Understanding Expected Value and Risk Tolerance With Your Investments

by Hank Coleman

I recently took a risk tolerance survey at FiLife.  It was one of their calculators, and after answering ten questions, you were provided with your most likely risk tolerance.  I am a moderate risk taker in my investments according to the website’s calculator for all of you scoring at home. 

I have briefly talked here on Own The Dollar before about how we, as a collective investing community, have lied to ourselves in the past about our actual risk tolerance given the severe drops we have seen in the stock market this past year.  Most of us told our financial planners and the man in the mirror last spring and before that we could stomach a short term drop in stock prices because we were investing for the long term.  Well, judging by the mass exodus of funds out of stock mutual funds last Spring, most of us lied.  When the actual 30% or more drop in value really happens, we cannot take the damage to our portfolios psychologically.  We jump ship and sell our investments at a low price which is exactly the wrong moment if we are trying to buy low and sell high.

But, I digress.  I really wanted to share with you one of the questions on FiLife’s risk tolerance calculator that really caught my eye.

Question – You have just reached the $10,000 plateau on a TV game show. Now you must choose between quitting with the $10,000 in hand or betting the entire $10,000 in one of three alternative scenarios. Which do you choose?

A) The $10,000 — you take the money and run
B) A 50% chance of winning $50,000
C) A 20% chance of winning $75,000
D) A 5% chance of winning $100,000

So, what’s the right answer?  This question may tackle your underlying risk tolerance, but there is one answer that will win you the most money.  But, which one?  It all comes down to expected value.  Expected value is probability-weighted sum of the possible values and a relatively simple concept in probability theory and statistics.

So, to break it down mathematically (stick with me for just a second)…

Answer A – A 100% chance of winning $10,000 = an expected value (EV) of $10,000
Answer B – A 50% chance of winning $50,000 = will give you an EV of $25,000 (50% x $50k + 50% x $0)
Answer C – A 20% chance of winning $75,000 = will give you an EV of $15,000 (20% x $75k + 80% x $0)
Answer D – A 5% chance of winning $100,000 = will give you an EV of $5,000 (5% x $50k + 95% x $0)

You should choose B! You have the best chance to win the most money.

So, what does this even matter to us as investors?  It matters a lot actually.  Expected value calculations are actually the underlying formula associated with diversification.  An investment must have a positive expected value relative to alternative investments and other opportunities to allocate that money.  Having proper perspective on choosing an investment relative to its risk compared with other investments is crucial to making a profitable and diversified choice.  Often an investor is so convinced of the profitability of the potential investment, and the downside risk of the investment is rarely considered.  Expected value of an entire portfolio will help you determine if you are overweighted in any one area based on your risk tolerance.

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{ 1 comment… read it below or add one }

Anonymoose October 31, 2016 at 3:10 pm

I disagree with this. Expected value is not a perfect formula that you can use to always make the right decision.

A 50% chance of winning $50,000 might be the right choice mathematically, but think about it emotionally. If you flipped a coin and walked away with nothing, you’re not going to be telling yourself that you made the right choice. You would regret getting greedy and not choosing the $10,000.

I think there should be a formula that includes factors such as the utility of money (less useful as you get more of it), and the sadness of walking away with $0.

I think that if you would be happy with $10,000, then there’s no reason to go for $50,000, even if the EV tells you to.

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