by Peter J. de Marigny
Statistical Mistakes Advisers Tell Clients
I was sitting at a table waiting for my appointment to show up at a local Starbucks when I overheard a financial adviser speaking to a client. The colored chart printouts for asset allocation relative to the client’s investment horizon, liquidity requirements and risk tolerance filtered down to representative investments to fill-in the asset classes. The investor looked unsatisfied, mentioning that he had gotten the same presentations from others over the last year with considerable differences, and that his actual results for the last ten years differed significantly from the expectations of the presentation. The investor was correct in recognizing that the presentation materials were based on assumptions that are not always true, including that variance and correlations are static. Additionally, the investor was interested in adding a new strategy for new funds and he wanted to know how many investing choices there were for his investment universe. These questions the adviser either could not answer or dismissed as having no relevance to investing.
Some answers that I overheard were just wrong.
Investment statistics are used both for valuation and asset allocation that, in turn, include inferences relating to risk. Today, most financial advisors adopt the paradigms of their respective professional associations: CFA, CAIA/CPWA, FRM/GARP, CIMA/IMCA, AFP and last, American College for various insurance and planning credentials. For those advisers without professional credentials, sell-side or buy-side firm tools provide the presentation materials to investors. CFA and FRM have the most in-depth information on the use of statistics for valuation, with CAIA providing alternative asset class models and CIMA/IMCA providing traditional models. Within the CFA study materials is a section on path dependent asset valuation utilizing the binomial model.
Probability and factor models are used in investment analytics and strategy, including game theory, binomials (for mortgages, contingent claim [biotechs], structured products with “knock-ins”), M&A, target returns testing (simple t tests), risk claim testing (variance – Chi^2), and asset allocation (Monte Carlo). However, there are several misstatements advisers make to clients, while there are other uses of probability that are not commonly practiced when needed. In this short article, I offer some common adviser errors resulting from improperly using statistics, and some potential uses of probability for investment analytics that are not generally used by advisers.
First, let’s talk about one common mistake I have heard many financial consultant advisers tell clients. There is an almost absurd reliance on Monte Carlo for inferences that are erroneous. For instance, I heard an advisor say that a certain manager or investment had a 70% average of beating the index in its long history, concluding that you should expect 7 out of the next 10 years to beat the index if that average is maintained (assuming a constant and independent probability). That is a false statement.
It seems logical, but is it true?
The truth is most advisers believe that the tools have the answers and all that is needed is some data entry and then to regurgitate the generated report as if they provided the “Rosetta Stone” panacea solution. To many advisers, their use of statistics is confined to a handful of performance measurement ratios.
What other simple statistics may be used that are not in general use as portfolio performance measurements?
Here’s another question that an investor asked that could not be answered by the adviser in his firm’s Monte Carlo mean-variance optimization tool: “What is the probability of the investment beating the index in the next two out of three years?”
Probability of beating the index =p^r where p=beating the index (p=.7) and r= #times beat the index
Probability of opposite =1-p^(n-r) where n=total choices and (n-r) is the #opposite choices
So p^r(1-p)^(n-r) = .7^2(1-.7)^(3-2)=.7x.7x.3=.147=probability of each desired outcome
And the total# of outcomes is n!/r!(n-r)!=3!/2!(3-2)!=3 so the #outcomes probability=3x.147=44.1% = the probability of the event that in the next 2 out of 3 years the index is beaten
Adviser misrepresenting statistics
The adviser knowing that with a 70% average of beating the index he falsely expects it to do so for 7 of the next 10 years. That is what he told the investor, but is it true?
(p=.7; n=10; r=7) p^r(1-p)^(n-r)=.7^7(1-.7)^(10-7)=.0022235661 is the probability of each event
Total# of those outcomes=n!/r!(n-r)!=10!/7!(10-7)!=10x9x8/3x2X1=120 Outcomes we want
#Desired Outcomes x Probability of Each Outcome=120x.002223566=27% probability not 70%
In the adviser meeting at Starbucks I overheard some questions that went unanswered. The investor was asking not so much about the investments themselves, but about the number of ways to purchase.
Questions that cannot be answered by advisers from Modern Portfolio Theory printouts
- “I have a list of ten investments that I want to invest in serially over the next ten periods. How many orders are there to choose?
- “How many ways are there to choose if I only invest serially over the next three periods?
Answer: 10!/7! = 720
- “How many ways can I buy three investments at a time?”
Answer: 10!/7!(3!) = 120
- “I have a list of nine investments. I want to invest a total of $125,000 in $25,000 lots either all in one or any in any number of 5 lots. How many choices do I have?
Answer: 5040/144 = 35 variations
Advisers offer presentations of portfolio construction and asset allocation. However, many investors are just as concerned with the methodology of how they invest according to their liquidity. Advisers assume that all money is invested in the ratio of their asset allocation and that timing has negligible effect. There are many investor questions that are simply not answered in an efficient frontier printout, and advisers should gain an understanding of these basic statistics to avoid misrepresentations and non-sequitur statements. *.*
Peter J. de Marigny, www.DITMo.net