The Probability of an 8 Percent Rate of Return Is Zero

Here is a fun math trick you can use the next time your friends start talking about investing. Many individuals like to say “If I average an 8 percent rate of return for the next 30 years I will have X dollars.” Or they say things like, “I assume I will average 7 percent for the next few years on my portfolio.” But, the probability of achieving those returns is zero. I know for a fact you will not average a return of 8.00 percent—or any other specific number—over the next 10, 20, 50 years.

If you flip a quarter one time, the odds of heads are 50 percent. If you flip it again the odds of landing on heads twice in a row falls to 25 percent. The odds of heads appearing three times in a row is 12.5 percent. The odds of heads 20 times in a row quickly approaches zero. In this simple example, you have two outcomes: heads or tails. In a portfolio you have a range of outcomes. Therefore, the odds of an exact 8.00 percent return, or any other specific number, quickly approaches zero over any given time period. What really matters is the range. For example, there is a big difference between having a 95 percent chance of being up between 6 and 12 percent and an 80 percent chance you will be up between –5 and +15 percent. The tighter the range and the higher the degree of confidence, the more useful it is for predicting future outcomes. The wider the range and the lower the degree of confidence, the greater the chance the data really is just a function of luck.

I don't count on luck. Therefore, I try to look at things that have a high probability of being within a certain range. A high probability in no way assures future results, it simply starts the conversation. Always remember that the probability of any given return over the rest of your lifetime is approximately equal to zero, including the returns in the data we are about to examine.

Risk, Return, and Diversification

We don't have a crystal ball, but we may have something better: it might be possible that with the right asset allocation, we don't even need a crystal ball. Figure 5.1 plots seven different asset classes over the past 46 years.

Many people are familiar with statements like “stocks average about 10 percent per year.” This happened to be the case during the 46-year period of 1970–2015 where U.S. stocks in fact did average about 10.2 percent each year.

We also want to consider risk. Risk is like golf because, all things being equal, we want to have a low score or low risk. Risk is reflected on the bottom, or X, axis. And, all things being equal, the lower the number the better.

When we look at data like this, people tend to think U.S. stocks did well, having high returns and lower risk than many other assets. Bonds had less risk but a lower return. Commodities and gold had both more risk and a lower return.

Many people use charts like this to conclude they only want to own U.S. stocks and bonds. I think there is something else worth considering.

Figure 5.2 shows an equally weighted, globally diversified portfolio of all assets gave the magical combination of high returns and low risk. During this time period, the diversified portfolio had a return similar to U.S. stocks and a risk similar to U.S. bonds.

I have friends who invest only in real estate, energy stocks, or gold. I don't understand this. In modern capital markets, investors have exposure to virtually every asset class at lower costs than ever before. Why would anybody pick just one asset when they can choose all of them?

Every individual asset has terrible years. Table 5.1 shows the six worst years of each of the assets individually. Diversified portfolios certainly have down years, but they're relatively bearable and not nearly as volatile. Risk is the standard deviation of the asset class returns over the time period. Steady, consistent returns are the key to long-term wealth accumulation.

Focusing on the worst years leads us to another important area to examine. Although these data represent one 46-year period, it is just that—a single 46-year period. It is a single data set, and a single data set that is unlikely, if not impossible, to repeat itself.

Therefore, while factually accurate, I think that long-term charts can be incredibly misleading. Figure 5.3 illustrates rolling 10-year periods. This gives us many data sets and sheds a better light on what type of returns we could expect on an asset class looking forward. By chopping the 46-year period into 37 different 10-year periods, we can get a better sense of historical reliability. We now have 37 data sets instead of one data set. This gives us a better sense of what historic returns were actually like and might give us a better sense toward the future.

Why can long-term averages with respect to individual assets be very misleading? Consider U.S. stocks. While the 46-year average was 10 percent per year with a risk of 17 percent, during some 10-year periods investors may have had returns of 15 percent or more per year with less risk than the 46-year average, but during other 10-year periods they could have had returns below 2 percent per year with much more risk.

This highlights the concept of risk. Any 10-year period was unlikely to look like the 46-year long-term average, with investors likely either getting much better results, or much worse results, than the average led them to expect. Average tells us something about the past, but nothing about the future and nothing about what type of returns we could expect over any 10-year period, including the next 10 years.

I believe you will not get returns close to the long-term average returns from U.S. stocks over virtually any 10-year period. Your returns will likely be much better or much worse.

This phenomenon is true with diversified portfolios as well. For example, as demonstrated by Figure 5.3, a 70/30 U.S. stock-and-bond portfolio has been fairly consistent with respect to risk, but not with return. You can draw two vertical lines shooting up from the risk line of 10 and the risk line of 14. You will see there is a channel of risk—the risk is fairly consistent—but the return ranges from 2 to 16 percent.

I believe a 70/30 stock-and-bond portfolio has a high level of predictability with risk and a very low level of predictability with respect to return.

What is interesting to me is that during this time period, the diversified portfolio had a much tighter cluster. This cluster generally occurs with returns between 7 percent and 14 percent and with risk generally ranging from about 6 to about 12.

Importantly, in the periods when the portfolio was riskier, the returns frequently skewed higher, meaning that investors were at least often compensated for the risk. This is in stark contrast to U.S. stocks, where periods of higher risk often yielded lower returns. High-risk strategies are hard to stick with over the long term because of the extreme ups and downs. There can be no assurances that this will be what the future holds but this process influences my asset allocation tremendously.

What about Interest Rates and Cost of Debt?

While the previous tables are somewhat helpful in determining future returns, they do not address future interest rates or returns relative to those interest rates. They also do not address inflation.

Long term, what matters is capturing the spread. An investor captures the spread when they earn a higher rate of return, after tax, than their after-tax cost of debt. Ideally, an investor is looking to capture two spreads: one that gives returns higher than inflation, the other that gives returns higher than their after-tax cost of debt. If an investor earns, on average, a higher rate of return on their assets than they are paying on their debt then the strategy of having debt is a good one.

The time between 1970 to 2015 comprises periods of both rising and falling interest rates. Similarly, it comprises periods of both high and low inflation.

Diving into the numbers, we discover that over any individual calendar year, a diversified portfolio has outperformed U.S. inflation plus 4 percent only 63 percent of the time. This means that in 37 percent of the years it underperformed inflation + 4 percent.

While these figures may sound disappointing, they begin to change over 10-year periods. A diversified approach outperformed inflation plus 4 percent in 34 of 37 rolling 10-year periods, or 92 percent of the time. In the periods that it outperformed, it did so by an average of 2.78 percent per year. Of the three times that it underperformed, it did so by an average of 0.81 percent per year. Historically, a diversified approach did very well in terms of providing a solid return over and above inflation.

Let's examine two different inflation-adjusted goals:

• With respect to an inflation plus 2 percent goal:
  • The S&P 500 outperformed inflation + 2 percent in 78 percent of every rolling 10-year period of time.
  • A 70/30 U.S. stock-and-bond portfolio outperformed inflation + 2 percent in 78 percent of every rolling 10-year period of time.
  • The diversified approach outperformed inflation + 2 percent in 97 percent of every rolling 10-year period of time.
• With respect to an inflation plus 6 percent goal:
  • The S&P 500 outperformed inflation + 6 percent in 59 percent of every rolling 10-year period of time.
  • A 70/30 U.S. stock-and-bond portfolio outperformed inflation + 6 percent in 54 percent of every rolling 10-year period of time.
  • The diversified process outperformed inflation + 6 percent in 54 percent of every rolling 10-year period of time.

History provides us with a framework to guide our actions for the future. But we must understand that we do not know future interest rates (and therefore future borrowing costs), future inflation rates, and future rates of return. These are impossible to know. We must recognize that past performance does not guarantee future results and that it is virtually impossible for the historical data series to repeat.

Based on rolling 10-year periods since 1970, if your cost of debt is higher than inflation + 6 percent, then we can conclude there is an approximate 50 percent chance that debt will destroy value and you will not capture a spread. Debt that is at a rate that is closer to inflation + 2 percent is likely to have a higher probability enabling an investor to capture the spread. Historically, and during this one data set with one diversified asset allocation model, the odds of accomplishing the objective were 97 percent.

The purpose of the data is to form the basis for testing the glide path I proposed. It will help shape our conversation and we will look at what could happen in upside or downside scenarios. While none of us knows the future, we now have a framework to look at some of the probabilities. Historically, the lower our cost of debt relative to inflation, the higher the chance that we can capture a spread. Also, we have seen that the higher our cost of debt relative to inflation, the lower our chance that we can capture a spread.

While it is possible that rates could stay lower longer than most people anticipate, it is also possible that crazy things could happen to interest rates and to inflation. This could come from a series of unprecedented monetary policy actions, a lack of fiscal policy discipline, or simply because rates are starting from generationally low levels. Depending on how debt and investments are structured, a prolonged period of rising interest rates may make it easier or harder to capture the spread, depending on how you are positioned. For example, if you lock in on generationally low interest rates, it could be easier to capture a spread in the future.

What about One of Your Biggest Assets? Your House

Your house might go up in value. Your house might go down in value. The simple truth is, we don't know the future returns on housing any more than we know the future returns on anything else.

Many people want to own their homes outright rather than waste money on mortgage interest, but it's important to look at something called opportunity cost before paying off a mortgage. The opportunity cost reflects the fact that you could pay down your mortgage or you could put that same amount of money into an investment.

If you believe that, on average and over time, you can earn returns at a higher rate than the after-tax cost of your mortgage, then you should consider investing the money instead of paying down on the house. If you believe that on average and over time your returns will be lower than your after-tax cost of debt, then you may want to consider paying down the debt. For example, if you have a mortgage at 4 percent and you are in the 33 percent tax bracket, your after-tax cost of that mortgage is 2.68 percent. If you invest that money, then 2.68 is what you need to beat to capture a spread.⁸

Keep in mind that when you pay down debt, you also generally lose a lot of the liquidity you had, so you also have to be comfortable with that risk. Liquidity is something to spend time thinking about, as it becomes very valuable at precisely the time when you need it the most.

Also, always keep in mind that the value of your house is 100 percent independent of the financing in place around it. If you own your house outright, it isn't worth any more. If you have a big mortgage, it isn't worth any less. You can't change your net worth or the value of an asset with financing.

When you list your house, you will not advertise the value of your mortgage as one of the attractive features. Your mortgage is completely independent of the buyer's perception of value. Your house may go up or down in value, but this movement is independent of the financing decisions you make.

What if you plan to hang onto the home for a while? Isn't real estate one of the best investments you can make in the long run? Residential real estate certainly may keep pace with inflation over long periods of time; just think about how much the home that your parents or grandparents lived in during the 1950s or 1960s is worth today. But it also may not. There are many examples around the world, such as in Japan, where the prices of real estate have fallen over extended periods of time.⁹

With housing, people often do bad math because determining a property's actual appreciation is tricky. This happens in part because we love to deceive ourselves into thinking we've done better than we actually have. If you buy a home for $500,000 and sell it for $1 million 10 years later, it does look like you doubled your money or had an approximate annual return of 7.2 percent. If during those 10 years, however, you paid $60,000 in property taxes and invested $150,000 in maintenance, upkeep, and remodeling, your actual basis is $710,000, which gives you just a 3.5 percent rate of return.

The total cost of ownership includes carrying costs plus financing (or opportunity) costs. In the current environment, and depending on the market, over a five-year period the total cost of ownership is likely to be between 6 percent and 8 percent per year. From these expenses, you can subtract any appreciation and add any depreciation. If the house goes down in value, that adds to the costs. And while appreciation is great, depreciation can be devastating. A leveraged asset's drop in value can be crushing to your finances.

Three Buckets of Money

“Let every man divide his money into three parts and invest a third in land, a third in business, and a third let him keep in reserve.”

– The Talmud

Whether you have $100,000 or $1 million to invest, you must have a clear, precise investment philosophy. In 1986, economist Gary Brinson released a watershed study called “Determinants of Portfolio Performance.”¹⁰ He concluded that 90 percent of an investor's returns are attributable to their investment policy, or asset allocation, and less than 10 percent of the return was due to market timing and stock selection. Asset allocation refers to how much of your portfolio is in a particular asset, such as U.S. stocks or emerging market bonds. A takeaway would be to center your investment philosophy around maximizing diversification in your portfolios, making the decision to always own a globally diversified, multi-asset class mix of investments.

In addition to diversified asset allocation, I believe accumulators should focus on having different buckets of money. To build wealth and mitigate risk, divide your investment assets into three buckets: Conservative, Core, and Aggressive.

Risk Matters—The Risk of Time

Return is not the only consideration in investment portfolios. Risk is just as important.

From my experience, many people in the accumulation phase hesitate to minimize risk in portfolios because they believe they'll have to sacrifice return. Most investors—both individual and professional—believe risk and return have a lockstep relationship. If I tell an investor with a goal of averaging a 10-percent return that she could decrease risk by half she thinks her rate of return will also drop by half. It would be great if the world worked so predictably.

Risk and return operate independently of each other. It's possible to drastically decrease your portfolio's risk and give up only a fraction of the return, or possibly give up none of the return. This happens because of correlation, the yin and yang of your portfolio.

Why does all of this matter? Rarely, if ever, will your expected returns be your actual returns. What matters is how far your returns are off the mark. In The Value of Debt in Retirement, we saw that when you retire, risk is equally important, if not more important, than return. This is because of the sequence of returns. Although it is true that in the accumulation phase you might be able to afford more risk and more volatility—more risk—it simply may not be worth it.

Any way you multiply numbers, you get to the same result. If you take 3 × 4 × 2 you get to 24. Similarly, if you take 2 × 4 × 3 you also get 24. As a result, some people argue that it is OK to have higher risk while you are accumulating because it evens out in the end. This might be true and it might not be true. You see, when you are accumulating you have the benefit of time—but you also have the risk of time.

The way risk and accumulation work may be different than you expect. As you get closer to retirement, you cannot afford to have a bad decade. If you have a bad decade the decade before you plan to retire, it is punitive to your overall returns.

Let's say Oliver starts with $100,000 and saves $10,000 per year every year for 30 years. He is an aggressive investor and averages a 9 percent rate of return. However, his returns are lumpy. He has one great decade, one OK decade, and one bad decade. Specifically, he has one 10-year period where his returns are a disappointing 3 percent per year, another decade that is exceptional at 16 percent per year, and a third that is in the middle at 8 percent per year.

It turns out that Oliver could end up with $2.2 million or $3.2 million depending on how lucky he was with the timing of the returns. Let me explain: If his first decade was the 3 percent decade and his second decade was the 8 percent decade, that would give him 20 years of saving and investing, and his portfolio would have grown to a considerable size making the final 16 percent per year decade really powerful. If he experienced the 16 percent decade first, the high returns would have a lesser impact because they are on a smaller portfolio. On average, you want your highest return years to be when your portfolio is largest. At the same time, this is the time that you can least afford a significant downturn. Therefore, I believe that in early years the risk isn't worth it and in the later years you can't afford it. Let me explain.

Original Scenario A Balance Sheet
Assets		Liabilities
Real estate	$ 500,000	-
Investments	$ 500,000	-
Total	$1,000,000	-
Net worth	$1,000,000

If instead Oliver simply averaged 9 percent the whole time, he would end up with $2.7 million. Granted, it is lower than the best-case scenario, but if the odds are equally distributed on the sequence, there is only a 33-percent chance that he would get better returns with the risky strategy. In this simple example, there is a 67-percent chance the consistent process is better than the risky process. More often than not, math will show not only that consistent returns are better, but also that slightly lower consistent returns are better than slightly higher but much riskier returns.¹⁴

Factoring Leverage into Returns

Used correctly, low-cost and tax-efficient debt may enhance your returns over time. Let's take a look at a few scenarios to understand how this works.

Erika and Raj rent a house, have no material assets, and just inherited $1 million. They are debt averse and decide to buy a home worth $500,000 outright, with no mortgage. This leaves them with a $500,000 investment portfolio. At this point, Erika and Raj have a net worth of $1 million, as shown in Table 5.3.

What about income? If their investment portfolio returns an average of about 6 percent, Erika and Raj would be making roughly $30,000 in income per year, as shown in Table 5.4. (To simplify things, we're ignoring other income sources.)

Now let's consider Scenario B. Erika and Raj purchase the same house by putting down 20 percent and taking on a $400,0000 mortgage. This allows them to keep their money invested without changing their net worth. Erika and Raj now have $1.4 million of assets and a 29-percent debt-to-asset ratio ($400,000 / $1.4 million = about 29 percent). This is illustrated in Table 5.5.

Scenario B Balance Sheet
Assets		Liabilities
Real estate	$ 500,000	$400,000
Investments	$ 900,000	-
Total	$1,400,000	$400,000
Net worth	$1,000,000

What happens from an income perspective in Scenario B? Let's assume Erika and Raj have the same portfolio return of 6 percent, their mortgage is at a 3 percent rate, and they're in the 33-percent tax bracket (so that the cost of that additional $400,000 in their portfolio is effectively 2 percent, resulting in an $8,000 cost). What happens to their net income?

As the income statement in Table 5.6 shows, Erika and Raj now receive a net income from their portfolio of $46,000, or $16,000 more than they received in Scenario A. By taking on the mortgage at 3 percent, they've increased their portfolio income by $16,000 a year (assuming a hypothetical 6-percent portfolio return). They have also substantially increased their overall liquidity.

In Scenario A, you would need a return of more than 9 percent on your investments to generate a $46,000 return ($500,000 × 9% = $45,000). In Scenario B, you can get to the same place with just a 6 percent average return.

There are two ways to get a 9 percent rate of return: Find assets that deliver a 9 percent rate of return or leverage assets that have a 6 percent rate of return.

Debt as an Integrated Part of Your Investment Philosophy

Debt can be an integrated part of your overall investment philosophy. As your balance sheet grows, you may choose to reduce your debt ratios during market environments where you think there is a low probability of capturing a spread for the next five years and you may choose to slightly expand your debt ratios in times where you think there is a high probability of capturing a spread.

I point out this strategy because it is interesting to consider, but it comes with a big caveat. There is risk to intentionally moving your debt ratio up and down—the risk that you are likely to be wrong. So many people increased their debt in 2007 and paid it off in 2009.¹⁵ In hindsight, they should have been doing the opposite. While you are in the L.I.F.E. glide path, I prefer a constant, systematic building up of assets rather than trying to change debt ratios based on market environments.

Equally important is that debt ideas are a way to express a view with respect to currencies. For example, Argentina has gone through a series of crises.¹⁶ At certain points in time, if you borrowed in Argentinian pesos and invested in an Argentinian stock and bond portfolio, your portfolio and your balance sheet could have been destroyed. At the same time, if you borrowed in Argentinian pesos and bought virtually any asset anywhere else in the world, you could have made a tremendous amount of money as the currency fell apart and you were able to pay back the devalued debt at pennies on the dollar.

In January 2016, the U.S. dollar appreciated by about 20 percent versus a basket of global currencies between January 1, 2014, and January 1, 2016.¹⁷ If you purchase a foreign bond at 4 or 5 percent and the dollar falls to its previous levels over the next 10 years, then you could average approximately a 7-percent annual rate of return, and have done so in bonds. Now, of course, there is considerable risk to the strategy as well. If the dollar continues to strengthen and the assets are denominated in other currencies, then you would receive the income but lose in the devaluation of the currency.

Similarly, borrowing is a great way to express views with respect to interest rates and inflation. While these strategies are best utilized with your advisors, here is the important point: It isn't the borrowing that is good or bad, it is the investment decisions that you make with respect to the borrowing. Debt is a magnifier of your investment decisions.¹⁸