I have found this challenge almost impossible because I don't want to use too technical jargon, just nice pictures, gestures and analogies to everyday life. So I created this pathological example with monkey A and B. Monkey A is believes that reserving a variety of food such as bananas, mangos and kiwis will result in lower risk shown with first curved frontier.

x-axis would be technically standard deviation but you can suppose it is a risk to lose food from the average, y-axis the amount of editable food.

Can you find any argument, rather than some Python lines, to support one of the models? What kind of monkeys are A and B?

Monkey A`s view

enter image description here

Monkey B only believes in the Banana so gathers only them. It is a bit risky endeavour because they stale at the same speed and there are times when B hits almost 0 bananas but then again there are times when B hits a huge amount of bananas during harvest, much more than A can ever imagine. B won't even try the next best alternative, mocking mangos and such things in trees being too inferior. How to explain this kind of monkey what an efficient frontier is and when B's view is totally correct or incorrect?

Monkey B`s view

enter image description here


  • the odd holes in the frontier and floating point err, more here
  • 9
    Dude - I'm not surprised the child is lost as I know I'm lost. Regardless, how old is the child you are teaching? - no answer will be possible without that basic piece of information.
    – gef05
    Mar 31 '11 at 14:14
  • +1 for a very well formed analogy, but it took me a while to understand the purpose of the analogy :)
    – Dheer
    Mar 31 '11 at 14:22
  • 2
    @hhh I gave you a +1 as well for effort, but it is much too complicated and I think you are using the wrong graph technique. I don't think a child can really think in terms of 3D graphs. Mar 31 '11 at 14:30
  • 2
    @hhh. I don't know what you mean by age discrimination. What I do know, as a former educator, is that basic pedagogy requires knowledge of the student - including age. No one answer will be correct. Your approach for teaching a ten-year old will differ vastly from that for a 15-year old (for example). I'll gladly bring 20 years of experience to the question if you can provide necessary guidance. :)
    – gef05
    Mar 31 '11 at 17:48
  • 1
    @Vitalik: suppose bananas were a fund A, Kiwis fund B and mangos fund C(or any other choices). Now try to explain efficient frontier to a random walker you may meet on the street, it is not just child to whom it can be hard to explain: diversificication revisited (again) and sad research about private investors. This kind of issues are very local, personal and are financial, perhaps day-work of some analysts. How with eff.frontier?
    – user1770
    Mar 31 '11 at 19:59

I would let them get their hands dirty, learn by practicing. Below you can find a simple program to generate your own efficient frontier, just 29 lines' python. Depending on the age, adult could help in the activity but I would not make it too lecturing. With child-parent relationship, I would make it a challenge, no easy money anymore -- let-your-money work-for-you -attitude, create the efficient portfolio!

enter image description here

If there are many children, I would do a competition over years' time-span or make many small competitions. Winner is the one whose portfolio is closest to some efficient portfolio such as lowest-variance-portfolio, I have the code to calculate things like that but it is trivial so build on the code below. Because the efficient frontier is a good way to let participants to investigate different returns and risk between assets classes like stocks, bonds and money, I would make the thing more serious. The winner could get his/her designed portfolio (to keep it fair in your budget, you could limit choices to index funds starting with 1EUR investment or to ask bottle-price-participation-fee, bring me a bottle and you are in. No money issue.).

Since they probably don't have much money, I would choose free software.

Have fun!

Step-by-step instructions for your own Efficient Frontier

  1. Copy and run the Python script with $ python simple.py > .datSimple

  2. Plot the data with $ gnuplot -e "set ylabel 'Return'; set xlabel 'Risk'; set terminal png; set output 'yourEffFrontier.png'; plot '.datSimple'" or any spreadsheet program.

  3. Your first "assets" could well be low-risk candies and some easy-to-stale products like bananas -- but beware, notice the PS.

enter image description here

Simple Efficient-frontier generator

#Author: hhh
#License: ISC license

global profit, stdDev, correlation

profit = [0.25,0.2]
stdDev= [0.2,0.15]
correlation = [[1,-0.5],[-0.5,1]]

def portfolioReturn(a,b):
   return profit[0]*a+profit[1]*b

def portfolioStdDev(a,b):

   for i in range(2):
      for j in range(2):
         variance = variance + values[i]*values[j]*stdDev[i]*stdDev[j]*correlation[i][j]

   return (variance)**(0.5)

def main():
   for x in [h/100.0 for h in range(100)]:
      if abs(x+y-1)<1e-10:
         print "%s\t%s"%(str(portfolioStdDev(x,y)), str(portfolioReturn(x,y)))


P.s. do not stagnate with collectibles, such as candies and toys, and retailer products, such as mangos, because they are not really good "investments" per se, a bit more like speculation. The retailer gets a huge percentage, for further information consult Bogleheads.org like here about collectible items.


I know you really like bananas, but don't you think you would get tired of them after a while? Better stock up on some kiwi and mango just to mix it up a bit.

I wouldn't want to risk eating only banana sandwiches, banana ice cream and banana bread for the rest of my life. I have don't think I could take it. Same goes for mango and kiwi, but I think if I had all three I could probably get along just fine.

  • wait, how old is this kid?
    – MrChrister
    Mar 31 '11 at 15:46
  • 7
    I'm going to start downvoting posts that make me hungry
    – James
    Mar 31 '11 at 18:33

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