To become successful investors we have to think like burglars, because we must be constantly on the lookout for windows of opportunity 😆 So today’s post is about finding those opportunities with the help of math and probability 🙂
In a recent Poll, I asked if readers would prefer to receive a guaranteed $3,000 or an 80% chance of getting $4,000. If you didn’t get a chance to vote, make a choice now, and remember your decision. You might be asked about it later 😉 Here are the poll results (^_^)
85% of you who voted chose the first outcome 😕
*Sigh* (-_-) Folks, this is NOT okay (>_<) Dagnabbit, you guys 😡 It’s time we had a serious discussion about this. I know it’s probably my fault for not blogging about this sooner but today’s concept is uber important and may change the way you look at money forever.
In probability theory, Expected Value means the “expected” average outcome if an event were to run an infinite number of times. And the law of large numbers dictates that the average of the results obtained from a large number of trials should be close to the Expected Value.
For example, a 6-sided die produces one of 6 numbers when rolled, each with equal probability. Thus, the expected value of a single die roll is 3.5.
According to the law of large numbers, if we rolled a die a large number of times (like 1,000 times) then the average of the produced values is likely to be very close to 3.5, with the precision increasing the more times it’s rolled.
Below is a graph showing a series of 1,000 rolls of a single die. As the number of rolls increases, the average of the values of all the results will automagically approach 3.5.
The same thing would happen with a coin toss. The Expected Value that a coin will land on heads is 50%. So if we flipped a coin a gazillion times eventually the actual data that we witness will come closer and closer to the expected value of 50%.
Now that we understand what expected value and law of large numbers mean we can approach the poll again from a mathematical angle. The expected value of the first outcome is $3,000 as there is a 100% chance of receiving exactly $3,000 every single time. The expected value of the second choice is $3,200 since (80% x $4,000)+(20% x $0)
If math isn’t your strong suit allow me to sum it up for you 😀 Basically we should choose the second outcome every time because it has a higher Expected Value.
So how can we use this information in real life? 😀 Investing in real estate in a foreign province may appear to be risky, but I did it anyway in 2012 because the Expected Value of growth looked better than comparable local properties. And thankfully it has paid off 🙂 because my property in Saskatchewan grew by over 10% while land in B.C. stayed relatively flat. In 2013 I borrowed money at 3.5% against my home’s equity in order to invest in blue chip U.S. companies which historically have an expected annual return of 8% to 10% which gives me a positive spread 🙂 Once again, this decision has paid off very nicely over the last year 😀
Much like the die roll diagram we saw above, my net worth may fluctuate a lot over the short term due to leverage and market volatility. But I make dozens of investment decisions every year, so by the time I’m in my thirties I should have a pretty large nest egg because the annual return from my basket of real estate, stocks, and bonds, has an Expected Value much higher than the current carrying cost of my loans. This is why I can sleep like a baby at night despite having over $500,000 of personal debt 😉
Financial risk can be mitigated because the long-run average of the results of many independent repetitions of an event, like the returns on a balanced portfolio, is made predictable thanks to the law of large numbers. Today’s new investment might fail, and tomorrow’s might fail also. But as long as there’s a solid argument for a positive expected value then sooner or later our ongoing strategy will become profitable 🙂 We can count on the rules of probability because it’s…
We can’t think about this poll as an isolated event either. In the real world the law of large numbers applies to everything we do and the trials spread across all the financial decisions we make every day, so it’s crucial that we have a consistent strategy. If we go through our entire lives choosing the outcomes with the better “Expected Value” every time we’re faced with such a dilemma, then despite the perceived risks, we will always be better off in the long run than others who choose the safer, guaranteed outcome or someone who flips back and forth between choices 🙂
Only 15% of voters chose the potentially better outcome. As for the rest of you, I’m curious to know if you would change your mind now or continue to stick with your first choice 😀
Random useless fact: The state of finding it difficult to get out of bed in the morning is called dysania