Beta is not Sharpe Enough ….

1. September 2010Steven P. Greiner, Ph.D. sgreiner@factset.com 0101.312.566.5109 Beta is not Sharpe Enough….

2. Sharpe-r Risk Measures Agenda • Tracking Error Measures • FactSet’s Balanced Risk Module in PA • Tracking Error Forecasts • Introducing the “g-Factor”, a robust Volatility Measure • Value-at-Risk • Stress Testing: Time & Event • Stress Testing: Black Swan Event • VAR Extreme Event Stress Testing • Fat-Tail VAR Raising the IQ of the Intelligent Investor

3. Sharpe-r Risk Measures… Ben Graham said: • In a Barron’s article, he said that what bothered him is that authorities equate beta with the concept of risk. Price variability yes, risk no • Excerpt from Barron’s, Sept 23, 1974, Dow Jones and Company • Real risk he wrote, is measured not by price fluctuations but by a loss of quality and earnings power through economic or management changes • As for variance or standard deviation of return being a useful risk measure, in the same Barron’s article he says that the idea of measuring investment risks by price fluctuations is repugnant to him, because it confuses what the stock market says with what actually happens to the owner’s stake in the business

4. Tracking Error: What it isn’t! • Usually, TE is reported as meaning that the portfolio’s return is “bounded” by being within +/- TE of the Benchmark 67% of the time. Is this True? σ= sqrt[Σ{(x-μ)/(n-1)}^2] Avg(x) = μ = 2.0

5. Tracking Error: What it isn’t! • Using the math from the previous slide, substitute “P-BM” for “x” and re-plot the graph… • This then implies TE is the stdev about the average value of the XS return, not the BM return.. σ’ = sqrt[Σ{((P-BM)-μ’)/(n-1)}^2] = TE Avg(P-BM) = XS Ret = μ’ = 1.4

6. Tracking Error… What it is!! • Consider the impact this has on interpretation • There can be considerable asymmetry around bench returns

7. Empirical Data for:S&P, 2 SPDR’s, Exxon, ISRG, LCV, Magellan, Nikkei & 2 Hypothetical's • Weekly returns downloaded from FactSet from December 31st, 2006 to August 31st, 2010

8. Empirical FactSet Data for:S&P, 2 SPDR’s, Exxon, ISRG, LCV, Magellan, Nikkei & 2 Hypothetical's True Defn => Usual Defn =>

9. Empirical Data for:S&P, 2 SPDR’s, Exxon, ISRG, LCV, Magellan, Nikkei & 2 Hypothetical's • For smaller TE, the effect is more pronounced!

10. Tracking Error Measures…. • If the TE is large and the abs(XS) return is small, you can stick to the old paradigm • If in 2008 one lowered TE hoping to lower relative risk while under-performing, one actually increased the likelihood of continued under-performance, hence risk actually increased. • This is because as TE goes down for a given XS return, one draws a narrower range around (P-BM) where the portfolio spends the majority of time in. If (P-BM) is negative, you lose the opportunity to out-perform as TE decreases. • If you have negative XS return, increase your TE to lower risk. E.g. • XS Ret = -200 bps & TE = 4%; -6% < Port Ret < 2% (67% of the time) • XS Ret = -200 bps & TE = 6%; -8% < Port Ret < 4% (67% of the time) • If you have positive XS return, decrease your TE to lower risk. • XS Ret = 200 bps & TE = 6%; -4% < Port Ret < 8% (67% of the time) • XS Ret = 200 bps & TE = 4%; -2% < Port Ret < 6% (67% of the time).

11. FactSet’s Balanced Risk Module….. • Components Uniting Equities, Fixed Income and Currencies.. • Monte Carlo Value-At-Risk • Stress Testing 1: Time & Event Weighting (Equity Only) • Stress Testing 2: Extreme Event (Equity Only) • MC Extreme Event Risk • Global Equities, Corp, Hi-Yld, Agencies, Tips, U.S.Treas, Sovereign, U.S. MBS, Exc-Trad Options • Four Equity Vendor Risk Models, Plus Factset’s Own.. • SUNGUARD – APT (Country, Regional, & Global, MT & ST, Equity only) • Axioma (Global, EMG, Euro, U.S., Canada & Japan, Equity only) • MSCI-Barra (Country, Regional and Global, Equity only) • Northfield Inf. Services (Country, Regional, Global, MT and ST, Equity only) • MAC-ST (Included in Balanced Risk Product & Required for FI) • Fast Re-Pricing Algorithm for FI.. • Yield Curve (Int. Rate) Risk Specific to Underlying Currency of Security • 17 KR Dur specified by 4 PCA of 6 Libor & Govt Curves (U.S., Can, Aus, EUR, Jap, UK) • Each Major Asset Class Has its Own Spread Model • 3 Base Currency (USD, EURO, GBP) Reporting Options w/ Exp. to 13 Currencies Available • Fully Integrated with Portfolio Attribution..

12. Example of Global Equity Portfolio… • Construct Global Portfolio and Compare VAR and TE computed through FactSet Balanced Risk Module

13. Tracking Error Forecasts…. • Computed TE using VAR and Historical (black) for Global Portfolio Measured with various risk models………Which is right?

14. Tracking Error Forecasts with CI’s…. • Which is right? Most are, whence you compute the 95% Confidence Interval on the Historical….Note Asymmetry…

15. Tracking Error… Bias • A cross-section of the TE at a point in time has the following form..

16. Using Betas for measures of Volatility… • What is the impact of the correlation on one’s interpretation of how volatile a stock or portfolio is? • Beta’s ~ XLK: 0.9, ISRG: 1.2 XOM: 0.7

17. Using Betas for measures of Volatility… • So a portfolio that has next to no correlation with it’s bench then, has essentially no volatility? • Beta’s ~ Norm: 0.08 & t-Dist-12: 0.01

18. The Way to a Better Volatility Measure…g-Factor A question we might ask is, what’s the amount of time the bench & portfolio spend in a constant vicinity of their mean return? Stdev of Bench = SD • Form the distribution of returns for a time period • Measure the area under curve between Mean +/- SD for both Bench and Portfolio….. Use the Bench’s SD for each… • Ratio of Bench area to Portfolio area is g-Factor

19. The “g-Factor”… • The g-Factor is independent of the correlation and just compares the amount of time the benchmark and portfolio “spend” within an identical distance of their mean values

20. Issues for Value-at-Risk.. • Trading or portfolio positions change over time, thus the longer horizon VAR calculated, the less realistic it’s going to be, which is why we use daily VAR • VAR techniques are subject to model risk. In particular, the parametric model used for the drawing in Monte Carlo influences the value of the VAR calculated, hence there’s no “correct” VAR, it’s just an estimate • VAR isn’t effective when macro-risks, extreme events (Black Swans or ELE) are occurring. The returns distribution obtained from either a covariance based method or a copula, predicated on modeling the past years dependencies, isn’t representative of how the returns will behave in extreme events. • Even in a copula fitting of the factor returns with an attempt to garner non-linear dependencies in the tail, VAR will not show how the dependency really behaves during a Black Swan event • Existing VAR models reflect risks that are not useful during transition periods or when “broken” correlation structures occurs across assets • For a given covariance matrix, there are many, many datasets whose variance or covariance will satisfy it. There is no unique set of factor returns for a given covariance matrix (or copula)

21. Value-at-Risk Example_1

22. Stress Testing One: Time & Event Weighting.. • Pick a “shock”, any risk model factor or exogenous factor that has a time-series (obviously, cause & effect economic variables, not weather forecasts) • Determine covariance/correlation of this “shock” to all risk model factors • Compute “Beta” between shocked factor “K” and all risk model factors from the covariance measurements • New Factor Return = Beta * Shock

23. Stress Testing One: Time vs. Event Weighting..

24. Stress Testing One: Example

25. Stress Testing One: Example…same data, but perspective has changed…

26. Stress Testing Two: Extreme Event Stress.. • Extreme Event Stress let’s us go back in time and measure the current portfolio’s response to factor returns garnered from the past • It’s like using the cross-security relationships, the dependence structure from the past, because the factor returns used from a chosen historical stressed market environment, were those used to construct the covariance matrix at that time • In this module, we use past factor returns, multiplied by current exposures to allow us to examine how a portfolio today might behave should history “almost” repeat itself

27. Stress Testing Two: Example • What’s the Internet Bubble’s impact on Global Equity Portfolio, “Today”? • Borrow factor returns from April 2000

28. Stress Testing Two: Example • Internet Bubble’s impact on Global Equity Portfolio is… • Wouldn’t be the worst since 1997!!

29. Monte-Carlo Extreme Event Risk.. • Monte-Carlo Extreme Event Risk is enabling and is a unique combination of FactSet’s stress testing platform combined with Value-at-Risk methodologies • Go back in time and literally take the covariance matrix from the past, decompose it via “Cholesky”, while separately and simultaneously, Monte Carlo-generated scenarios are made, and multiplied by this historically fashioned Cholesky matrix to compute “factor returns” • The Monte Carlo VaR is computed by multiplying each set of Monte-Carlo generated factor returns by the current exposure matrix In this way, we use the dependence structure from a “Black Swan” event and past co-variances to see what a current portfolio’s VaR would look like under that past stressed situation

30. Monte-Carlo Extreme Event Risk Example.. • LTCM occurred August of 1998 • Retns ~ -10% to -20%

31. Monte-Carlo Extreme Event Example.. • When LTCM happened, the covariance matrix defined more lepokurtic return distributions • Whereas now, it shows a much broader distribution of returns • So today’s VAR is greater than that of this past extreme event

32. Monte-Carlo Extreme Event Risk Example Two • Credit Crisis of November 2008

33. Monte-Carlo Extreme Event Risk Example Two.. • Using Global Portfolio of Equities, FI, Options and Currencies (Balanced..) • Examine impact of Credit Crisis (11/30/2008) on VaR

34. Monte-Carlo Extreme Event Risk Example Two.. • It’s clear that if the crisis of 2008 were to occur again, the addition of derivatives in the portfolio would offer a strong hedge against losses

35. Exchange Traded Options • Barone-Adesi & Whaley (JOF Vol42, No.2, June 1987) • Analytical approximation of American option pricing starting with European formula • Many times faster than most other methods • Loses accuracy for long dated options unfortunately (e.g. LEAPS) but acceptable accuracy for short to mid-maturity options • “They” used a normal approximation for the implied volatility, but that was written in 1987 before the 19 Oct 1987 “Black Monday” event inaugurated the volatility “smile” • ThereforeFactSet uses an implied vol that’s fit to “f(strike/price, time to maturity)” from stock’s option chain, incorporating the observation that implied vols vary as the stock’s price varies from the option strike (volatility smile effects). This is a very smart methodology • The option pricing first involves solving iteratively for a critical stock price (Eq. 19 in their paper), below which the option’s call value is given by the Black-Scholes equation and above which the option’s call value is given by its exercisable proceeds (Price-Strike) • The critical price solution is placed into an analytical expression involving the addition of a early exercise premium to the Black-Scholes equation (Eq. 20 of their paper) • The next step, given option strike, vols, risk-free rate, time to maturity and stock price from the MC generating process, is simply to “plug-and-chug” to compute the option’s price

36. Ramifications for Fixed Income.. • Due to liquidity issues, seldom have real FI security returns to regress against factor exposures to compute Betas • Hence we used previously calculated “sensitivities” (dur, convex..) • Monte-Carlo generated Interest Rate (yield curve) moves, spread and currency changes • Fast Re-Pricing (Taylor Series expansion) schema utilizes these changes to price “FI” instruments along with time decay • All securities of same currency have same yield curve exposure to the same set of 17 key rate risk factors (6 Libor & Govt Curves: U.S., Can, Aus, EUR, Japan, UK) • Different types of instruments have differing spread models, currently configured for: • Corporates Sovereigns (that we have yield curves for) • High Yield U.S. MBS • Agency Treasury Inflation-Protected Securities • U.S. Treasuries Exchange Traded Derivatives

37. Rotund Posteriors, Hefty Backsides & Pudgy Extremities.. • Fat-Tails should be considered when skewness &/or kurtosis are prevalent

38. Rotund Posteriors, Hefty Backsides & Pudgy Extremities.. • Q-Q Plots of 12 randomly selected small cap stocks • Most stocks are non-normal, the evidence is overwhelming..

39. VAR techniques are subject to model risk so the parametric model used for drawing in Monte Carlo influences the value of the VAR calculated.. • Normal is acceptable at 95% VAR • Fat-Tails underestimate 95% VAR, but are closer to it than normal method • Normal approximation leads to overly optimistic forecasts at 99% VAR • Fat-Tails generally result in conservative and accurate 99% VAR

40. VAR techniques are subject to model risk so the parametric model used for drawing in Monte Carlo influences the value of the VAR calculated.. • Our own work suggests that normal method under-estimates the VAR compared to Fat-Tailed methods, even at 95% confidence level

41. Fat-Tail Value-at-Risk • No “magic bullet” as it doesn’t capture correlation structural changes which occur in real “Black Swan” events (not modeling the volatility of volatility) Currently @ FactSet • Internal discussions on methodology • Robustness tests, ease of use, computation time • On-going development continuing..