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ARE YOU MODELING WHAT YOU INTENDED? Presented by: David B. Loeper, CIMA®, CIMC® Providing WEALTHCARE ©Copyright Financeware, Inc., d/b/a Wealthcare Capital Management 2004 -2008 All rights reserved What are Capital Market Assumptions (CMAs) Anyway? For Purposes of Monte Carlo Simulation OR Optimization: The Average (mean, arithmetic mean) of Millions of Returns • Center of the distribution The Standard Deviation of Returns (uncertainty) • Extent and frequency returns vary from the mean The Correlation of Returns to Other Assets • Degree of association between two random variables Providing WEALTHCARE ©Copyright Financeware, Inc., d/b/a Wealthcare Capital Management 2004-2008 All rights reserved PAGE 2 What are Capital Market Assumptions (CMAs) Anyway? For Purposes of Monte Carlo Simulation OR Optimization: The Average (mean, arithmatic mean) of Millions of Returns • Center of the distribution The Standard Deviation of Returns (uncertainty) • Extent and frequency returns vary from the mean The Correlation of Returns to Other Assets • Degree of association between two random variables Together, these define the shape of a RANDOM distribution and ARE NOT A FIXED RELATIONSHIP in A Monte Carlo TRIAL Providing WEALTHCARE ©Copyright Financeware, Inc., d/b/a Wealthcare Capital Management 2004-2008 All rights reserved PAGE 3 Statisticians draw these distributions as a bell curve (Log normal distributions have a slightly longer tail at one end) Mean Frequency Extent Standard Deviation Providing WEALTHCARE ©Copyright Financeware, Inc., d/b/a Wealthcare Capital Management 2004-2008 All rights reserved PAGE 4 Statisticians draw these distributions as a bell curve The bell curve can define AN ASSET CLASS Low Mean & Risk Low Risk Asset Class High Risk Asset Class High Mean & Risk Providing WEALTHCARE ©Copyright Financeware, Inc., d/b/a Wealthcare Capital Management 2004-2008 All rights reserved PAGE 5 Statisticians draw these distributions as a bell curve The bell curve can define AN ASSET CLASS Or A PORTFOLIO when two or more classes are combined (based on the correlation between the two) Low Mean More Efficient Portfolio Mean Degree of Covariance Low Risk Asset Class High Risk Asset Class High Mean Providing WEALTHCARE ©Copyright Financeware, Inc., d/b/a Wealthcare Capital Management 2004-2008 All rights reserved PAGE 6 Imagine the “bell” flipped over and filled with a million numbers -28 -45 4 8 12 14 26 41 48 61 -21 -5 -38 38 52 11 18 -22 -9 4 7 27 45 13 -11 -1 5 10 12 16 26 35 -3 2 9 11 13 19 28 24 Mean 1 8 18 12 14 7 9 10 11 Frequency Extent Providing WEALTHCARE ©Copyright Financeware, Inc., d/b/a Wealthcare Capital Management 2004-2008 All rights reserved PAGE 7 Imagine the “bell” flipped over and filled with a million numbers The CMAs define the population of numbers in the “bell” -28 -45 4 8 12 14 26 41 48 61 -21 -5 -38 38 52 11 18 -22 -9 4 7 27 45 13 -11 -1 5 10 12 16 26 35 -3 2 9 11 13 19 28 24 Mean 1 8 18 12 14 7 9 10 11 Frequency Extent Providing WEALTHCARE ©Copyright Financeware, Inc., d/b/a Wealthcare Capital Management 2004-2008 All rights reserved PAGE 8 The CMAs define the population of numbers in the “bell” If we stirred them, blind folded you, & asked you to pick A SMALL percentage of the numbers What’s your chance of picking?…. -28 -45 4 8 12 14 26 41 48 61 -21 -5 -38 38 52 11 18 -22 -9 4 7 27 45 13 -11 -1 5 10 12 16 26 35 -3 2 Just these? 9 11 13 19 28 24 Mean 1 8 18 12 14 7 9 10 11 Frequency Extent Providing WEALTHCARE ©Copyright Financeware, Inc., d/b/a Wealthcare Capital Management 2004-2008 All rights reserved PAGE 9 The CMAs define the population of numbers in the “bell” If we stirred them, blind folded you, & asked you to pick A SMALL percentage of the numbers What’s your chance of picking?…. -28 -45 4 8 12 14 26 41 48 61 -21 -5 -38 38 52 11 18 -22 -9 4 7 27 45 13 -11 -1 5 10 12 16 26 35 -3 2 Just these? 9 11 13 19 28 24 Mean 1 8 18 12 14 7 9 10 11 Or, Just these? Frequency Extent Providing WEALTHCARE ©Copyright Financeware, Inc., d/b/a Wealthcare Capital Management 2004-2008 All rights reserved PAGE 10 The CMAs define the population of numbers in the “bell” What’s your chance of picking?…. -28 -45 4 8 12 14 26 41 48 61 -21 -5 -38 38 52 11 18 -22 -9 4 7 27 45 13 -11 -1 5 10 12 16 26 35 -3 2 Just these? 9 11 13 19 28 24 Mean 1 8 18 12 14 7 9 10 11 Extent Providing WEALTHCARE ©Copyright Financeware, Inc., d/b/a Wealthcare Capital Management 2004-2008 All rights reserved Or, Just these? Frequency Monte Carlo Simulates this random “picking” BASED ON THE BELL (bowl) DEFINED BY THE CMAs PAGE 11 The CMAs define the population of numbers in the “bell” In Seeking RATIONAL confidence, WITHOUT undue -28 -45 4 8 12 14 26 41 48 61 -21 -5 -38 38 52 11 18 sacrifice, do we -22 -9 4 7 27 45 13 -11 -1 5 10 12 16 26 35 advise clients to -3 2 9 11 13 19 28 24 live their life Mean 1 8 18 Or, Just Frequency 12 Just 14 7 9 based on 10 11 these? these? 5% 5% Chance REMOTE Chance EXTREMES Extent THAT NEVER HAPPENED? Providing WEALTHCARE ©Copyright Financeware, Inc., d/b/a Wealthcare Capital Management 2004-2008 All rights reserved PAGE 12 The CMAs define the population of numbers in the “bell” In Seeking RATIONAL <18% Chance or 82% confidence, Confidence of EXCEEDING WITHOUT undue -28 -45 4 8 12 14 26 41 48 61 -21 -5 -38 38 52 11 18 sacrifice do we -22 -9 4 7 27 45 13 -11 -1 5 10 12 16 26 35 advise clients to -3 2 9 11 13 19 28 24 live their life Mean 1 8 18 Or, Just Frequency 12 Just 14 7 9 based on 10 11 these? these? 5% 5% Chance REMOTE Chance EXTREMES? Extent Or REASONABLE CONFIDENCE? Providing WEALTHCARE ©Copyright Financeware, Inc., d/b/a Wealthcare Capital Management 2004-2008 All rights reserved PAGE 13 The CMAs define the population of numbers in the “bell” But, IF WE MAKE POOR ASSUMPTIONS in the SHAPE of the Bell, we could be CREATING: 10% <18% Chance -28 -45 4 8 12 14 26 41 48 61 -21 -5 -38 38 52 11 18 -22 -9 4 7 27 45 13 -11 -1 5 10 12 16 26 35 -3 2 Just these? 9 11 13 19 28 24 Mean 1 8 18 12 14 7 9 10 11 Extent Providing WEALTHCARE ©Copyright Financeware, Inc., d/b/a Wealthcare Capital Management 2004-2008 All rights reserved Or, Just these? Frequency UNDUE SACRIFICE or TOO MUCH UNCERTAINTY PAGE 14 The CMAs define the population of numbers in the “bell” IN THIS CASE, 82% Confidence is likely FAR worse than any market we have ever seen! SACRIFICE!! Missing only a Only 50% Confidence of few returns (some 7% EXCEEDING What Had Been 82% HIGH ones) -28 -45 4 8 12 14 26 41 48 61 -21 -5 changes ALL of -38 38 52 11 18 -22 -9 4 7 27 45 13 the odds -11 -1 5 10 12 16 26 35 -3 2 9 11 13 19 28 Mean 1 8 12 14 7 9 10 11 24 18 Remote outcome no longer within population Frequency Extent Providing WEALTHCARE ©Copyright Financeware, Inc., d/b/a Wealthcare Capital Management 2004-2008 All rights reserved PAGE 15 The CMAs define the population of numbers in the “bell” 82% Confidence of DOING ABOVE AVERAGE?! TOO MUCH UNCERTAINTY Missing only a 13% 82% Confidence of EXCEEDING What Had Been only 50% -28 -45 4 8 12 14 26 41 48 -21 -5 -38 38 11 18 -22 -9 4 7 27 45 13 -11 -1 5 10 12 16 26 35 Remote outcome no longer within population -3 2 9 11 13 19 28 24 Mean 18 8 1 12 14 7 9 10 11 61 Higher Confidence of previously remote Frequency extreme few returns (some LOW ones) changes ALL of the odds Extent Providing WEALTHCARE ©Copyright Financeware, Inc., d/b/a Wealthcare Capital Management 2004-2008 All rights reserved PAGE 16 CRITICAL POINTS TO UNDERSTAND With more COMPLETE populations, we can understand: Where reasonable confidence falls Remote extremes (those possible but never seen events) It is intuitive that if you select a small sample, it is very unlikely they will ALL be one extreme or the other -45 -28 -38 -21 4 -5 -22 -9 4 -11 -1 -3 8 2 14 11 7 5 12 10 12 18 16 7 27 9 10 26 11 13 19 12 61 52 45 35 28 24 Mean 8 41 48 38 13 9 1 26 18 Frequency 14 11 Extent Providing WEALTHCARE ©Copyright Financeware, Inc., d/b/a Wealthcare Capital Management 2004-2008 All rights reserved PAGE 17 CRITICAL POINTS TO UNDERSTAND With more COMPLETE populations, we can understand: Where reasonable confidence falls Remote extremes (those possible but never seen events) It is intuitive that if you select a small sample, it is very unlikely they will all be one extreme or the other -45 -28 -38 -21 4 -5 -22 -9 4 -11 -1 -3 8 2 14 11 7 5 12 10 12 18 16 7 27 9 10 26 11 13 19 12 61 52 45 35 28 24 Mean 8 41 48 38 13 9 1 26 18 14 11 Extent Providing WEALTHCARE ©Copyright Financeware, Inc., d/b/a Wealthcare Capital Management 2004-2008 All rights reserved Frequency What is harder to understand is how unlikely it is that a LARGER sample would be representative of the entire population…Thus skewed… or fooled? PAGE 18 We Can Easily Be Fooled (by randomness) How Many Of You Think a Compound Return for Large Cap should be 10% or less? Providing WEALTHCARE ©Copyright Financeware, Inc., d/b/a Wealthcare Capital Management 2004-2008 All rights reserved PAGE 19 We Can Easily Be Fooled (by randomness) How Many Of You Think a Compound Return for Large Cap should be 10% or less? Think we should be careful in using 30 Years 1974- 2003: 12.08% a 30 year data set? ONE year 30 Years 1973-2002: 10.55% changed compound return by 30 Years 1927-1956: 1.5%!!!! Providing WEALTHCARE ©Copyright Financeware, Inc., d/b/a Wealthcare Capital Management 2004-2008 All rights reserved PAGE 20 We Can Easily Be Fooled (by randomness) How Many Of You Think a Compound Return for Large Cap should be 10% or less? 30 Years 1974- 2003: 12.08% 30 Years 1973-2002: 10.55% 30 Years 1927-1956: 10.06% (expecting depression as NORM?) 20% of Historical 30 Year Periods <10% 50% of Historical 30 Year Periods >10.82% 51% of Historical 30 Year Periods >10.85% (monthly data) Our CMAs: 12.32% (mean) & 18.38% SD= 10.85% Compound Our CMAs at 77th %-tile: 8.30% at 87th%-tile: 7.17% Worst 30 Years of History (annual data): 8.47% (1929-1958) Worst 30 Years of History (monthly data): 7.17% Providing WEALTHCARE ©Copyright Financeware, Inc., d/b/a Wealthcare Capital Management 2004-2008 All rights reserved PAGE 21 We Can Easily Be Fooled (by randomness) How Many Of You Think a Compound Return for Large Cap should be 10% or less? 30 Years 1974- 2003: 12.08% 30 Years 1973-2002: 10.55% 30 Years 1927-1956: 10.06% (expecting depression as NORM?) 20% of Historical 30 Year Periods <10% 50% of Historical 30 Year Periods >10.82% 51% of Historical 30 Year Periods >10.85% (monthly data) Our CMAs: 12.32% (mean) & 18.38% SD= 10.85% Compound Our CMAs at 77th %-tile: 8.30% at 87th%-tile: 7.17% Worst 30 Years of History (annual data): 8.47% (1929-1958) Worst 30 Years of History (monthly data): 7.17% Providing WEALTHCARE ©Copyright Financeware, Inc., d/b/a Wealthcare Capital Management 2004-2008 All rights reserved PAGE 22 RANDOMNESS Doesn’t Look Random! How Many Of You Think a Compound Return for Large Cap should be 10% or less? 30 Years 1974- 2003: 12.08% 30 Years 1973-2002: 10.55% 30 Years 1927-1956: 10.06% (expecting depression as NORM?) 20% of Historical 30 Year Periods <10% 50% of Historical 30 Year Periods >10.82% 51% of Historical 30 Year Periods >10.85% (monthly data) Our CMAs: 12.32% (mean) & 18.38% SD= 10.85% Compound Our CMAs at 77th %-tile: 8.30% at 87th%-tile: 7.17% Worst 30 Years of History (annual data): 8.47% (1929-1958) Worst 30 Years of History (monthly data): 7.17% Providing WEALTHCARE ©Copyright Financeware, Inc., d/b/a Wealthcare Capital Management 2004-2008 All rights reserved PAGE 23 RANDOMNESS Fooling Us? Have you been fooled by?… RECENT low returns? Previously high returns (14% assumptions 5 years ago) Data sets that are too small to have any confidence in assumptions? (20-30 Years? 10 Years?) • • One trading discipline (MLM index) “New” asset classes (foreign stocks, mid cap, growth/value, hedge funds) “Seeing Cycles or Streaks” in Random Data? • Roulette Wheel Spun 15 reds in a row! – “Red Streak” Or “Black is Overdue” (As if the ball remembers where it fell) • Growth & Value “Cycle” Providing WEALTHCARE ©Copyright Financeware, Inc., d/b/a Wealthcare Capital Management 2004-2008 All rights reserved PAGE 24 Familiar with Growth RANDOMNESS? & Value Cycles? Heads vs.Tails Peformance vs. Large CapReturns Random Relative Trailing 3 Year Returns - Growth Value Headsvs.vs. Tails 15.00% 10.00% Growth Heads Tails Value Randomness DOES NOT appear to be Random! TAILS Value Outperforms 5.00% 0.00% -5.00% HEADS Growth Outperforms nJa 81 nJa 82 nJa 83 nJa 84 nJa 85 nJa 86 nJa 87 nJa 88 nJa 89 nJa 90 nJa 91 nJa 92 nJa 93 nJa 94 nJa 95 nJa 96 nJa 97 nJa 98 nJa 99 nJa 00 nJa 01 n02 -10.00% 24 36 48 60 72 84 96 Ja Flip# 12 Providing WEALTHCARE 3 Year Period Ending Trailing 12 Flips ©Copyright Financeware, Inc., d/b/a Wealthcare Capital Management 2004-2008 All rights reserved PAGE 25 Your Advice (output) is only as good as the input… (Capital Market Assumptions) If we are going to make the most of the one life each client has, then we must: »Have comfort & confidence in achieving the goals each client VALUES »Which therefore requires avoiding undue sacrifice to their lifestyle »And would include avoiding unnecessary investment risk (risk=concern=contradiction to comfort) These are the premises of what we call: Wealthcare Providing WEALTHCARE ©Copyright Financeware, Inc., d/b/a Wealthcare Capital Management 2004-2008 All rights reserved PAGE 26 Capital Market Assumptions SHOULD NOT CONTRADICT Wealthcare PREMISES… If we are too conservative, the price to the client’s life is: NEARLY CERTAIN UNDUE LIFESTYLE SACRIFICE REMEMBER: 1. How we were fooled by recent history? 2. How missing a few data points changed ALL the outcomes 3. How ONE YEAR of data changed the trailing returns (1.5%) 4. How reasonably large samples can be very skewed? 5. How our brains are “wired” to see streaks & cycles in random data? To avoid UNDUE SACRIFICE, we should avoid being too conservative Providing WEALTHCARE ©Copyright Financeware, Inc., d/b/a Wealthcare Capital Management 2004-2008 All rights reserved PAGE 27 Client Desires Maximum Income and has no desire to leave more than $1 million estate: Which is Wealthcare? PRICE OF BEING TOO CONSERVATIVE! $43,000 retirement income and 83% chance of exceeding $1 million estate with (Our CMAs): -90% chance of exceeding $450k estate? -75% chance of exceeding $1.5 million estate? OR… $24,000 retirement income, also 83% confidence but 2% lower return assumption than our CMAs: -96.5% chance of exceeding $1 million? -90% chance of exceeding $1.5 million? Providing WEALTHCARE ©Copyright Financeware, Inc., d/b/a Wealthcare Capital Management 2004-2008 All rights reserved PAGE 28 Client Desires Maximum Income and has no desire to leave more than $1 million estate: Which is Wealthcare? PRICE OF TOO CONSERVATIVE! $43,000 retirement income and 83% chance of exceeding $1 million estate with (Our CMAs): With $43k income starting -90% chance of exceeding $450k estate? in 1926, they’d -75% chance of exceeding $1.5 million estate? have an $875K OR… estate $24,000 retirement income, also 83% confidence but 2% lower return assumption than our CMAs: With $24k income starting chance of exceeding $1 million? in 1926, they’d have a -90% chance of exceeding $1.5 million? $2.6 million estate Being too conservative prioritizes estate above all else! Providing WEALTHCARE ©Copyright Financeware, Inc., d/b/a Wealthcare Capital Management 2004-2008 All rights reserved PAGE 29 I’d be very uncomfortable targeting low 80ish confidence with return assumptions less than ours… Nearly certain sacrifice! I’m fairly confident of our assumptions for stocks, bonds & cash because there is a lot of data to validate & test reasonableness Funny thing, a lot of the advisors that think our assumptions are “too high” (currently) or “too low” (eight years ago) despite all the data, turn around and complain about our assumptions for “new classes” despite NOT having enough data to validate & test these “new classes” Isn’t a premise of Wealthcare having RATIONAL CONFIDENCE? What happens to CONFIDENCE in DELIVERING the client’s goals when we make ASSUMPTIONS about “classes” we do not have the data to validate??? Providing WEALTHCARE ©Copyright Financeware, Inc., d/b/a Wealthcare Capital Management 2004-2008 All rights reserved PAGE 30 I’d be very uncomfortable targeting low 80ish confidence with return assumptions less than ours… Nearly certain sacrifice! I’m fairly confident of our assumptions for stocks, bonds & cash because there is a lot of data to validate & test reasonableness Funny thing, a lot of the advisors that think our assumptions are “too high” (currently) or “too low” (five years ago) despite all the data, turn around and complain about our assumptions for “new classes” despite NOT having enough data to validate & test these “new classes” Isn’t a premise of Wealthcare having RATIONAL CONFIDENCE? What happens to CONFIDENCE in DELIVERING the client’s goals when we make ASSUMPTIONS about “classes” we do not have the data to validate and test reasonableness??? Providing WEALTHCARE ©Copyright Financeware, Inc., d/b/a Wealthcare Capital Management 2004-2008 All rights reserved PAGE 31 First Question Would Be…What Explains 90%+ Of The Variance Of Returns? (to see if targeted confidence is in the ballpark?) ANSWER: Asset Allocation Source: Two Studies by Brinson, Beebower & Hood Asset Allocation TO WHAT? STOCKS, BONDS & CASH LESS THAN 10% of variance was explained by small cap, midcap, growth, value, foreign, real estate, etc. Providing WEALTHCARE ©Copyright Financeware, Inc., d/b/a Wealthcare Capital Management 2004-2008 All rights reserved PAGE 32 First Question Would Be…What Explains 90%+ Of The Variance Of Returns? (to see if targeted confidence is in the ballpark?) ANSWER: Asset Allocation Source: Two Studies by Brinson, Beebower & Hood Asset Allocation TO WHAT? STOCKS, BONDS & CASH LESS THAN 10% of variance was explained by small cap, midcap, growth, value, foreign, real estate, etc. Providing WEALTHCARE ©Copyright Financeware, Inc., d/b/a Wealthcare Capital Management 2004-2008 All rights reserved PAGE 33 Sample Client Confidence with 100% Large Cap as Investment Policy: Based upon randomizing actual historical returns from ’26-’02 1000 times Providing WEALTHCARE ©Copyright Financeware, Inc., d/b/a Wealthcare Capital Management 2004-2008 All rights reserved PAGE 34 How big a difference do you think it would make if the client were OVERWEIGHTED by 60% to Small Cap? 82% 60% Small/40% Large Based upon randomizing actual historical returns from ’26-’02 1000 times Providing WEALTHCARE ©Copyright Financeware, Inc., d/b/a Wealthcare Capital Management 2004-2008 All rights reserved PAGE 35 Shouldn’t it make a HUGE difference??? It does…so long as we are planning on coin flip odds… 82% 54% 45% 60% Small/40% Large 60% Small/40% Large 100% Large Based upon randomizing actual historical returns from ’26-’02 1000 times Assuming you consider 9 pts of confidence “HUGE” near the median Providing WEALTHCARE ©Copyright Financeware, Inc., d/b/a Wealthcare Capital Management 2004-2008 All rights reserved PAGE 36 Measuring with a micrometer…cutting with a chain saw… Would You Get Different Results With These Allocations? Asset Class #1 #2 #3 #4 Large Large Value Large Growth Small Small Value Small Growth 40% 0% 0% 60% 0% 0% 10% 15% 15% 0% 30% 30% 0% 20% 20% 40% 10% 10% 20% 10% 10% 10% 25% 25% SHOULD YOU? THEY ARE ALL THE SAME! Providing WEALTHCARE ©Copyright Financeware, Inc., d/b/a Wealthcare Capital Management 2004-2008 All rights reserved PAGE 37 Provided you use appropriate indices, your results would be statistical equivalents – 10 Years Ending 2002 Would You Get Different Results With These Allocations? Allocations: Large Large Value Large Growth Small Small Value Small Growth #1 #2 #3 #4 40% 10% 0% 20% 0% 15% 20% 10% 0% 15% 20% 10% 60% 0% 40% 10% Are we getting 0% better 30%assumptions 10% 25%by slicing the into more pieces? 0%pie 30% 10% 25% Mean Compound Standard Deviation Sample Confidence Providing WEALTHCARE ©Copyright Financeware, Inc., d/b/a Wealthcare Capital Management 2004-2008 All rights reserved 9.46 8.22 16.59 49% 9.35 8.13 16.46 48% 9.39 8.16 16.52 48% 9.37 8.15 16.49 48% PAGE 38 Or are we increasing our estimation error by limiting our data set? Since the results are statistically the Would You Get Different These Allocations? sameResults betweenWith the allocations… Allocation: #1 #2 #3 #4 11 Years 2003: Mean Compound Standard Deviation Sample Confidence 10.62 9.45 16.21 64% 10.57 9.41 16.14 63% 10.63 9.46 16.20 64% 10.58 9.42 16.14 63% 10 Years 2002: Mean Compound Standard Deviation Sample Confidence 9.46 8.22 16.59 49% 9.35 8.13 16.46 48% 9.39 8.16 16.52 48% 9.37 8.15 16.49 48% Providing WEALTHCARE ©Copyright Financeware, Inc., d/b/a Wealthcare Capital Management 2004-2008 All rights reserved PAGE 39 Which “Error” Reduces My OVERALL Confidence More? Since the results are statistically the Would You Get Different These Allocations? sameResults betweenWith the allocations… Allocation: 25 Years 2000: #1 #2 #3 18.13% Sample 99% 11 YearsConfidence 2003: 11 Years 2003 Mean: 10.62 10.57 10.63 10.58 Sample Confidence 64% 63% 64% Ignoring 10 Years 2002: Subclasses? Mean 9.46 9.35 9.39 Compound 8.22 8.13 8.16 Standard Deviation 16.59 16.46 16.52 Sample Confidence 49% 48% 48% Providing WEALTHCARE ©Copyright Financeware, Inc., d/b/a Wealthcare Capital Management 2004-2008 All rights reserved #4 63% 9.37 8.15 16.49 48% PAGE 40 Which “Error” Reduces My OVERALL Confidence More? Since the results are statistically the Would You Get Different These Allocations? sameResults betweenWith the allocations… Allocation: #1 #2 #3 #4 25 Year Mean 2000: 18.13% Sample 11 YearsConfidence 2003: 11 Year 2003 Mean: Sample Confidence 99% Or ignoring the of limiting +/- 35% 10.62 10.57 10.63 effect 10.58 my sample 64% 63% 64% 63% 10 Year 2002: +/- 50% Mean Compound Standard Deviation Sample Confidence 9.46 8.22 16.59 49% Providing WEALTHCARE ©Copyright Financeware, Inc., d/b/a Wealthcare Capital Management 2004-2008 All rights reserved population so I can include SubClasses? 9.35 9.39 +/- 15% 8.13 8.16 16.46 16.52 48% 48% 9.37 8.15 16.49 48% Ignoring Subclasses? +/- 1% PAGE 41 Making assumptions from limited data, usually has the opposite effect of excessive conservatism Instead of nearly certain sacrifice… We MIGHT be subjecting the client to: TOO MUCH UNCERTAINTY Providing WEALTHCARE ©Copyright Financeware, Inc., d/b/a Wealthcare Capital Management 2004-2008 All rights reserved PAGE 42 Making assumptions from limited data, usually has the opposite effect of excessive conservatism Instead of nearly certain sacrifice… We MIGHT be subjecting the client to: TOO MUCH UNCERTAINTY If the effect of “new classes” on the overall portfolio is 1-2% standard deviation and/or 50-100 bps of return… You could very well be assuming the value of the “new” class is the same as moving the 50th %-tile to the comfort zone! HOW CAN YOU ASSUME THAT?! Providing WEALTHCARE ©Copyright Financeware, Inc., d/b/a Wealthcare Capital Management 2004-2008 All rights reserved PAGE 43 Making assumptions from limited data, usually has the opposite effect of excessive conservatism Instead of nearly certain sacrifice… We MIGHT be subjecting the client to: TOO MUCH UNCERTAINTY If the effect of “new classes” on the overall portfolio is 1-2% standard deviation and/or 50-100 bps of return… You could very well be assuming the value of the “new” class is the same a moving the 50th %-tile to the comfort zone! HOW CAN YOU ASSUME THAT?! The best evidence your assumptions are wrong about a class, come from Mean Variance Optimizers… Providing WEALTHCARE ©Copyright Financeware, Inc., d/b/a Wealthcare Capital Management 2004-2008 All rights reserved PAGE 44 If the results of an MVO are “Wacky” And you obviously need to constrain it because it shows: Everyone holding stocks (we have good data) is stupid But should own managed futures or hedge funds (we have little data) and is therefore “enlightened” There is probably a stupid assumption in there somewhere… But Dave, isn’t that why optimizers have constraint inputs? A lesson in Algebra… Providing WEALTHCARE ©Copyright Financeware, Inc., d/b/a Wealthcare Capital Management 2004-2008 All rights reserved PAGE 45 The output is only as good as the input… (Capital Market Assumptions) If you get wacky unconstrained allocations, IT MEANS YOUR INPUTS ARE WRONG! If you have to constrain your optimizer to avoid “wacky” results, YOUR INPUTS ARE WRONG! A lesson in Algebra… Solve this equation: Providing WEALTHCARE ©Copyright Financeware, Inc., d/b/a Wealthcare Capital Management 2004-2008 All rights reserved 4x=4 x=1 PAGE 46 The output is only as good as the input… (Capital Market Assumptions) Now, solve our simple equation but constrain x to be < or = to .5 (just like an optimizer constraint) If you have to constrain your optimizer to avoid “wacky” results, YOUR INPUTS ARE WRONG! A lesson in Algebra… Algebra… Solve this equation: 4x=4 x=1 OR OR Providing WEALTHCARE ©Copyright Financeware, Inc., d/b/a Wealthcare Capital Management 2004-2008 All rights reserved 4x=4 If x is < or = to .5 then xx =.5 =.5 2=4 2=4 PAGE 47 The output is only as good as the input… (Capital Market Assumptions) Now, solve our simple equation but constrain x to be < or = to .5 (just like an optimizer constraint) If you have to constrain your optimizer to avoid “wacky” results, YOUR INPUTS ARE WRONG! A lesson in Algebra… Algebra… Solve this equation: ANY constrained allocation is as silly as saying 2=4! Providing WEALTHCARE ©Copyright Financeware, Inc., d/b/a Wealthcare Capital Management 2004-2008 All rights reserved 4x=4 x=1 OR OR 4x=4 If x is < or = to .5 then xx =.5 =.5 2=4 2=4 PAGE 48 Finally, What About Forecasts? Mean Reversion? Forecasts (mean reversion is just a forecast by another name) do not mix well with measuring confidence in random outcomes. This is not to say you are unskilled at forecasting… But, what is the confidence level measuring if it was based on a distribution created by a forecast? Worst of Median History 10.85% Best of History Long Term Nature of Market Providing WEALTHCARE ©Copyright Financeware, Inc., d/b/a Wealthcare Capital Management 2004-2008 All rights reserved PAGE 49 Finally, What About Forecasts? Mean Reversion? Forecasts (mean reversion is just a forecast by another name) do not mix well with measuring confidence in random outcomes. This is not to say you are unskilled at forecasting… But, what is the confidence level measuring if it was based on a distribution created by a forecast? Worst of Median History 10.85% Best of History Best of history near “norm”? Long Term Nature of Market Providing WEALTHCARE ©Copyright Financeware, Inc., d/b/a Wealthcare Capital Management 2004-2008 All rights reserved PAGE 50 Finally, What About Forecasts? Mean Reversion? Forecasts (mean reversion is just a forecast by another name) do not mix well with measuring confidence in random outcomes. This is not to say you are unskilled at forecasting… But, what is the confidence level measuring if it was based on a distribution created by a forecast? Worst of Median History 10.85% Best of History Worst of history near “norm”? Effect of +/2.5% Best of history near “norm”? Long Term Nature of Market Providing WEALTHCARE ©Copyright Financeware, Inc., d/b/a Wealthcare Capital Management 2004-2008 All rights reserved PAGE 51 Which mean are we reverting to? Market Returns Ending in 2003: 5 Years, bottom 10%-tile of all 5 year periods » Raise Assumption? 10 Years, 51st %-tile of all 10 year periods » Keep the Same Assumption? 25 Years, top 16%-tile of all 25 year periods » Lower Assumption? Providing WEALTHCARE ©Copyright Financeware, Inc., d/b/a Wealthcare Capital Management 2004-2008 All rights reserved PAGE 52 So, how can we be confident about our CMAs for all the asset classes??? WE CAN’T!!! But… The “main driver” is stocks, bonds and cash • There we have a lot of good data • We have reasonable confidence in the assumptions • And it is how we invest • Other classes with less evidence cannot by definition do anything other than introduce more uncertainty (risk) Isn’t Wealthcare about avoiding unnecessary risk? Providing WEALTHCARE ©Copyright Financeware, Inc., d/b/a Wealthcare Capital Management 2004-2008 All rights reserved PAGE 53 How our assumptions are built… For classes with a lot of good data (i.e. domestic stocks, bonds & cash) • Risk & Return= Average of 700+ 10 year periods • Correlations based on all historical data • Tested in engine (30,000 simulated years vs. 76 years of history) • Extremes of simulations wider than history (based on SD) • Middle of simulated distribution near middle of historical data For other assets… • If possible, use a proxy (i.e. foreign stocks are still stocks) • Adjust for added uncertainty (i.e. currency risk for foreign, limited data for alternative classes) • Use correlations but test with a Cholesky decomposition • Perform MVO test (i.e. adjust as needed to avoid excessive assumed alpha but still shows some incremental value) Providing WEALTHCARE ©Copyright Financeware, Inc., d/b/a Wealthcare Capital Management 2004-2008 All rights reserved PAGE 54 How our assumptions are built… For classes with a lot of good data (i.e. domestic stocks, bonds & cash) • Risk & Return= Average of 700+ 10 year periods • Correlations based on all historical data • Tested in engine (30,000 simulated years vs. 76 years of history) • Extremes of simulations wider than history (based on SD) • Middle of simulated distribution near middle of historical data For other assets… • If possible, use a proxy (i.e. foreign stocks are still stocks) • Adjust for added uncertainty (i.e. currency risk for foreign, limited data for alternative classes) • Use correlations but test with a Cholesky decomposition • Perform MVO test (i.e. adjust as needed to avoid excessive assumed alpha but still shows some incremental value) Providing WEALTHCARE ©Copyright Financeware, Inc., d/b/a Wealthcare Capital Management 2004-2008 All rights reserved PAGE 55 In summary… If we are really providing: Confidence in exceeding goals, without undue sacrifice or unnecessary risk… We cannot bet our clients’ future, or worse, misrepresent the confidence level based on: » Skewed data » Lack of evidence » Hope or Prophesies… » These all contradict the premises of Wealthcare Providing WEALTHCARE ©Copyright Financeware, Inc., d/b/a Wealthcare Capital Management 2004-2008 All rights reserved PAGE 56 In summary… If we are really providing: Confidence in exceeding goals, without undue sacrifice or unnecessary risk… We cannot bet our clients’ future, or worse, misrepresent the confidence level based on: » Skewed data » Lack of evidence » Hope or Prophesies… » These all contradict the premises of Wealthcare Providing WEALTHCARE ©Copyright Financeware, Inc., d/b/a Wealthcare Capital Management 2004-2008 All rights reserved PAGE 57 Questions? Providing WEALTHCARE ©Copyright Financeware, Inc., d/b/a Wealthcare Capital Management 2004-2008 All rights reserved PAGE 58