Portfolio Management Masterclass

Portfolio Management Economics and Investment Markets 1 Exam Key • Real risk-free interest rate determination • Risk premia for inflation, default risk, equities, RE • Hedge against poor consumption outcomes © Kaplan, Inc. Real Short-Term Interest Rates Intertemporal rate of substitution = mt marginal utility of consuming 1 unit in the future = u ___t marginal utility of current consumption of 1 unit u0 u0 > u1 and m1< 1 • • • P0 = price of zero-coupon, $1 par inflation indexed risk-free bond = E(m1) 1–P 1 . R = real risk-free rate = P 0 = [ E(m ) – 1 ] 0 t Due to diminishing marginal utility, utility of consumption is higher during periods of scarcity (e.g., economic contractions) © Kaplan, Inc. 2 Real Short-Term Interest Rates • • If investors expect higher incomes in future, utility of consumption in future relative to current consumption is lower and real rates will be higher Investors increase their savings rate (1) when expected returns are high or (2) when uncertainty about future income increases © Kaplan, Inc. Long-Dated Bonds • For a risk-free, inflation-indexed zero-coupon bond with long-dated maturity: E(P ) P0 = • • • 1 (1+R) + Cov ( P1,m1 ) The uncertainty of price at t = 1 introduces a risk premium, which is captured by the covariance term For risk-averse investors, covariance between future price of the bond and the intertemporal rate of substitution is negative When future price is higher, utility of future consumption relative to current consumption is low © Kaplan, Inc. 3 Short-Term Rates • • • If GDP growth rates are forecast to be high: • Investors expect higher incomes in the future; hence, they prefer current consumption relative to future consumption • Intertemporal rate of substitution will be low and interest rates high Havetoofferhigherrates toincentivize saving Evidenced in rapidly growing developing countries Due to risk premium, interest rates are also higher if expected volatility in GDP growth rate is high © Kaplan, Inc. Nominal Risk-Free Rates • • • r(short-term) = R + π r(long-term) = R + π + θ • R = real risk-free rate • π = expected inflation • θ = risk premium for inflation uncertainty Per Taylor rule, short-term policy rates are positively related to inflation gap (π – π*) and output gap (y – y*) © Kaplan, Inc. 4 Yield Curve and Business Cycle • • • Short-term rates are low during recessions and due to expectations of higher GDP growth and inflation in the future as the economy expands, longer-term rates are high Hence, positively sloped yield curve is common during recessions Similarly, inverted yield curve is indicative of late stages of economic expansions and is often considered a predictor of future recessions © Kaplan, Inc. Term Spread • • • Term spread = yield on longer-term bond – yield on shorter-term bond Normal term spread is positive and is attributable to risk premium for uncertainty in inflation (θ) θ is higher for longer maturities © Kaplan, Inc. 5 Break-Even Inflation Rate (BEI) • • BEI = yield on default-free nominal bond – yield on default-free real bond BEI = π + θ Expected inflation Risk premium for inflation uncertainty © Kaplan, Inc. Equity Risk Premium • • • • Equity is more risky than debt; hence, an additional risk premium is needed Corporate earnings and equity prices tend to rise during economic expansions Equity provides a poor hedge against bad consumption outcomes (i.e., pays poorly in bad states of the economy) Poor consumption hedging property causes equity risk premium to be positive © Kaplan, Inc. 6 Real Estate • • • • Additional risk premium for lack of liquidity Commercial real estate with long-term leases have bond-like characteristics due to stable cash flows The uncertainty in value of real estate at the end of lease term gives it an equity-like character Similar to equities, real estate tends to be a poor hedge for bad consumption outcomes (i.e., has lower value during economic recessions) © Kaplan, Inc. Analysis of Active Portfolio Management 7 Exam Key • Value added • IR vs. Sharpe ratio • Optimal level of active risk • Fundamental law © Kaplan, Inc. Measuring Value Added Expected active return E(RA) = E(RP) – E(RB) Can be computed ex ante or ex post Risk adjusted active return (alpha) = α P = R P – β PR B Incorporating the managed portfolio’s systematic risk relative to the benchmark if different (we will assume the systematic risk of the portfolio is the same as the benchmark in this reading) © Kaplan, Inc. 8 Measuring Value Added Active return (value added) Positive active returns are generated by: • Overweighting assets with higher returns • Underweighting those with lower returns N E(R A )= ∆Wi × E(Ri ) i =1 Active weight = WPi – Wbi Wportto Wenchmark 0 Sum of active weights = zero © Kaplan, Inc. Example: Measuring Value Added Weight % Portfolio Benchmark Active Weight Ri RA Equity 75 50 +25% 15% 3.75% Bonds 25 50 –25% 5% –1.25% Total active return 2.50% Benchmark return = (0.5 × 15%) + (0.5 × 5%) = 10% Portfolio return = (0.75 × 15%) + (0.25 × 5%) = 12.5% © Kaplan, Inc. 9 Value Added Active return (value added) M Benchmark weighting for asset class j M Benchmark return for asset class j E(RA )= WPj × E(RPj ) −  WBj × E(RBj ) j =1 j =1 Portfolio weighting Portfolio return for for asset class j asset class j © Kaplan, Inc. Decomposition of Value Added Decomposition into asset allocation and stock selection: Return differences in an asset class E(RPi) – E(RBi) Active return (value added) M M j=1 j=1 E(RA )= ∆W j × E(RBj ) +  WPj × E(RAj ) Active return from asset allocation Active return from stock selection © Kaplan, Inc. 10 Example: Decomposition • • • • Assume two asset classes: stocks and bonds. Using the data on the following slides, decompose the active return of the fund manager’s portfolio. The benchmark has a 60% exposure to the bond market and 40% to equity. The manager’s portfolio has a 70% exposure to the equity market and 30% to bonds. The portfolio generated a return of 13.20% compared to the benchmark return of 8.32%. © Kaplan, Inc. Example: Decomposition Market WB WP Benchmark Portfolio Return Return Equity 0.4 0.7 10.00% 16.80% Bond 0.6 0.3 7.20% 4.80% Total 8.32% 13.20% Portfolio active return = 13.20% – 8.32% = 4.88% © Kaplan, Inc. 11 Example: Decomposition Active return from stock selection(RAj) Active return from asset allocation (ΔWj) WPj × RAj ΔWj × RBj Equity 0.7 × 6.8% = 4.76% 0.3 × 10.0% = 3.00% Bond 0.3 × –2.4% = –0.72% –0.3 × 7.2% = –2.16% Total 4.04% 0.84% Portfolio active return = 4.04 + 0.84% = 4.88% Summary © Kaplan, Inc. Comparing Risk and Return • Sharpe ratio (SR): excess return per unit of risk excessreturn SRP = RP – RF (P • Risk and return are absolute (i.e., not benchmark relative) • Sharpe ratio is unaffected by addition of leverage or cash Moreleverage multipliesexcessreturn numerator thesame multiple eg 2x so SR isunchanged Op denominator by © Kaplan, Inc. 12 The Information Ratio (IR) Active return (R − R ) R IR = P B = A ( (RP − RB ) ( (RA ) Can be computed ex ante or ex post Active risk © Kaplan, Inc. The Information Ratio • • • Unlike the Sharpe ratio, the IR is affected by leverage and cash. The IR is unaffected by the aggressiveness of the active weights. If the active weights (deviations from benchmark weights) are multiplied by a constant, the IR will remain unaffected. Investors will always choose the active manager with the highest information ratio. © Kaplan, Inc. 13 The Information Ratio • • The investor cannot adjust the active risk of an existing fund (no control over manager’s asset weightings). The investor can split the portfolio between the fund and the benchmark to achieve the desired active risk: • • To decrease active risk  invest in both the fund and benchmark To increase active risk  short sell benchmark and invest the proceeds in the fund © Kaplan, Inc. Sharpe Ratio of an Active Portfolio SRP2 = SRB2 + IR 2 Implication: choosing the manager with the highest information ratio (skill) will produce the highest Sharpe ratio IR ( * (RA ) = × ( (RB ) SRB ( (RP )2 =( (RB )2 +( (RA )2 Sharpe ratio maximizing optimal level of active risk (aggressiveness) for an unconstrained portfolio Total portfolio return volatility = benchmark return volatility + volatility of active return © Kaplan, Inc. 14 Example: Optimal Portfolio Fund Benchmark IR 0.4 Sharpe ratio 0.5 Active risk 6% Total risk 12% Optimal aggressiveness ( *(RA ) = 0.4 ×12% = 9.6% 0.5 Sharpe ratio (with optimal aggressiveness) SRP2 = 0.52 + 0.42 = 0.41 SRP = 0.41 = 0.64 © Kaplan, Inc. DonotforgettotakeGrip togetSRp WeknowsRpcannotbethe answer since Skip SR Example: Optimal Portfolio • • • Optimal portfolio has an active risk of 9.6% compared to the fund’s active risk of 6% 9.6% / 6% = 1.6 = proportion invested in the actively managed Proportion in benchmark = –0.6 (i.e., short position) Optimal investmentmultiple Foractiveportfolio 81optimal multipleactive optimalinvestment Benchmark 1 © Kaplan, Inc. 15 Example: Optimal Portfolio Verifying the Sharpe ratio: E(RA ) = IR×((RA ) = 0.4 × 9.6% = 3.84% S RB = Note that the original actively managed fund only has an active return of 2.4% (IR × active risk) R B – RF ) RB – RF = SRB × ( (RB ) ( (RB ) RB – RF = 0.5 × 12% = 6% Portfolio excess return = Rp – Rf = 6% + 3.84% = 9.84% © Kaplan, Inc. Example: Optimal Portfolio Verifying the Sharpe ratio: Portfolio total risk = 12%2 + 9.6%2 = 15.3675% Sharpe ratio of portfolio: SRP = RP – R F 9.84% = = 0.64 ( (RP ) 15.3675% © Kaplan, Inc. 16 Risk-Return Diagram Optimal portfolio Optimal Sharpe ratio Benchmark Sharpe ratio Forecast excess return 9.84% = individual assets 6% Benchmark portfolio 12% 15.37% Risk σ © Kaplan, Inc. SR Slopeof line The Fundamental Law of Active Management Three components affect expected information ratio: 1. Information coefficient (IC) Measures manager skill • Ex ante IC is expected correlation between active returns and forecast active returns • Ex post IC measures actual correlation between active returns and forecast active returns • • Ex post IC is typically a small positive value (< 0.2) Higher IC is better © Kaplan, Inc. 17 The Fundamental Law of Active Management 2. Transfer coefficient (TC) Onlyapplicablewhenportfoliois constrained • Correlation between actual active weights (ΔWi) and optimal active (ΔWi*) weights • TC = 1 for unconstrained portfolios • TC < 1 w/constraints: ΔWi and ΔWi* will differ O TC 1 3. Breadth (BR) • Number of independent bets (forecasts of active return) PerYear © Kaplan, Inc. The Fundamental Law Expected active portfolio return = Basic fundamental law: E(RA)*= IC BR( A IR* = IC BR E(R A ) = N  ∆Wμ i i i=1 Unconstrained portfolios TC = 1, * = optimal weights Full fundamental law: E(RA)= (TC)IC BR( A IR = (TC)IC BR Constrained portfolios TC < 1, actual weights ≠ optimal weights JustmultiplyingthebasicfundamentallawbyTC © Kaplan, Inc. 18 The Full Fundamental Law • • Constrained portfolios: actual security weights ≠ optimal weights (TC < 1) TC = risk-weighted correlation between optimal active weights and actual active weights: • or, TC = COR(∆Wi*( i,∆Wi ( i ) = correlation (Δwiσi, μi / σi) © Kaplan, Inc. Optimal Level of Active Risk SRP2 = SRB2 + IR2 ( * (RA ) = IR × ( (RB ) SRB SRP2 = SRB2 + (TC)2 (IR)2 IR* ( (RA ) = TC × ( (RB ) SRB Sharpe ratio and optimal active risk for unconstrained portfolios Sharpe ratio and optimal active risk for constrained portfolios © Kaplan, Inc. 19 Comparison of Active Management Strategies • Market timing vs. security selection • Information coefficient of a market timer: IC = 2 ( % correct ) –1 • Note: a market timer that is only correct about the direction of the market or a sector half the time will have an IC = 0 © Kaplan, Inc. Example: Active Management Strategies • • • • Ben Dash, a market timer, makes bets on the direction of the market and is correct 53% of the time. IC 2 0.53 1 0.06 Ricardo Nunos, a security selector, makes monthly bets on 10 stocks with an information coefficient of 0.04. Both investors are unconstrained. Calculate the number of bets Dash needs to make to match the information ratio of Nunos. © Kaplan, Inc. 20 Solution: Active Management Strategies • Nunos’s IR = IC BR = 0.04 10 × 12 = 0.438 • Dash’s IC = 2(% correct) – 1 = 2(0.53) – 1 = 0.06 )0.06 BR = 0.438 Solved rearranging IR ILER by 0.438 = BR 0.06 2  0.438   0.06  = BR = 53.29 (approximately 53) © Kaplan, Inc. Add EOC Q's Probhaveto getfromvideo Exchange-Traded Funds: Mechanics and Applications 21 Purposes of Creation/Redemption Process • • • Lower cost: in-kind creation/redemption eliminates transaction cost Tax efficiency: creation/redemption is not a taxable event; also, redemption basket may specify low-basis stock to boost tax efficiency of the fund Market prices in line with NAV: APs can arbitrage away any price discrepancy © Kaplan, Inc. Arbitrage Gap • • • APs incur transaction costs and service fees for creation/redemption. These are passed on in the form of bid-ask spreads (and borne only by transacting shareholders). Hence, ETFs should trade within a band of the NAV, known as the arbitrage gap. The arbitrage gap is wider for the following: • index ETFsmacaroon wETFs with illiquid holdings • Foreign ith time zone differences (stale pricing) © Kaplan, Inc. 22 Tracking Error: Sources • ETF fees and expense • Sampling and optimization • Depository receipts/other sector ETFs • Index changes • Regulatory and tax requirements • Fund accounting practices • Asset manager operations Morefees © Kaplan, Inc. Spreads Maximum spread = creation/redemption fees plus other trading costs + spread of the underlying securities + risk premium for carrying until close of day + AP’s normal profit margin – discount based on probability of offsetting the trade in secondary market © Kaplan, Inc. 23 ETF Risks • • Counterparty risk • ETNs • Settlement risk • Security lending Fund closures • • Creation/redemption halts Expectation-related risk © Kaplan, Inc. Using Multifactor Models 24 Arbitrage Pricing Theory (APT) Describes the equilibrium relationship between expected returns for well-diversified portfolios and their multiple sources of systematic risk: Risk premiums E(RP) = RF + βP1(λ1) + βP2(λ2) + … + βPk(λk) Portfolio factor betas or loadings © Kaplan, Inc. Example: Arbitrage Opportunity Arbitrage • No risk • No net investment • Positive profit Arbitrage = free lunch Portfolio A,B,C = single-factor portfolios Expected Return Factor Sensitivity Portfolio A 10% 1.00 Portfolio B 20% 2.00 Portfolio C 13% 1.5 © Kaplan, Inc. 25 Solution: Arbitrage Opportunity Create portfolio (D) equally weighted to A and B E(RD) = 15% Factor sensitivity (β) = 1.50 1  1  × 10% + × 20%  2   2  1  1   2 × 1 +  2 × 2 Arbitrage opportunity: Long D, Short C: Profit = E(RD) – E(RC) = 2% Portfolio C does not generate sufficient return for its factor risk (market not in equilibrium) © Kaplan, Inc. Example: Fama-French Three-Factor Model Fama-French Model 1992: • Risk-free rate of 3% Market risk factor Risk Premium Sensitivity (Market index – Rf) 5% 1.1 (Small – big) returns (SMB) 3% 0.4 High/B/M – low B/M (HML) 2% –0.8 Factor Ri = 3% + 1.1(5%) + 0.4(3%) – 0.8(2%) = 8.1% © Kaplan, Inc. 26 Three Types of Multifactor Models 1. Macroeconomic factors • E variable Surprises in macro variables that explain differences in stock returns • Interest rates, inflation, business cycle, credit spreads, etc. Variable 2. Fundamental factors • • Attributes of stocks that are important in explaining cross-sectional differences in returns B/M, market cap., P/E, leverage, etc. © Kaplan, Inc. Three Types of Multifactor Models 3. Statistical factors Principal components models • Factors are portfolios of securities that best reproduce historic return variances Factor analysis models • Factors are portfolios of securities that best reproduce historic return covariances Issue = attaching economic meaning to statistical factors difficult © Kaplan, Inc. 27 Macroeconomic Factor Model Ex ante return (no surprises) Sensitivity to INT surprises Interest rate surprise = (actual – consensus predicted) Two-factor example: Ri = E(Ri) + bi1FGDP + bi2FINT + εi Sensitivity to GDP surprises GDP surprise = (actual – consensus predicted) Company-specific surprise return* *Assuming all sources of common risk (risk factors) have been included © Kaplan, Inc. Fundamental Factor Model • Factors are returns, not surprises • Intercept ≠ expected return • Factor sensitivities are standardized: βi = • Think Z-statistic value of attribute k for asset i – average value of attribute k ( (values of attribute k ) Scaling allows all factor sensitivities to be interpreted similarly, regardless of units of measure © Kaplan, Inc. 28 Fundamental Factor Model Two-factor example: Ri = ai + bi1FP/E + bi2FSIZE + εi Interpretation ai Intercept βi1 Standardized P/E for stock i βi1= P/Ei – P/E (P/E βi2 = SIZEi − SIZE ( SIZE βi2 Standardized SIZE for stock i FP/E Return difference between high and low P/E stocks FSIZE Return difference between high and low SIZE stocks © Kaplan, Inc. Macro Models vs. Fundamental Models Macro Factor Model Fundamental Factor Model Time series of surprises Cross-sectional asset returns Regression based Standardized from attribute data Factor returns (F) Surprises in macro variables Computed from multiple regression Intercept Expected return Undefined Regression Factor sensitivity (β) © Kaplan, Inc. 29 Multifactor Models in Return Attribution Fundamental factor model • Use = decompose sources of an asset manager’s return relative to a benchmark • • • Model uses easily understood and communicated factors Can express investment style choices and security characteristics in detail More commonly used than macro or statistical factor models © Kaplan, Inc. Sources of Active Return active return = factor return + security selection return Product of managers’ factor tilts and factor returns K  (Portfolioβ − Benchmarkβ ) × λk  + security selection k=1 Managers’ skill in individual asset selection (residual) © Kaplan, Inc. 30 Active Risk Decomposition Active risk squared: ( 2 (RP −RB ) = active factor risk + active specific risk Active risk attributable to factor tilts n Active risk attributable to stock selection 2 2 Active specific risk = ( WPi – WBi ) ( + i i =1 Active factor risk = residual Residual risk of the ith asset © Kaplan, Inc. Strategic Portfolio Decisions Two questions for investors: 1. What kind of risk do I have a competitive advantage in bearing? 2. What kind of risk do I have a comparative disadvantage in bearing? Examples • Pension funds have long investment horizons—and, as a result, are not exposed to liquidity risk. • An employed worker reliant on income is exposed to business cycle risk. © Kaplan, Inc. 31 Measuring and Managing Market Risk Using VaR to Measure Portfolio Risk Value at risk (VaR): an estimate of the minimum loss with a given probability over a specified period • Expressed as a $ amount or % of portfolio value Three components to VaR 1. Loss size 2. Probability (of a loss > specified loss size) 3. Time frame © Kaplan, Inc. 32 Methods for Estimating VaR VaR estimation methods • • • Parametric method: uses variances and covariances; often assumes normal distribution Do notuse if non normaldistribution Historical simulation: uses some prior lookback period to get a distribution of possible values Monte Carlo simulation: draws from an assumed distribution; repeated thousands of times to get a distribution of possible portfolio values © Kaplan, Inc. Estimating and Interpreting VaR The x% VaR is calculated as the minimum loss for the current portfolio, x% of the time. Example • Annual mean return = 9% • Annual standard deviation = 20% One-tailed 5% annual VaR = 0.09 – 1.65(0.20) = –24% For $10 million portfolio, the 5% annual VaR is: 10 million (0.24) = $2,400,000 © Kaplan, Inc. itiiii k 28.533 24m1.1m 0.9m 33 Extensions of VaR • • • • Conditional VaR (CVaR): expected loss given that the loss exceeds the VaR Incremental VaR (IVaR): estimated change in VaR from change in size of a portfolio position Marginal VaR (MVaR): change in VaR for a small change in a portfolio position Ex ante tracking error (“relative VaR”): VaR of difference between portfolio vs. benchmark returns © Kaplan, Inc. 241 Sensitivity and Scenario Risk Measures • • • Sensitivity analysis: estimate change in portfolio value for incremental change in risk factor Canbeusedtoinformhedgingdecisions Scenario analysis: estimate effect on portfolio value of a specific set of changes in risk factors A scenario of changes in risk factors can be one of these: • • Historical: based on a past set of risk factors changes that actually occurred Hypothetical: based on a selected set of changes in the risk factors of interest © Kaplan, Inc. 34 Equity/Fixed Income/Option Exposure Equity risk: measured by . . . • Beta (market sensitivity) Fixed-income risk: interest rate risk is measured by . . . • Duration (sensitivity to change in yield) • Convexity (second order; change in duration) Options risk: measured by . . . • Delta (sensitivity to price changes) • Gamma (sensitivity to changes in delta) secondorder • Vega (sensitivity to asset price volatility) © Kaplan, Inc. Sensitivity and Scenario Risk Measures VaR, sensitivity analysis, and scenario analysis are complements. You should not rely on only one! Sensitivity risk measures give a view of the vulnerability of a portfolio to various risk factors. Scenario risk measures are used to estimate how a portfolio will respond to extreme market conditions. • Scenario measures can be based on: • Actual historical scenarios—repeat of a period • Hypothetical scenarios—that haven’t occurred © Kaplan, Inc. 35 Risk Measures of Various Institutions Banks are concerned with: • Asset-liability mismatches/liquidity gap • Market risk for their investment portfolios • Leverage • Duration and convexity fixed-income securities • Overall risk to their economic capital Asset managers are concerned with: • Returns volatility • Losses—either absolute or vs. a benchmark Tracking error © Kaplan, Inc. Risk Measures of Various Institutions Pension fund managers are concerned with: • Mismatch between assets and liabilities • Volatility of the surplus (assets – liabilities) Property & casualty insurers are concerned with: • Sensitivity of investment portfolio to risk factors • The VaR of their economic capital • Stress test scenarios of market/insurance risk Life insurers are concerned with: • Market risks to assets and liabilities • Mismatches between assets and liabilities • Scenarios leading to large decrease in surplus InvestedPremiums © Kaplan, Inc. EOC Q's 36 Backtesting and Simulation Exam Key • Define the different tools • Pros and cons of each tool • Suitability of individual approach given a situation © Kaplan, Inc. 37 Problems in Backtesting a Strategy Problems in a backtest of an investment strategy • • • Survivorship bias: when using data that only includes entities that have persisted until today Look-ahead bias: when using data that would have been unavailable at the time of the investment decision Ex UsingFYdataforJan1ˢᵗwhenit isn'tavailable Data snooping: when a model is chosen based on backtesting results (e.g., large t-statistic or small p-value) © Kaplan, Inc. Interpreting Historical Scenario Analysis Scenario analysis is a method for investigating the performance and risk of investment strategies under different structural regimes. For example: • Recession vs. nonrecession • High volatility vs. low volatility Stress testing examines the performance of a strategy under the most adverse combinations of events and scenarios. Lookingat tail risk © Kaplan, Inc. 38 Monte Carlo vs. Historical Simulation • • Monte Carlo and historical simulation approaches are methods used to account for the following: • Skewness • Excess kurtosis • Tail dependence Both approaches are nondeterministic and random. © Kaplan, Inc. Simulation Historical simulation • Relatively simple • Shares many of the advantages and disadvantages of rolling-window backtesting • Like rolling-window backtesting, historical simulation depends on assumption that randomness in the future can be predicted using return distributions from the past If nottrue useMonteCarlo © Kaplan, Inc. 39 Simulation • • In historical simulation, observations are randomly chosen from a historical dataset so each observation has an equal probability of being selected Bootstrapping is sometimes used in historical simulation: • Random samples are drawn with replacement • Useful when number of simulations needed is large relative to the size of the historical dataset © Kaplan, Inc. Sensitivity Analysis Sensitivity analysis • A method for evaluating how a target variable (e.g., portfolio return) varies due to changes in input variables (e.g., asset or factor returns) Conducting a sensitivity analysis • • Fit factor return data to a distribution that accounts for skewness and excess kurtosis Then, repeat Monte Carlo simulation © Kaplan, Inc. 40 Sensitivity Analysis • Sensitivity analysis can overcome shortcomings of a traditional Monte Carlo simulation • It is not limited to multivariate normal distributions (which do not take into account fat tails or negative skewness) Skewed multivariate t-distribution • Helps to take fat tails and skewness into account • But also increases possibility of estimation error • Because it requires estimates of more parameters © Kaplan, Inc. 41 t marginalutilityofconsumption 1 time t Intertemporal Rate of substitution my marginalutilityofconsumption fine 0 Pxof a 0CPN Iindexed riskfreebond Po ECM Real riskfreeRor R Eim 1 coucp m pyggoueggy.iq fly To f h gqgyfyggo.gq.gg É edit sk s It I For premium Él ÉdÉs sk DiscountRateforEquity RtTL Of A ERP 7 k riskpremiumofequities over FI DiscountRatefor RealEstate Reto fivereturn f Active EñtRa Ra KEY iiqiiifjip.tv R Ro ExAnteRA E Ra E Rp E Ro EDW ECR Dwi activeweights Wpi Woi WoiERoi WpERpi Efi.EE ieinativewtsxRotwhort.xoutpaormanain assetcrass hlIRIi É sR I II Fifi Ft 0h Er Or IR InformationRatio OptimalActiveRisk SR IR After L ECRA Irxon SRw̅ 0A VSR IR TotalRiskof Portfolio 0 OptimalPortfolioAllocation 0 Wound Allocationtobenchmark Wo mfk.tn 0 8 1 Wfund 1 0 1 Transfer Coefficient TC Corr u Q AW O Breadth BR PositiontakenperperiodX If makingcorrelateddecisions GrinoldRuffy i pe ActiveReturn ECRa IR yr BR 11Eur EDwilli If unconstrained IR If constrained periodsper Ic0iSkscoreofsec. Optimal IR Corr Dwioi BW O IC BR TC IC BR 99 Chancewillbegiven iii If a EffiFI cBR0a3makessnse sinceIr E Err 0A É Optimal Risk for a Constrained makessensesince Ir Effon portfolio Ota TC Optimal SharpeRatio If unconstrained SRE IR If constrained SRE TC IR E RaICR TC ICR BRAOA Information Coefficient of a mkttimer ActiveRiskof SectorRotation Annualizedactive risk Annualizedactivereturn MaximumSpread Oc On ECRA 0 premiumcascounty effigy correct 1 20 0 rxy 0,2 fee Tradingcosts mgn 2 Ex BR IC X BR On creation redemption AP'sprofit IC spreadofunderlying Riskpremiumforcarryingtrade discount basedon probability of offsettingtradein 2ⁿᵈmkt Naups cont'd as man nap Round triptradingcosts Roundtripcommission spread factosensitivity E Rp Rer A risk premium Can re arrange to solvefor othervariable any ex Solve for Rfr Isolate Rfr inoneequation Sub1in solveforRfr 1 Standardized sensitivities 6 factoryfactor SubintoequationforPort B factor avg offactoracrossallsecurities ActiveReturn factorreturn Security selection return Where factorreturn BpiBoi X di Bp βportfolio Bo Securityselection return Ractive Rfactor Bbenchmark ActiveRiskSquared activefactorrisk activespecificrisk Activespecific risk WpiWB Oe Activefactor risk activerisksquared activespecific risk Portfolio Variance 0 Watch EstimatingVaR of a Portfolio 1 Calc meanreturn Rp EWR wO 2wawocova.ee Annualized return returnperperiod X annualized 2 Calc Oh Op Of Annualized StDev NyrOpcan 3 Calc VaRx Rp Zx Op x 1 isthe ZscorefortheVaR 4 If usingt'sabove VaR Principal Vary periodsperyr 1.65for st 2.33for 1 Solvefor ΔBond Px Duration DY ΔCall Px delta DS Convexity DY Gamma DSP VegaDV AnalysisofActiveportfolioManagement © CFA Institute The following information relates to Questions 1–4 1. Wei Liu makes two statements about active portfolio management: Statement 1 The “active return” of an actively managed portfolio is the difference between the portfolio’s return and the return on the benchmark portfolio, and it is equal to the managed portfolio’s alpha.x Statement 2 The active weights are the differences in the managed portfolio’s weights and the benchmark’s weights. Are Liu’s statements correct? A. B. C. Only Statement 1 is correct. X Pt1 iscorrectbutAlphais riskadjreturnoverthebenchmark Only Statement 2 is correct. True Both statements are correct. 2iscorrect only 2. The benchmark weights and returns for each of the five stocks in the Capitol Index are given in the following table. The Tuko l Fund uses the Capitol Index as its benchmark, and the fund’s portfolio weights are also shown in the table. Stock Portfolio Weight (%) Benchmark Weight (%) 20X2 Return(%) 1 30 24 14 2 30 20 15 3 20 20 12 4 10 18 8 5 10 18 10 What is the value added (active return) for the Tuko l Fund? A. 0.00% B. 0.90% C. 1.92% f Activereturn R Wp Woi RaWpa Wos RsWps Wos RaWpr Wor RsWps Wos 140.30.24 150.30.2 120.20.2 80.10.18 0.10.10.18 0.84 1 5 0 0.64 0.8 09I 3. Consider the following asset class returns for calendar year 20X2: Portfolio Weight (%) Benchmark Weight (%) Portfolio Return (%) Benchmark Return (%) Domestic equities 55 40 10 8 International equities 20 30 10 9 Bonds 25 30 5 6 Asset Class What is the value added (or active return) for the managed portfolio? A. 0.25% B. 0.35% C. 1.05% ActiveReturn Roort Roench 10 0.25 5 0.4840.3940.3 6 11.050 4. Gertrude Fischer mentions two properties of the Sharpe ratio and the information ratio that she says are very useful. Property 1 The Sharpe ratio is unaffected by the addition of cash or leverage in return a portfolio. w̅leveragereturnsmayincreasebutsowill proportionally SR Excess Property 2 The information ratio for an unconstrained portfolio is unaffected by the aggressiveness of the active weights. we meritai E Are Fischer’s two properties correct? 5 A. Yes. B. No .Only Property 1 is correct. C. No. Only Property 2 is correct. ie ei git t Seeabove bycombiningtheS P500 benchmark Indigofund WhatistheMaxSharperatio achievable Note SRsepsoo 0 333 A 0.333 C 0.365 0.448 B SR IR 0.15 Shoenchmark 8.3331 0.152 SR IR FRE 50.1334 0.3650 6 What Weightswouldbeused toachievethehighest SR optimalamtof riskin Note 00 181 IR 0 IS A B C SR 0.33 Dindigo 8 Windigo 1.014 Wsep 0.014 Oktive Windigo 1.450 Wsep 0.450 Windigo Windigo 1.500 Wsep 0.500 8 3 181 8.111 811L 8 1 1.014 Eko S P500 benchmark ExechnicsApplications Howie Rutledge is a senior portfolio strategist for an endowment fund. Rutledge meets with recently hired junior analyst Larry Stosur to review the fund’s holdings. Rutledge asks Stosur about the mechanics of exchange-traded funds (ETFs). Stosur responds by making the following statements: Statement 1 Unlike mutual fund shares that can be shorted, ETF shares cannot be shorted. Statement 2 In the ETF creation/redemption process, the authorized participants (APs) absorb the costs of transacting securities for the ETF’s portfolio. Statement 3 If ETF shares are trading at a discount to NAV and arbitrage costs are sufficiently low, APs will buy the securities in the creation basket and exchange them for ETF shares from the ETF sponsor. Rutledge notes that one holding, ETF 1, is trading at a premium to its intraday NAV. He reviews the ETF’s pricing and notes that the premium to the intraday NAV is greater than the expected arbitrage costs. Stosur is evaluating three ETFs for potential investment. He notes that the ETFs have different portfolio characteristics that are likely to affect each ETF’s tracking error. A summary of the characteristics for the ETFs is presented in Exhibit 1. Exhibit 1: ETF Characteristics Affecting Tracking Error Portfolio Construction Approach Type of Foreign Holdings Engagement in Securities Lending ETF 2 ETF 3 ETF 4 Full Replication Representative Sampling Full Replication Local shares ADRs* ADRs* Yes Yes No *ADRs are American Depositary Receipts. Rutledge and Stosur discuss the factors that influence ETF bid–ask spreads. Stosur tells Rutledge that quoted bid–ask spreads for a particular transaction size are (1) negatively related to the amount of the ongoing order flow in the ETF, (2) positively related to the costs and risks for the ETF liquidity provider, and (3) positively related to the amount of competition among market makers for the ETF. As ETF shares may trade at prices that are different from the NAV, Rutledge examines selected data in Exhibit 2 for three ETFs that might have this problem. Exhibit 2: Selected Data on ETFs ETF 5 ETF 6 ETF 7 Percentage of Foreign Holdings 10% 50% 90% Trading Frequency High Low Low Rutledge considers a new ETF investment for the fund. He plans to own the ETF for nine months. The ETF has the following trading costs and management fees: „ Annual management fee of 0.32% „ Round-trip trading commissions of 0.20% „ Bid–offer spread of 0.10% on purchase and sale Rutledge asks Stosur to compute the expected total holding period cost for investing in the ETF. 1. Which of Stosur’s statements regarding ETF mechanics is correct? A. B. C. Statement 1X opposite ETFscanbeshortedbutnotMFs Statement 2 APspaytransactioncoststhenmake offbidaskspread Statement 3 Wrong undervaluedAPwill buyETF redeemforsecurities way If ETF 2. Given the current pricing of ETF 1, the most likely transaction to occur is that: A. B. C. new ETF shares will be created by the APs. APwillbuysecuritiesforcheap gethigherpx in ETF redemption baskets will be received by APs from the ETF sponsor. Doif ETFis undervalued retail investors will exchange baskets of securities that the ETF tracks for creation units. Retailinvestorscannot exchangebaskets ETFS 3. Which ETF in Exhibit 1 is most likely to have the lowest tracking error? A. ETF 2 B. ETF 3 C. ETF 4 Fullreplication localshares lowtracking securitieslendingoffsetscosts willalwayshavehighertrackingerror Sampling ADRsaresubjecttohighertrackingerror costs lackofsecuritieslendingleadstohigher 4. Stosur’s statement about quoted bid–ask spreads is incorrect with respect to the: A. amount of the ongoing order flow in the ETF. orderflow liquidity correcthigher B. costs and risks for the ETF liquidity providers. correcthigher C. amount of competition among market makers for the ETF.rig fi ftp.fi Eii.Eioaserea 5. Which ETF in Exhibit 2 is most likely to trade at the largest premium or discount relative to NAV? A. ETF 5 B. ETF 6 C. ETF 7 One tolargeforeignholdings lowtradingfrequency 6. Excluding the compounding effect, the expected total holding period cost for investing in the ETF over a nine-month holding period is closest to: A. 0.54%. B. 0.62%. C. 0.64%. period trading Mgmtfeeholding co spread 0.32 1 t0.270.1 0.540 BAspread Multifactormodel Carlos Altuve is a manager-of-managers at an investment company that uses quantitative models extensively. Altuve seeks to construct a multi-manager portfolio using some of the funds managed by portfolio managers within the firm. Maya Zapata is assisting him. Altuve uses arbitrage pricing theory (APT) as a basis for evaluating strategies and managing risks. From his earlier analysis, Zapata knows that Funds A and B in Exhibit 1 are well diversified. He has not previously worked with Fund C and is puzzled by the data because it is inconsistent with APT. He asks Zapata gather additional information on Fund C’s holdings and to determine if an arbitrage opportunity exists among these three investment alternatives. Her analysis, using the data in Exhibit 1, confirms that an arbitrage opportunity does exist. Exhibit 1: Expected Returns and Factor Sensitivities (One-Factor Model) Fund Expected Return Factor Sensitivity A 0.02 0.5 B 0.04 1.5 C 0.03 0.9 Using a two-factor model, Zapata now estimates the three funds’ sensitivity to inflation and GDP growth. That information is presented in Exhibit 2. Zapata assumes a zero value for the error terms when working with the selected two-factor model. Exhibit 2: Expected Returns and Factor Sensitivities (Two-Factor Model) Factor Sensitivity Fund Expected Return Inflation GDP Growth A 0.02 0.5 1.0 B 0.04 1.6 0.0 C 0.03 1.0 1.1 Altuve asks Zapata to calculate the return for Portfolio AC, composed of a 60% allocation to Fund A and 40% allocation to Fund C, using the surprises in inflation and GDP growth in Exhibit 3. Exhibit 3: Selected Data on Factors Factor Research Staff Forecast Actual Value Inflation 2.0% 2.2% GDP Growth 1.5% 1.0% 0.2 0.5 Finally, Altuve asks Zapata about the return sensitivities of Portfolios A, B, and C given the information provided in Exhibit 3. 1. Which of the following is not a key assumption of APT, which is used by Altuve to evaluate strategies and manage risks? A. A factor model describes asset returns. B. Asset-specific risk can be eliminated through diversification. C. Arbitrage opportunities exist among well-diversified portfolios. Correct RequiredforAPTto work Correct LET Incorrecttheydonot 2. The arbitrage opportunity identified by Zapata can be exploited with: A. B. C. Strategy 1: Buy $50,000 Fund A and $50,000 Fund B; sell short $100,000 Fund C. Combinedfactorsensitivity 1 FSshort whichis 0.9 Strategy 2: Buy $60,000 Fund A and $40,000 Fund B; sell short $100,000 Fund C.X ECR 0.6 2 0.4 4 2 ECRshort 3 notprofitable long Strategy 3: Sell short $60,000 of Fund A and $40,000 of Fund B; buy $100,000 Fund C. ERiong 3 ECR short 2 seeaboveforcalc FSiong 0 9 FSshort 06 0 5 t0.4 1 5 0.370.6 0.9 3. The two-factor model Zapata uses is a: A. statistical factor model. B. fundamental factor model. C. macroeconomic factor model. 4. Based on the data in Exhibits 2 and 3, the return for Portfolio AC, given the surprises in inflation and GDP growth, is closest to: A. 2.02%. B. 2.40%. C. 4.98%. ECR WaERA FSinfa Surpriseinftfsaop.axsur.cop two ER FSinfo Surpriseinftfsaop.oxsur.cop 0.6 2 f o 5 0.2 f 1 0.5 0.4 31 t 1 0.2 f 1.1 0.5 0.61.6 f0.42.651 2.02 5. The surprise in which of the following had the greatest effect on fund returns? A. Inflation on Fund BX B. GDP growth on Fund A 1 0.5 0.51 C. GDP growth on Fund C 1.1 0.5 0.55 FSXSurprise 1 6 0.2 0.321 0 sinceithasthehighestabsoluteValue 6. Based on the data in Exhibit 2, which fund is most sensitive to the combined surprises in inflation and GDP growth in Exhibit 3? A. Fund A B. Fund B x C. Fund C X FSinfXSurpriseinftFSaopXSuraop 0 5 0.2 1 0.5 1.6 0.2 0 0.5 0.321 1 0.2 1.1 0.5 0 35 0.4 HighestabsoluteValue ElanagingIMeasuringMarketRisk © CFA Institute. The following information relates to Questions 6–11 Hiram Life (Hiram), a large multinational insurer located in Canada, has received permission to increase its ownership in an India-based life insurance company, LICIA, from 26% to 49%. Before completing this transaction, Hiram wants to complete a risk assessment of LICIA’s investment portfolio. Judith Hamilton, Hiram’s chief financial officer, has been asked to brief the management committee on investment risk in its India-based insurance operations. LICIA’s portfolio, which has a market value of CAD 260 million, is currently structured as shown in Exhibit 1. Despite its more than 1,000 individual holdings, the portfolio is invested predominantly in India. The Indian government bond market is highly liquid, but the country’s mortgage and infrastructure loan markets, as well as the corporate bond market, are relatively illiquid. Individual mortgage and corporate bond positions are large relative to the normal trading volumes in these securities. Given the elevated current and fiscal account deficits, Indian investments are also subject to above-average economic risk. Hamilton begins with a summary of the India-based portfolio. Exhibit 1 presents the current portfolio composition and the risk and return assumptions used to estimate value at risk (VaR). EXHIBIT 1. Selected Assumptions for LICIA’s Investment Portfolio Allocation Average Daily Return Daily Standard Deviation India government securities 50% 0.015% 0.206% India mortgage/infrastructure loans 25% 0.045% 0.710% India corporate bonds 15% 0.025% 0.324% India equity 10% 0.035% 0.996% Infrastructure is a rapidly growing asset class with limited return history; the first infrastructure loans were issued just 10 years ago. Hamilton’s report to the management committee must outline her assumptions and provide support for the methods she used in her risk assessment. If needed, she will also make recommendations for rebalancing the portfolio to ensure its risk profile is aligned with that of Hiram. Hamilton develops the assumptions shown in Exhibit 2, which will be used for estimating the portfolio VaR. EXHIBIT 2. VaR Input Assumptions for Proposed CAD 260 Million Portfolio Method Monte Carlo simulation Parametric approach Historical simulation Average Return Assumption Standard Deviation Assumption 0.026% 0.026% 0.023% 0.501% 0.501% 0.490% Hamilton elects to apply a one-day, 5% VaR limit of CAD 2 million in her risk assessment of LICIA’s portfolio. This limit is consistent with the risk tolerance the committee has specified for the Hiram portfolio. The markets’ volatility during the last 12 months has been significantly higher than the historical norm, with increased frequency of large daily losses, and Hamilton expects the next 12 months to be equally volatile. She estimates the one-day 5% portfolio VaR for LICIA’s portfolio using three different approaches: EXHIBIT 3. VaR Results over a One-Day Period for Proposed Portfolio Method 5% VaR Monte Carlo simulation CAD 2,095,565 Parametric approach CAD 2,083,610 Historic simulation CAD 1,938,874 The committee is likely to have questions in a number of key areas—the limitations of the VaR report, potential losses in an extreme adverse event, and there liability of the VaR numbers if the market continues to exhibit higher-than-normal volatility. Hamilton wants to be certain that she has thoroughly evaluated the risks inherent in the LICIA portfolio and compares them with the risks in Hiram’s present portfolio. Hamilton believes the possibility of a ratings downgrade on Indian sovereign debt is high and not yet fully reflected in securities prices. If the rating is lowered, many of the portfolio’s holdings will no longer meet Hiram’s minimum ratings requirement. A downgrade’s effect is unlikely to be limited to the government bond portfolio. All asset classes can be expected to be affected to some degree. Hamilton plans to include a scenario analysis that reflects this possibility to ensure that management has the broadest possible view of the risk exposures in the India portfolio. 1. Given Hamilton’s expectations, which of the following models is most appropriate to use in estimating portfolio VaR? A. B. C. Parametric method Sincereturndistributions arenotnormal Historical simulation method SincehistoricaldatadoesnotreflectfutureVol Monte Carlo simulation method modes allowedforother utsidethose ewitatypgramamnt.fr Estitathing 2. Which risk measure is Hamilton most likely to present when addressing the committee’s concerns regarding potential losses in extreme stress events? A. Relative VaR B. Incremental VaR C. Conditional VaR RelativeVaRcomparesto a benchmark Notrelevanthere decrease afactorin themodel sonotrelevant here When youincrease Measures VaRgiven a certaineventwhichis whatwe arelookingfor Eloss intheleftfail 3. The scenario analysis that Hamilton prepares for the committee is most likely a: A. stress test. B. historical scenario. C. hypothetical scenario. Literallysaysscenario in Q Nottestinganeventthathasoccurred Testingahypothetical scenariothathasnotoccurred yet 4. The scenario analysis that Hamilton prepares for the committee is a valuable tool to supplement VaR because it: A. B. incorporates historical data to evaluate the risk in the tail of the VaR distribution. Nohistorical precedenttoevaluate enables Hamilton to isolate the risk stemming from a single risk factor—the ratings downgrade. Nota singlerisk factorrather a scenariothatimpactsmanyfactors C. allows the committee to assess the effect of low liquidity in the event of a ratings downgrade. Downgrade lessliquidity sinceitnolongermeetsrequirement stillmustbesold leadingto major losses 5. Using the data in Exhibit 2, the portfolio’s annual 1% parametric VaR is closest to: A. CAD 17 million. B. CAD 31 million. C. CAD 48 million. 82 35 Annualreturn Dailyreturn days 0 Annualstdev Dailyst.dev Fdays 0.00501 Vary Annualreturn VaR VaR 550 7.92 6.5 2.33 7.921 260mm 31.01mmG ZXannualstdev Principal 11.96 6 sy 11.96 6. What additional risk measures would be most appropriate to add to Hamilton’s risk assessment? A. B. C. Delta Onlyapplicable iflargeportionofport is in derivativesoptions Duration Since90 ofportfoliois in FI Tracking error thecasehere Onlyapplicableifheavilyinvested in ETFs orgivenbenchmarknot Backtesting simulations Kata Rom is an equity analyst working for Gimingham Wealth Partners (GWP), a large investment advisory company. Rom meets with Goran Galic, a Canadian private wealth client, to explain investment strategies used by GWP to generate portfolio alpha for its clients. Rom states that GWP is recognized in the Canadian investment industry as a leading factor-based value portfolio manager and describes how GWP creates relevant investment strategies and explains GWP’s backtesting process. Rom notes the following: Statement 1 Using historical data, backtesting approximates a real-life investment process to illustrate the risk–return tradeoff of a particular proposed investment strategy. Statement 2 Backtesting is used almost exclusively by quantitative investment managers and rarely by fundamental investment managers, who are more concerned with information such as forward estimates of company earnings, macroeconomic factors, and intrinsic values. Galic, who is 62 years old, decides to allocate C$2 million (representing 10% of his net worth) to an account with GWP and stipulates that portfolio assets be restricted exclusively to domestic securities. Although GWP has not backtested its strategies with such a restriction, it has backtested its strategies using a global index that includes domestic securities. Rom shows the following risk measures to Galic for three factor portfolios. Exhibit 1: Downside Risk Measures for Model Factors Risk Measure Factor 1 Factor 2 Factor 3 Value at risk (VaR) (95%) (6.49%) (0.77%) (2.40%) Conditional VaR (CVaR) (95%) (15.73%) (4.21%) (3.24%) 35.10% 38.83% 45.98% Maximum drawdown Galic asks Rom, “What happens if the future is different from the past?” Rom gives the following replies: Statement 3 Although backtesting can offer some comfort, you are correct that it does have a weakness: Backtesting generally does not capture the dynamic nature of financial markets and in particular may not capture extreme downside risk. Statement 4 As a result, we have captured extreme downside risk and the dynamic nature of financial markets by using the Value-at-Risk and Conditional Value-at-Risk measures. In an effort to make Galic fully aware of the risks inherent in GWP’s strategies, Rom describes a recent study that investigated the return distributions of value and momentum factors that GWP uses to construct portfolios. The study found that these distributions were non-normal based on their negative skewness, excess kurtosis, and tail dependence. Rom indicated that investment strategies based on this type of data are prone to significantly higher downside risk. Rom informs Galic that GWP also uses a technique commonly referred to as scenario analysis to examine how strategies perform in different structural regimes. Exhibit 2 compares the performance of two of GWP’s factor allocation strategies in different regimes: Exhibit 2: Scenario Analysis Using the Sharpe Ratio Strategy/Regime High Volatility Low Volatility Recession Non-recession Strategy I 0.88 0.64 0.20 1.00 Strategy II 1.56 1.60 1.76 1.52 Galic is surprised to see that some of the backtest results are unfavorable. He asks, “Why has GWP not considered strategies that perform better in backtesting?” Galic recently met with Fastlane Wealth Managers, who showed much better performance results. The portfolio manager at Fastlane told Galic that the company selects the top-performing strategies after performing thousands of backtests. 1. Which of Rom’s statements concerning backtesting is correct? A. Only Statement 1 B. Only Statement 2 C. Ya Morecommonlyusedforfundamentalmugrs Easytobackfestsay firmsw̅PIECISetc Both Statement 1 and Statement 2 2wrong 2. Which key parameter needs to be changed for a new backtest that includes Galic’s restrictions? A. Start and end dates B. Consideration of transaction costs C. Investment universe A. Sensitivity analysis B. Backtesting C. Monte Carlo simulation usesglobalstocksto comparetodomesticShouldusedom.in back test too 3. Galic’s concern embedded in the question “What happens if the future is different from the past?” is a problem most relevant for which investment strategy evaluation technique? Relieson historical data 4. Which of the following conclusions of Exhibit 1 is least likely to be true? A. 5% of the time, losses from Factor 1 would be at least 6.49%. B. When the VaR is exceeded in Factor 1, we should expect an average loss of 15.73%. True see C. True see0 5% of the time, losses from Factor 2 are likely to be worse than losses from Factor 1. NottrueVaRforfactor2 VaRfactor1 5. Based on the statistical study performed by GWP, which of the following represents a suggested course of action if GWP were to conduct Monte Carlo simulation analyses on the factor strategies? A. Inverse transformation B. Bootstrapping C. Sensitivity analysis totesttheimpactofthetail events Sensitivityanalysiswillallowyou 6. Based on Exhibit 1, which factor has the smallest downside risk as measured by the weighted average of all losses that exceed a threshold? AK A CVar A. Factor 1 B. Factor 2 C. Factor 3 Hasthelowest CVar 7. The approach used by Fastlane Wealth Managers most likely incorporates: A. risk parity. B. data snooping. C. cross-validation. Lookingbackandpickingwinners on an Ex antebasis 8. Comparing the two strategies in Exhibit 2, the best risk-adjusted performance is demonstrated by: A. Strategy II in periods of low volatility and recession. B. Strategy I in periods of high volatility and non-recession. C. Strategy II in periods of high volatility and non-recession. Stratahas higherSharperatiounder lowVol recession HighestcombinedSharperatio Strattunderperforms inallscenarios