(This article first appeared in *Real Estate Investor's Monthly*.)

Risk represents half the parameters that define all investments. The other is reward. Investors too often focus only on the reward half. A recent book on the business-book best-seller list, Against the Gods, tells “The remarkable story of risk.”

I do not recommend the book to readers of this newsletter. It tells far more than most of you probably want to know about the lives of ancient mathematicians. But I think it would be very useful to use a synopsis of the book as a take off point for discussing the subject.

Against the Gods tells the story of risk as a series of mathematical discoveries from the thirteenth century to the present. The author does a great job of showing how modern society has been transformed by these discoveries and that many of the things we take for granted, like insurance, medicine, engineering, and space travel, would be impossible without them.

Not all aspects of society have been equally transformed. Real estate investment is one area that is clearly behind in understanding and managing its risks. It’s high time it were brought up to date.

You subscribe to this newsletter to gain expertise. When you think about it, all expertise is knowledge of probabilities. For example, cooks and physicists have expertise. One item in their expertise is their knowledge that water will boil at sea level when its temperature is raised to 212 degrees Fahrenheit. In other words, they know that the probability of water boiling at 212 is 100%. Denver Broncos coach Mike Shanahan knows that the probability of his kicker, Jason Elam, succeeding on a field-goal attempt of 30 to 39 yards is 80%. Medical doctors know that the high-blood-pressure drug Pindolol has a 17% probability of causing dizziness in the people who take it.

The word “risk” is vague. The more precise word is “probability,” “the mathematical heart of the concept of risk,” according to Against the Gods author Peter L. Bernstein.

To be a competent real estate investor, there are two special math courses which you must master above and beyond what the average person has learned. One is the **time value of money** (Explained in a chapter in my book *How to Use Leverage to Maximize Your Real Estate Investment Return* [now 3 separate books, that chapter is in *Fundamentals of Real Estate Finance*], **$29.95** + $4 shipping, CA residents add sales tax) and the other is **probability and statistics**.

When you treat risk as mathematical probability rather than some will-o’-the -wisp concept, you do a much better job of managing it. Understanding probabilities will enable you to calibrate more competently your investment program in the areas where you have probabilities, and your inability to ascertain probabilities in other areas will reveal how blind you often fly.

When you confront the typical investor about his risk-taking, he typically responds that he is taking only “calculated risks.” Oh, really?

Show me the calculations. In the vast majority of cases, investors who claim they take calculated risk are kidding themselves. They have done no calculations. And if pressed, they could not do them in the future either.

They don’t have the numbers they need to do the calculations. In some cases, they do not have the numbers because they have been careless about obtaining them. In other cases, they don’t have the numbers because no one on earth has them and no one ever could.

Jacob Bernoulli discovered the Law of Large Numbers in the early eighteenth century. According to Bernstein, it says,

The difference between the observed value of a sample and its true value will diminish as the number of observations in the sample increases.

It is probably better defined by example. A coin has a 50% chance of coming up heads. But if you flip a coin ten times, you may get seven heads and three tails. However, the more times you flip the coin, the greater the probability heads will come up half the time.

Real estate investors ignore this law big time. Unlike stock market investors, who often invest in hundreds of companies at a time through mutual funds, real estate investors typically have “all their eggs in two or three baskets.” Such small numbers make it extremely difficult for investors to have confidence in the few events whose probabilities they have meaningful experience with.

Better you should pursue a real estate investment strategy like the **judgment investing** I wrote about in the 7/89, 2/91, and 5/94 issues and in my book *How to Buy Real Estate for at Least 20% Below Market Value*. In that strategy, you buy hundreds of judgments secured by real estate for an average of about $320 each. (Their face value and payoff would be around $4,000 each.) In time, you would see a clear pattern of risk and reward that would enable you to invest with confidence. In contrast, the typical real estate investor’s portfolio of three to six properties is a crap shoot.

In 1730, Abraham de Moivre figured out the bell curve, known more formally as the normal distribution. Again, an example is the best way to understand it. If you test a group of students in a class in virtually anything from height to weight to IQ to athletic ability or whatever, you will find a few below average, a few above average, and the bulk around average. If you make a bar graph of the variable you are testing, it will have a bell shape.

I did an article based around a bell-shaped curve in the 7/88 issue. It was called “Eleven percent cap rates really are obtainable.” A cap rate is the net-operating income of a rental property divided by the value of the property. Another way to put it is the cap rate is the cash-on-cash return the building would produce if you owned it free and clear.

The average rental property has a cap rate in the 6% to 8% range. Such lousy rates, in turn, typically mean negative cash flow. Investors want better returns. But most get discouraged. They look at dozens of properties and find no double-digit-cap-rate deals.

In the ’88 article, which was based on about 200 apartment building deals in the Seattle area over two years, I showed that only the top .5% to 2% of the deals done in the Seattle area were worth doing.

A related concept is standard deviations. 68.27% of cases (e.g., real estate deals) fall within one standard deviation of the average, 95.45% fall within two standard deviations, and 99.73% fall within three standard deviations.

The deals than were worth doing in Seattle were out at the third standard deviation. I once mused in print about renaming this newsletter Third Standard Deviation Monthly to reflect its aim of trying to help educated investors to achieve returns that are satisfactory, which means in the current market, in the top one percent of all deals.

Knowing what the actual bell curve looks like does not make finding good deals any easier. But it does give the investor a more accurate picture of how much work he is in for when he seeks a good investment. That, in turn, shows him he must efficiently screen hundreds of properties to find the very few worthwhile ones.

Knowing the numbers that apply to the bell curve in whatever type of investing you do is required knowledge. I suspect most have never tried to figure it out.

In 1738, Jacob Bernoulli’s brother Daniel described a risk phenomenon which may seem like common sense, but I remember being surprised by it when I encountered it in my own life. He said that the satisfaction from any increase in wealth will be inversely proportional to the person’s wealth before the increase.

I used to want to be a multimillionaire and was driven to reach that goal. Indeed, I became a millionaire in 1983. However, I was surprised at the lack of effect being a millionaire had on my life. I discovered that you can spend only so much money on things that are worthwhile, mainly a house, cars, and education. The other stuff, food, clothing, vacations, and so forth, are things that anyone can afford.

I was surprised at how low the point of diminishing returns was. At the time, I wrote an article saying a net worth of more than $500,000 and an annual income of more than $150,000 seemed to me to put you in the “more-than-anyone-needs” category.

At the time, my kids were toddlers. A reader said I apparently had not yet encountered college costs. My oldest is now 16 and those $12,000 to $30,000 per student per year college costs are breathing down my neck. So I’ll revise my numbers up to a net worth of $1,000,000 and an annual income of $200,000 if you have college-age kids.

One of the risk mistakes investors make is that they set themselves on a course to make millions when they are young, then belatedly discover that their goals are radically changed by age and having so much more to lose.

You often read of Hollywood movie stars who can afford almost any house, selling the “I’ve made it to the big time” mansion they bought early in their career and moving into a smaller home. “Less to take care of,” they explain.

It is also common for successful real estate investors to scramble around when they reach their fifties trying to hide their wealth in Cayman Islands Trusts and all that. Marshall McLuhan made a very wise observation when he said, “To the spoils belongs the victor.”

I have heard many a middle-aged real-estate investor complain about how his property empire, or more specifically, his tenants and employees, were interfering with his golf game or visiting his grandchildren or his new interest in flying or philanthropy or politics.

Gail Sheehy wrote a book called Passages about the phases of adult life. For example, many men, myself included, go through a becoming-one’s-own-man phase in their late twenties or early thirties. Young investors should read it and expect and plan for those phases. The vast majority behave as though getting old was something their parents’ generation did, but which they plan to skip.

The typical career pattern of real estate investors is to hustle their butts off in the early years, achieve success, then become risk averse and increasingly annoyed at how the day-to-day demands of owning millions of dollars of rental property are interfering with their new-found interests. Guru John Schaub often asks the rhetorical question, “Have you ever met an old property manager?” It always draws a laugh.

Rather you should make your million then phase out the demanding aspects of rental-property ownership by exchanging into less management-intensive properties like shopping centers or industrial buildings or raw land. Or you may exit real estate by deeding your properties to a charitable remainder trust (see the 8/90 issue) or by converting them into homes and selling one every two years to take advantage of the $500,000 homeowner capital-gains exclusion ($250,000 for bachelors).

Recognize that you will become more and more risk averse as your net worth increases and plan for it.

Widespread belief in a statistical principle called “regression to the mean” is the driving force behind a lot of real estate investors’ approaches to real estate.

Roughly speaking, it says the world is like a pendulum. It swings from one extreme to the other but always ends up back in the middle. The common phrase “return to normal” drips of belief in regression to the mean. The vast majority of real estate investors are enamored of the business cycle, trying to buy at the bottom and sell at the top. In fact, many aspects of life follow that pattern. But not all. And many other aspects follow that pattern for a while, then flatline, like the buggy-whip business.

Bernstein says, “Decision theory is the theory of deciding what to do when it is uncertain what will happen.” The mathematical technique for dealing with that is a **decision tree**. Most of you have seen those used in my book, Aggressive Tax Avoidance for Real Estate Investors. Indeed, they seem to be one of the most popular parts of that book.

A decision tree compares weighted averages of the probabilities and outcomes of various decisions. You then select the decision with the best weighted average—or “expected value” as it’s known in probability. Here’s an example: You have been sued and the plaintiff has offered to settle for $50,000.

Research causes you to conclude that the probability of prevailing at trial is 70% and will result in a legal bill of $22,000. Loss has a probability of 30% and a cost of $80,000. Should you settle or go to trial?

In a decision tree, boxes represent decisions, and circles are events beyond your control. The total probability at each event node must equal 1.

In this example, you multiply 70% by $22,000 and 30% by $80,000 and get an expected value of the fight choice of 70% x $22,000 + 30% x $80,000 = $15,400 + $24,000 = $39,400. In this case, fighting is the best choice because it has a lower expected value than settling.

But the rule of garbage in, garbage out applies. If you do only one lawsuit every few years, or if the particular suit in question is not one which offers much actuarial data, you cannot come up with reliable probability figures.

The obvious best way to deal with that is to change to a strategy like judgment investing where you have large numbers and few lawsuits.

Another way to deal with it is to calculate the breakeven probability, then see if you think the actual probability is above or below that mark. For example, in the above example, the breakeven victory probability to match the $50,000 settlement is $50,000 = $22,000X + $80,000(1 - X) = $22,000X + $80,000 - $80,000X then $50,000 - $80,000 = -$58,000X or -$30,000 = -$58,000X so X = $30,000 ÷ $58,000 = 52%. In other words, you should fight if your probability of winning is 52% or better and settle if it’s less. You may feel somewhat confident about that decision even if you cannot pinpoint the probability exactly.

One of the unexpected things I learned in graduate business school was the enormous overlap between finance, insurance, investing, and gambling. They are essentially all variations on the same theme. If you are a real estate investor, you are a financier, an insurer, and a gambler.

Financiers and insurers are a bunch of tight-lipped twits. But professional gamblers will tell many of their secrets. By professional gamblers I am not referring to unsavory characters who engage in illegal betting. Rather I am referring to people like Harvard MBA Ken Uston, a professional gambler who lived in Las Vegas and used his knowledge of probability to win consistently enough to make a good living.

Professional gamblers deal with pure risk. They abide by the Law of Large Numbers. They get burned instantly when they make a mistake. Inflation never bails them out. I’ll discuss them and other aspects of risk and probability next month. JTR