Law of Large Numbers Explanation

What is the Law of Large Numbers?

Most people have heard of Einstein’s Theory of Relativity (E=mc2).   Many people are familiar with the Rule of 72. But very few people are familiar with The Law of Large Numbers. Let's start with a simple example. If I rolled a typical, 6-sided die, what would be the chances of getting a 5? 1 in 6, right? Theoretically, if I rolled the die 6 times, pure mathematics would indicate that I should get a different number each time, right?   You and I know it is extremely unlikely that it would happen that way.  But, if you rolled the die 10 million times, you would get a 6 almost exactly one sixth of the time; you would get a 5 almost exactly one sixth of the time.  It's a mathematical law called "The Law of Large Numbers".

There's a city you may be familiar with in the U.S. that built it's  entire economy around it. LAS VEGAS! When you go to the casinos in Vegas, only one side is gambling; you. The Casino is not gambling because they have The Law of Large Numbers on their side. They have built fantastic hotels and attractions just to get enough people through the doors to get 10 million rolls of the dice or 10 million flips of the cards or 10 million spins of the wheel and, if they get that, they know what their profit is.

Why are insurance companies able to guarantee you an income stream when investments cannot?

Insurance companies do the same thing as Las Vegas. Many people think of insurance as gambling but actually it's the opposite of gambling. That's why they call it actuarial science. All mortality tables are based on 10 million lives, and they use reinsurance to share the mortality risk to make sure they get the 10 million lives. Therefore, insurance companies are the only ones who can hedge mortality.

If we self-insure our retirement expenses, we must commit enough money to fund them for our entire lives, no matter how long that happens to be. Since that’s uncertain, the only way to do that is to live off the income and conserve principal. Also, you have to prepare for the sequence of return risk so you don’t have to invade assets for lifestyle expenses in down markets. Insurance companies only have to fund this income to life expectancy. At life expectancy, 50% of the people have died but 50% are still alive. They can actually invade principal to do this. So, the withdrawal rate they use can be higher. That’s because they have the law of large numbers on their side. They also have another hedge against longevity. It’s called life insurance, which most companies balance against their annuity portfolios. Life insurance is the actuarial opposite of income annuities. With life insurance, the longer people live, the better it is for the insurance company. With annuities, it's the exact opposite.  So they hedge one against the other. They’ve been doing this for over 200 years through the great depression as well as plagues and pandemics.

So, if you commit less capital to provide for your necessary living expenses, it leaves more money available for all your other lifetime and legacy goals. This allows you to use a more aggressive asset allocation if you want for your other goals to get a higher potential long term rate of return because you won’t have to invade assets for necessary expenses during down markets.


To find out why annuities are such an effective option for guaranteeing your income, go to our Why Annuities page.

To find out if you're using the "Swiss Army Knife Approach" to investing, click here.



Pair of Dice on cards and money