Portfolio A vs. Portfolio B…rational people….irrational choices

First of all a huge THANK YOU to everybody who participated in the study and responded to my question which I had posted in multiple forums yesterday. This is part of a project that I am helping a group of students with. Really appreciate your help.

A background:

Yesterday I had posted the below survey in all the social media forums/groups that I am a part of:

Question: You have been given $10,000 to invest and you must choose only one of the two options (A or B mentioned below. Which option will you choose? Note: Assume both options are safe.

Option A portfolio : Invest $2,000 each in 5 different investments…where each of them give you an annual return of exactly 10%…so your overall annual return is exactly 10%

Option B portfolio : Invest $2,000 in 5 different investments where the individual annual returns are all different for each 5 component investment …some are negative…some are positive…but the arithmetic average of all these 5 return figures is 10%…(please note this 10% is NOT the overall return of the portfolio but just the arithmetic average of the individual return %s….so the overall annual return of the portfolio is different) Example: Investment 1: (16%) Investment 2 : (- 6%) Investment 3: (0%) Investment 4 : (60%) Investment 5: (-20%) The arithmetic average of 16, -6, 0, 60 and -20 is (16-6+0+60-20)/5 = 10 Which option will you chose? P.S.: Kindly do not worry about whether this is a real life scenario or not….the question can be answered with the information provided

As of this writing I have received 426 responses  (and the responses are still trickling in) and the break up is

Portfolio B : 59%

Portfolio A : 41%

(However several of the respondents changed their choice after some discussions, rethinking and calculation)

This is not to judge anyone as frankly this was supposed to be an individual choice and people make choices based on what they feel comfortable with. The respondents came from a very diverse background….seasoned finance professionals, students (with no income), CEOs/Senior Management, home makers, entrepreneurs, investors, teachers, doctors, cops, pilots, retirees…you name it….and certain things that came out are very very interesting to me.

First let me get the mathematical fact (based on the information provided in the question) out of the way:

Given the info provided, Option B is always a superior choice irrespective of the duration of the investment (some people questioned the duration). If the time horizon is only 1 year, then the results of Portfolio A and Portfolio B are the same…both portfolios would return 10%…but over any longer time frame, the results of investing in Portfolio B will be superior 100% of the time. Because of compounding, the annualized return of Portfolio B for any time period > 1 year will always become > 10%…whereas that of A will remain fixed at 10%  (arithmetic average of the returns on individual investments of both portfolios = 10%)

However the more interesting  fact is that…the more the variability of the returns of the individual investments in Portfolio B are…the higher the overall return for B would be, and this is the point which most people who seek stability and shun variability, overlook. (I am a nerd and I always enjoy mathematical explanations….so fellow nerds can click here to see the math behind this fact)

For example…if the individual returns of the investments in portfolio B were 8%, 9%, 10%, 11%, 12% (still keeping the arithmetic average = 10%) then the value of Portfolio B would become ~ $26,131 in 10 years (which is > $25,937 for Portfolio A)….however if the variability increases significantly…as in the example (16%,-6%, 0%, 60%, -20%), the value after 10 years for Portfolio B becomes $232,017. In the above scenario, Portfolio A is always going to be the worst possible performing portfolio.

Many respondents commented that 60% return over a long period is not realistic….of course it is not! however this was basically not meant to be a question about investment expertise…this is a study on behaviour and human biases and I have just used a higher variability of returns to highlight a concept.

The baffling part of the whole exercise is that such a high % of respondents, a lot of whom are way smarter than I am and who are all perfectly able to calculate compounding, opted for the sub-optimal choice just because it provided a ‘sense of stability’. BTW…I am not even pretending that I always make the best choices. If I am faced with a similar situation in real life, part of me (my stomach) would also tend to go for Option A, even though I am very well aware of the math favouring B…..and I am very confident that a % of the respondents who chose B on social media would in real life tend to go for A too….the initial responses (which probably involved less of calculating and more of intuition) were at least 5% higher in favour of A then the final figures…and I know for sure that the in real life even if someone is invested in an ‘asymmetric return’ portfolio like B (inspite of some individual duds in the portfolio), there will often be a burning desire to take profits and shift to the comforts of certainty in an ‘A’ kind of a portfolio.

The urge to seek stability and reduce variability/volatility is often so strong that even in a controlled environment, where no real money was being staked and enough data was available for everyone to do the calculations, very smart people made the sub-optimal choice. Some of the people who chose A are even accomplished finance professionals. Interestingly, people from all walks of life demonstrated this bias.

For people who made the sub-optimal choice, the decision was clearly based on their intuition (as it could not have been based on their calculation…they would have chosen B otherwise). There could have been absolutely no other reason for a large number of otherwise rational people to opt for A, other than seeking to reduce variability and unconsciously equating variability with ‘RISK’.

Some A respondents even justified their choice saying ‘they want to sleep well’…all they had to do is a simple calculation to realise that in reality their sleep would be sounder if they chose B…because 100% of the time B would perform better. I am probably not smart enough to explain this human bias but it could very well be people’s preference to think ‘linear’ instead of ‘exponential’ (and ignore 2nd order outcomes…longer term compounding being one of them).

No wonder study of such human biases have given Kahneman and Thaler their Nobel prizes.