• Investing & Markets

Odds Are You Don’t Know the Odds of Investing

November 17, 2011 | Daily Capital

Investing – The Odds Are You Don’t Know the Odds

Understanding the odds of investing is one key to success. Unfortunately, people take mental short-cuts called heuristics that lead us to miss simple calculations. What if your portfolio lost 50 percent in the first half of the year and then gained 50 percent? Most will get this right and realize the portfolio is still down 25 percent (1 x 0.5 x 1.5) even though the simple average of plus 50 percent and minus 50 percent is zero.

Monte Hall – The Father of All Heuristic Biases

My favorite of all heuristic biases comes from the long-running game show “Let’s Make Deal.” As originally played, Monte Hall tells you that there is a shiny new car behind door number one, two, or three. Behind the other two doors are goats. Monte Hall knows what is behind each door.

Let’s imagine that you are a contestant and pick door number one. It’s easy to compute that there is a one in three chance that you’ll be driving home in that beautiful new car. Monte Hall then turns over door number three revealing a goat. But wait, all is not lost, Monte is giving you a chance to change your pick from door number one to door number two. Do you take it? Which of the options do you think is right?

a) Stay with door number one
b) You are indifferent
c) Switch to door number two

The correct answer is to switch to door number two as you will increase your chance of winning the car from 1/3 to 2/3. Few that haven’t heard this before get the answer right. If you don’t buy this yet, here are three ways I’m going to try to get you there.

Consider this diagram. Remember that Monte Hall knows where the car is. No matter what door you picked, there is always a goat behind another door that he will turn over. Thus, your original 1/3 probability of getting the car remains unchanged. You can now eliminate door #3 and, since there really is a beautiful new automobile, the total probability of the three doors must still add to 1.0, or 100 percent. Thus, the probability of the Car being behind door #2 must be 2/3.

If you’re still not buying this, don’t worry. Less than half of the students in a behavioral finance class I teach at the University of Denver are convinced at this point.

Monte Hall Card Simulator

Next, I’ll get one class member who objects to my explanation to play a similar game with a deck of cards. I tell the participant that if he picks the Ace of Spades from a deck of cards, he gets the Car. He selects one card and puts it face down on the table without looking at it. Now he realizes that his odds are 1/52.

Holding the cards where I can see what each card is but the contestant can’t, I turn over any card that isn’t the Ace of Spades and leave it face up on the table. I then offer him a chance to return his original card and pick a new card from the remaining 50 cards in the deck. He turns it down, just as he did with the original Monte Hall problem when one door was turned over revealing the goat.

Now, one at a time, I turn over cards that aren’t the Ace of Spades, putting them face up on the table. I stop when I have one card left in my hand and 50 cards face up that aren’t the Ace of Spades. I then offer the student the chance to change his mind and switch cards with me. The student quickly realizes that his odds have gone from 1/52 with his original choice being the Ace of Spades to 51/52 that the remaining card in my hand will be the Ace of Spades. He switches cards.

This card simulation is merely the same Monte Hall game, only with 52 doors instead of three. Switching cards improved the odds from 1/52 to 51/52. With three doors, switching only improved the odds from 1/3 to 2/3.

There are usually one or two students who still don’t buy into this by now. I tell them not to feel bad, as a renowned mathematician is said to have written a letter violently objecting to the logic when it was first published. If you do as well, try this Monte Hall Simulator. I bet you can’t do it 20 times without coming out ahead by switching. On average, you’ll win twice as many times as staying put.

Odds of Investing

I am among the vast majority of people who got this problem wrong when it was first given to me. Like everyone, I have heuristic biases that led me to quickly and falsely believe the odds were now 50 -50.

It may seem like the odds of picking the next hot stock or strong performing mutual fund is high but there are a whole host of biases that lead us to grossly overestimate our odds. People tend to brag about their winning investments and don’t mention their many losers. We only see winners advertised.

Though it may not seem like it, your odds of investing are much greater by using a disciplined approach of building a low-cost diversified portfolio and rebalancing regularly. Your odds of building wealth by finding the next Google are nearly as low as winning the lottery.

However, the odds are nearly 100 percent that investors don’t know the odds of beating the stock market.


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