor1985: Value or HML factor1991: Low volatility or VOL factor1993: Momentum or WML factor2000: Quality or QMJ factor
Factor investing is a subset of smart (new) beta
Thierry Roncalli New Trends in Asset Management 19 / 67
Foundations of portfolio managementThe risk management revolution
The rationale for factor investingA subset of smart betaFact and fantasiesNew paradigms for the equity active management
What is the rationale for factor investing?
What lessons can we draw from this?Idiosyncratic risks and specific bets disappear in (large) diversifiedportfolios. Performance of institutional investors is then exposed to riskfactors.
Alpha is not scalable, but risk factors are scalable.
⇒ Risk factors are the only bets that are compatible with diversification.
Thierry Roncalli New Trends in Asset Management 25 / 67
Foundations of portfolio managementThe risk management revolution
The rationale for factor investingA subset of smart betaFact and fantasiesNew paradigms for the equity active management
Facts and fantasies
FactLong-only and long/short risk factors have not the same behavior.This is for example the case of BAB and WML factors.
Risk factors are local, not global. It means that risk factors are nothomogeneous. For instance, the value factors in US and Japan cannotbe compared (distressed stocks versus quality stocks).
Factor investing is not a new investment style. It has been largelyused by asset managers and hedge fund managers for a long time.
4
Thierry Roncalli New Trends in Asset Management 29 / 67
Foundations of portfolio managementThe risk management revolution
The rationale for factor investingA subset of smart betaFact and fantasiesNew paradigms for the equity active management
Facts and fantasies
FantasyRisk factors are not dependent on size. It is a fantasy. Some riskfactors present a size bias, like the HML risk factor.
HML is much more rewarded than WML.
WML exhibits a CTA option profile. This is wrong. The option profileof a CTA is a long straddle whereas WML presents some similaritiesto a short call exposure.
Long-only risk factors are more risky than long/short risk factors.This is not always the case. For instance, the risk of the long/shortWML factor is very high.
8Thierry Roncalli New Trends in Asset Management 31 / 67
Foundations of portfolio managementThe risk management revolution
The rationale for factor investingA subset of smart betaFact and fantasiesNew paradigms for the equity active management
Facts and fantasies
FantasyHML is riskier than WML. It is generally admitted in finance thatcontrarian strategies are riskier than trend-following strategies.However, this is not always the case, such as with the WML factor,which is exposed to momentum crashes.
Strategic asset allocation with risk factors is easier than strategicasset allocation with asset classes. This is not easy, in particular in along-only framework. Estimating the alpha, beta and idiosyncraticvolatility of a long-only risk factor remains an issue, implying thatportfolio allocation is not straightforward.
8
Thierry Roncalli New Trends in Asset Management 32 / 67
Foundations of portfolio managementThe risk management revolution
The rationale for factor investingA subset of smart betaFact and fantasiesNew paradigms for the equity active management
A new opportunity for active managers
Active management does not reduce to stock pickingUnderstanding the diversification of equity portfoliosStock investing � Sector investing � Factor investingNew tactical products
Thierry Roncalli New Trends in Asset Management 35 / 67
Foundations of portfolio managementThe risk management revolution
Skewness risk premia & market anomalies��HHValueCarry and momentum everywhereThe puzzle of skewness aggregation
Skewness risk premia & market anomalies
A risk premium is a compensation for being exposed to anon-diversifiable risk (e.g. equity risk premium vs bond risk premium)Risk factors are the systematic components that explain the returnvariation of diversified portfolios (e.g. the Fama-French-Carhart riskfactors)A market anomaly is a strategy that exhibits a positive excess return,which is not explained by a risk premium (e.g. the trend-followingstrategy)
Risk premia and market anomalies are generally risk factorsThe converse is not true
⇒ The cat bond premium is a risk premium, but it is not a risk factor⇒ A risk factor may have a positive or negative excess return
Thierry Roncalli New Trends in Asset Management 38 / 67
Foundations of portfolio managementThe risk management revolution
Skewness risk premia & market anomalies��HHValueCarry and momentum everywhereThe puzzle of skewness aggregation
����XXXXValueCarry and momentum everywhere
What is the problem?For traditional risk premia, the cross-correlation between severalindices replicating the TRP is higher than 90%For alternative risk premia, the cross-correlation between severalindices replicating the ARP is between −80% and 100%
Examples (2000-2015)In the case of the equities/US traditional risk premium, thecross-correlation between S&P 500, FTSE USA, MSCI USA, Russell1000 and Russell 3000 indices is between 99.65% and 99.92%In the case of the equities/volatility/carry/US risk premium, thecross-correlation between the 14 short volatility indices is between−34.9% and 98.6% (mean = 43.0%, Q3−Q1 > 35%)
Thierry Roncalli New Trends in Asset Management 44 / 67
Foundations of portfolio managementThe risk management revolution
Skewness risk premia & market anomalies��HHValueCarry and momentum everywhereThe puzzle of skewness aggregation
����XXXXValueCarry and momentum everywhere
The identification protocolStep 1 Define the set of relevant indices (qualitative due diligence).
Step 2 Given an initial set of indices, the underlying idea is to find thesubset, whose elements present very similar patterns. For that, we usethe deletion algorithm using the R2 statistic:
Rk,t = αk +βkR(−k)t +εk,t ⇒ R2
k
Step 3 The algorithm stops when the similarity is larger than a giventhreshold for all the elements of the subset (e.g. R2
k > R2min = 70%).
Step 4 The generic backtest of the ARP is the weighted average of theperformance of the subset elements
Thierry Roncalli New Trends in Asset Management 45 / 67
Foundations of portfolio managementThe risk management revolution
Skewness risk premia & market anomalies��HHValueCarry and momentum everywhereThe puzzle of skewness aggregation
����XXXXValueCarry and momentum everywhere
���XXXValue Carry and momentum everywhereSome ARP candidates are not relevant (e.g. liquidity premium inequities, rates and currencies; reversal premium using variance swaps;value premium in rates and commodities; dividend premium; volatilitypremium in currencies and commodities; correlation premium;seasonality premium.)Hierarchy of ARP
Skewness risk premia & market anomalies��HHValueCarry and momentum everywhereThe puzzle of skewness aggregation
The skewness puzzle
ARP are not all-weather strategies:Extreme risks of ARP are high and may be correlatedAggregation of skewness is not straightforward
Skewness aggregation 6= volatility aggregationWhen we accumulate long/short skewness risk premia in a portfolio, thevolatility of this portfolio decreases dramatically, but its skewness riskgenerally increases!
The lost generation of value investorsThe diversification enigmaThe impact of low/negative interest ratesThe rise of robo-advisorsThe liability dilemma
The lost generation of value investors
The value of value investorsA value strategy exhibits a high skewness risk (' default risk)Markets need value investors in order to exist, because they are theonly investors who are able to reverse the market (in a bull market,but more important in a bear market)Value investors also provide liquidityMarkets have to reward value investors
Since 2008The equity market has not rewarded value investorsThe bond/credit market has rewarded value investorsWho are the value investors in illiquid markets?
⇒ The number of value investors decreases dramatically!Thierry Roncalli New Trends in Asset Management 56 / 67
Foundations of portfolio managementThe risk management revolution
The lost generation of value investorsThe diversification enigmaThe impact of low/negative interest ratesThe rise of robo-advisorsThe liability dilemma
The diversification enigma
Consider a portfolio with 2 assets: R = x1R1 + x2R2. We have:
var(R) = x21σ21 + x22σ22 +2x1x2ρσ1σ2
Best solution in terms of volatility diversificationLong-only portfolios:
ρ=−1
Long/short portfolios:ρ= 0
⇒ Long/short portfolio management can not mimick long-only portfoliomanagement
The notion of diversification is not universal
Thierry Roncalli New Trends in Asset Management 57 / 67
Foundations of portfolio managementThe risk management revolution
The lost generation of value investorsThe diversification enigmaThe impact of low/negative interest ratesThe rise of robo-advisorsThe liability dilemma
The impact of low/negative interest rates
Gordon-Shapiro (or dividend discount) modelThe stock price P is equal to:
P = Dr −g
where D is the current dividend, g is the growth rate of dividends and r isthe interest rate. When r −g ≈ 0, P goes to ∞.
⇒ The level of interest rates has an impact on all asset classes (equities,sovereign bonds, credit, commodities)⇒ The “low-long-rate-high-asset-prices”(Shiller, 2007)⇒ In low interest rate environment, investors have a greater appetite forrisk taking and reach for yield (Lian et al., 2016)
Interest rates are not always included in quantitative models
Thierry Roncalli New Trends in Asset Management 58 / 67
Foundations of portfolio managementThe risk management revolution
The lost generation of value investorsThe diversification enigmaThe impact of low/negative interest ratesThe rise of robo-advisorsThe liability dilemma
The rise of robo-advisorsUS: Betterment, Wealthfront, Personal Capital, FutureAdvisor,Schwab Intelligent Portfolios, Vanguard Personal Advisor, TradeKingAdvisors, SigFig, Hedgeable, etc.UK: Nutmeg, Scalable Capital, True Potential, Wealthify, WealthHorizon, Wealth Wizards, etc.France: Marie Quantier, Yomoni, WeSave (Anatec), Advize,Fundshop, etc.
Source: FINRA (2016)
Thierry Roncalli New Trends in Asset Management 59 / 67
Foundations of portfolio managementThe risk management revolution
The lost generation of value investorsThe diversification enigmaThe impact of low/negative interest ratesThe rise of robo-advisorsThe liability dilemma
The rise of robo-advisors
The response of the quantitative asset management forindividual/household investors
Mass customization (Martellini, 2016)
The problem of distribution costs:
retrocession payments⇒ fee-based models?
Thierry Roncalli New Trends in Asset Management 60 / 67
Foundations of portfolio managementThe risk management revolution
The lost generation of value investorsThe diversification enigmaThe impact of low/negative interest ratesThe rise of robo-advisorsThe liability dilemma
The lost generation of value investorsThe diversification enigmaThe impact of low/negative interest ratesThe rise of robo-advisorsThe liability dilemma
The lost generation of value investorsThe diversification enigmaThe impact of low/negative interest ratesThe rise of robo-advisorsThe liability dilemma
References I
Ang, A., Goetzmann, W., and Schaefer, S.Evaluation of Active Management of the Norwegian GPFG.Norway: Ministry of Finance, 2009.
Brinson, G.P., Hood, L.R., and Beebower, G.L.Determinants of Portfolio Performance.Financial Analysts Journal, 42(4), 1986.
Bruder, B., Kostyuchyk, N. and Roncalli, T. (BKR)Risk Parity Portfolios with Skewness Risk: An Application to Factor Investing andAlternative Risk Premia.SSRN, www.ssrn.com/abstract=2813384, 2016.
Carhart, M.M.On Persistence in Mutual Fund Performance.Journal of Finance, 52(1), 1997.
Thierry Roncalli New Trends in Asset Management 63 / 67
The lost generation of value investorsThe diversification enigmaThe impact of low/negative interest ratesThe rise of robo-advisorsThe liability dilemma
References II
Cazalet, Z., and Roncalli, T.Facts and Fantasies About Factor Investing.SSRN, www.ssrn.com/abstract=2524547, 2014.
Financial Industry Regulatory Authorithy (FINRA).Report on Digital Investment Advice.www.finra.org, March 2016.
Grinblatt, M., Titman, S. and Wermers, R.Momentum Investment Strategies, Portfolio Performance and Herding: A Study ofMutual Fund Behavior.American Economic Review, 85(5), 1995.
Hamdan, R., Pavlowsky, F., Roncalli, T. and Zheng, B. (HPRZ)A Primer on Alternative Risk Premia.SSRN, www.ssrn.com/abstract=2766850, 2016.
Thierry Roncalli New Trends in Asset Management 64 / 67
The lost generation of value investorsThe diversification enigmaThe impact of low/negative interest ratesThe rise of robo-advisorsThe liability dilemma
References III
Hendricks, D., Patel, J. and Zeckhauser, R.Hot Hands in Mutual Funds: Short-Run Persistence of Relative Performance.Journal of Finance, 48(1), 1993.
Lian, C., Ma, Y., and Wang, C.Low Interest Rates and Risk Taking: Evidence from Individual InvestmentDecisions.SSRN, www.ssrn.com/abstract=2809191, 2016.
Maillard, S., Roncalli, T. and Teïletche, J.The Properties of Equally Weighted Risk Contribution Portfolios.Journal of Portfolio Management, 36(4), 2010.
Markowitz, H.Portfolio Selection.Journal of Finance, 7(1), 1952.
Thierry Roncalli New Trends in Asset Management 65 / 67
The lost generation of value investorsThe diversification enigmaThe impact of low/negative interest ratesThe rise of robo-advisorsThe liability dilemma
References IV
Martellini, L.The Rise of the Robo-Advisors.EDHEC-Risk Institute, 2016.
The lost generation of value investorsThe diversification enigmaThe impact of low/negative interest ratesThe rise of robo-advisorsThe liability dilemma
References VShiller, R.J.Low Interest Rates and High Asset Prices: An Interpretation in terms of ChangingPopular Economic Models.National Bureau of Economic Research, 13558, 2007.
Sironi, P.From Robo-Adviors to Goal Based Investing and Gamification.Wiley, 2016.
Tibshirani, R.Regression Shrinkage and Selection via the Lasso.Journal of the Royal Statistical Society B, 58(1), 1996.
Tobin, J.Liquidity Preference as Behavior Towards Risk.Review of Economic Studies, 25(2), 1964.
Varian, H.Big Data: New Tricks for Econometrics.SSRN, 2013.
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