by Brandon Reiter

A growing concern in America these days is the health of the middle class. The wealth gap has continuously been expanding for over a decade, and has been the main topic of political debates for as long as I can recall. This isn’t a post about which side of the isle is right, who should be taxed what, but rather an explanation of *why basic statistics allows for people with more money to grow their wealth faster than those with less money.*

A famous, yet concerning statistic is that most Americans would not be able to afford an unexpected $400 bill. That’s very concerning considering unexpected bills come up all the time. Flat tires, floods, a terrible war that causes a tremendous rise in gas prices, a global pandemic that shuts down the entire world, and whatnot. Because so many Americans are just $400 away from bankruptcy, that brings us to my first point of how probability makes the rich richer: ** insurance**.

Insurance companies make billions of dollars by utilizing probability. To make things simple, let’s say that you own a car worth $20,000 and you pay a $400 monthly premium. In exchange for your monthly payments, the insurance company will pay to replace your $20,000.00 should it be lost, stollen, or damaged *(yes, I’m ignoring plenty other contingencies for simplicity) (and deductibles)*. If buy this policy and your car is stolen one month later, the insurance policy was well worth it, and a loss for the insurance company. However, the insurance company has predetermined the likelihood of your car being stolen or damaged to be 4% in any given year. For the insurance company to make money on this policy they want you to make it at least 4 years without needing the $20,000 payout ($20,000/$400/12mos=4.1 years). If there is a 4% chance per year that you will need a payout, there is a 16% chance over a 4 year period; that’s pretty good odds for the insurer. Also, the further into your policy you need to make a claim, the less of a loss the insurance company bears (If you crash one month into the term, you’ve only paid them $400 and they need to cough up $20,000, if it’s one year in than you’ve paid them $4,800). Despite the odds being in insurance company’s favor, they have a risk you will crash and they will lose on your policy. The goo thing for them is that you’re not their only customer. The insurers make sure they will be profitable by providing many policies to many people with similar odds. The collection of all these premiums allows them to pay you in the event you smash that car into a tree. *I’m not even going to mention the reinsurance industry. That’s right, there are insurance companies that insure insurance companies.*

So why should you be paying a policy that only has a 16% chance of being “worth it?” Well, as I just mentioned, most Americans cannot afford an unexpected $400 bill. So we can safely assume wayyy more Americans cannot afford an unexpected $20,000 bill. The idea here is that you’d rather pay $400 each month to avoid a situation that would completely derail your life. *You can’t afford the risk. *

Let’s replay this scenario but now pretend you’re Warren Buffet *(or any billionaire of your choosing)*. I highly doubt you’d be buying a $20,000 car, but let’s just pretend you are for some weird reason. $20,000 won’t even make a dent in your bank account, so it would actually make sense for you to forego the car insurance *(ignoring the fact that it’s required by law)* because there is only a 16% chance that it will be worth it, and even if you do end up having to pay $20,000 to replace the car, it will not derail your life. This principle shows that being rich literally affords you to the ability avoid a monthly payment that those with less money need to make. If both you and Warren Buffet bought the same $20,000 car, you essentially have to pay an additional $19,200 over 4 years than for the same car because *you cannot afford the risk*.

Risk is another way of describing probability. I know what you’re thinking,* rich people aren’t getting richer because they’re avoiding insurance premiums. *No, but the same principle applies to investment and generating wealth. A core investing concept is that the riskier an investment is the greater the rate of return needs to be. This is due in large part to the fact that there are such things as risk free investments. I can put a dollar into a savings account that pays 1% interest each year with zero risk. Given that fact, I would never make an investment that pays the same 1% rate but also has a 10% chance of failing, because I can make the same amount of money with no risk. Because there is such thing as risk-free rates, risk needs to be compensated when it is taken on.

Let’s say the 10% risky investment will pay off 25% if it is successful. You have a decision to make now: do you want to make a guaranteed $0.01 on your $1 investment or do you want to risk losing that $1 investment for a 90% chance to walk away with $1.25?

We can use simple math to evaluate this: since the risky investment has a 10% of failing, the law of probability tells us that if you make this investment nine times out of ten you end up with $1.25 nine times and nothing one time. Therefore the expected value of the investment is $1.125 ($1.25 x 90% + $0 x 10%). Based on this principle, it makes sense to take on the risk as you have a greater chance to make more money than the mere penny you get from taking on no risk.

*But wait! Think back to the insurance dilemma. *

You bought the policy, not because you think its a sound investment, but because you want to avoid the situation that will leave you homeless. You, unlike Warren Buffet, cannot afford the risk of foregoing the insurance. Circling back to the investment scenario you can obviously afford to lose $1.00, *if not then you should probably stop reading this and file for unemployment.* But let’s say the investment was $100,000 instead of $1.00. The same percentages still apply and it still makes sense to make the risky investment from a math standpoint. The expected value is you’ll end up with is now $112,500 compared to the risk free option where you would walk away with $101,000. There’s only a 10% chance you end up with nothing and a 90% chance you make a $25,000 profit. But if that 10% were to happen would you lose your house? Your car? Your spouse? *Probably (pun intended)*. Would Warren Buffet? He probably wouldn’t even notice.

You decide that you can’t pass up the opportunity. *Uh oh! *The investment backfires! The dreaded 10% outcome happens and you lose $100,000 quicker than you can say *“I should’ve just kept my money under my mattress”*. Perhaps you still have some savings left, and you convinced your spouse things will be fine. Life is fine… *for now.*

But now a new opportunity comes your way. This one requires the same $100,000 investment and has the same 10% risk rate, but the potential earning is a whopping 50%! You can make half your loss back! There’s just one problem: you no longer have $100,000 to invest again. You need it to pay for your $20,000 car loan and the $400 insurance premiums. *Not to mention your mortgage, daycare, gas, and all your other bills.* Unfortunately, you have to pass up the opportunity, and wouldn’t you know it? It’s a winner. Not only did it go up 50% it went up 200%!! You would have made up your loss and then some!

Now imagine you’re Warren Buffet again, you hardly noticed the loss of the original $100,000 so invest in the winner without much thought. Your investment is now worth $300,000! You’re up $100,000 even after losing out on the first investment.

Do you see what I’m getting at?

Risk is a type of probability. The richer you are the more risk you can afford. Warren Buffet can afford to make millions of these $100,000 investments (literally) because he can afford the risk/probability of losing $100,000 a few times and still be able to continue on with his way of life. By being able to invest in many different opportunities the law of probability tells us that he will indeed continue to keep making money in the long run, as the likelihood that every investment with a 10% risk rate failing gets smaller and smaller the more there are.

Another large factor I haven’t brought up yet is that by having more money you have access to more investment opportunities than those with less money. For example many private investment opportunities are only available for very large minimal investment amounts. Warren Buffet can invest $10 Million into a company that wouldn’t even bother with you even if you were willing to invest your entire life savings, despite the percentages being the same.

There’s an old saying that goes something along the lines of “the first million is the hardest to make”. That’s true,* to some degree*. Of course, *most* people do have to work hard to generate their initial wealth, but growing that wealth once it exists is a lot easier than building it from scratch. Wealth generation is like inertia; it takes a lot more energy to get started than it does to keep going. Probability tells us that the more investment opportunities you participate it, the more money you will make in the long run. However, opportunities are costly, and you’re risk tolerance (should be) determined by the amount you can afford to lose without derailing your life. Risk tolerance cost money, and the more money you have the more risk you can afford.

Probability keeps the rich rich, and the poor poor. What do you think?