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© 2002 - 2004
Douglas A. Ruby


The Digital Economist
Thinking about Asset Returns

The recent steep decline in the Dow Jones Industrial Average, as well as in the other major averages, has forced many people to rethink their savings and retirement strategies. There is still some debate as to whether the run-up and subsequent drop in share prices between 1998 and 2000 was representative of an asset price 'bubble'. What did become evident is that as the major averages increased dramatically in the late 1990's many investors began to think that 10 - 20% returns were becoming the norm and with some skill at investing, these returns could be realized. People were basing their investment behavior on the assumption that the underlying nature of the U.S. and global economy had changed. The Internet and related technological innovations were thought to have changed the economic rules. Many people began thinking about early retirement. The exceptional performance in the stock market led many to rethink the returns on Social Security and advocate privatization as a solution to potential insolvency of the Social Security system within the next generation. As the bubble burst these plans have, for many, been vanquished.

So what is a realistic rate of return on a well-diversified portfolio? What is the true metric for measuring this and other returns? Are 8%, 10%, or larger returns realistic? Are they sustainable?

According to Ibbotson Associates (www.ibbotson.com), the historical (1926-2000) growth rate on the S&P 500 has been in the range of about 10.7% per year. This represents a nominal measure that includes capital gains, retained earnings and the reinvestment of dividends paid. In real terms (adjusting for inflation -- the percentage change in the Consumer Price Index) this growth rate is roughly 7.7% per year (10.7% - 3.0 annual rate of inflation).

This started me thinking about how long it would take for someone with an average net worth, say around $50,000, to turn this sum into something significant. What would be a significant accumulation? How about the value of U.S. Gross Domestic Product 'GDP'?

Historically, Real GDP (RGDP -- growth in the output of an economy) in the U.S. grows at a rate of about 3% per year and stands at a value of $9,200,000,000,000 ($9.2 trillion).

Now given the nature of compound growth, it is only a matter of time before a smaller sum growing at a roughly 8% annual rate exceeds a much larger sum growing at a lower rate. How long will it take before my $50,000 will allow me to purchase all of the U.S. GDP? We can compute the answer using the following:

$50,000(1.08)N = $9,200,000,000,000(1.03)N
solving for 'N' we have:
(1.08)N / (1.03)N = $9,200,000,000,000 / $50,000
or
[(1.08)/(1.03)]N = $184,000,000

[1.0485]N = $184,000,000
or
log1.0485[184,000,000] = N
or
ln(184,000,000)/ln(1.0485) = N = 402 years!

Now I won't be around 400 years from now. According to these numbers, If I put $50,000 into the stock market today and am able to earn the historical rate of return of 8% per year, my descendants will be able to purchase the whole of U.S. GDP at that time. Too bad for the other 350 million people in the U.S. economy that try to buy food, housing, or education for their kids.

We can generalize the above formula as follows:

N = ln(RGDP / X) / ln[(1 + θ)/(1 + ρ)]
where 'X' represent an amount invested by an individual today in stocks, 'θ', the annual growth rate in equities, and 'ρ' the growth rate in Real GDP.

Now my $50,000 perhaps reflects the net worth of someone with average intelligence and average ability. Imagine if someone truly exceptional (perhaps a CEO of a telecommunications firm having just exercised stock options for a $100 million gain) does the same thing. The much larger amount of $100 million means that the heirs of this exceptional person will be able to buy the whole of U.S. GDP in about 250 years. For the descendants of a founder of a major software firm with a current net worth of $20 billion the wait is only 120 years.

I realize that individual's do not just cash in their financial assets at a single point in time and go on a spending spree. However, as we talk about the stock market as a vehicle for Social Security Privatization, retirees in increasing numbers are going to do exactly that -- cash in. The value of these assets is based on the ability to convert this financial wealth in to real goods and services if someone chose to do so -- real goods and services produced and provided by an economy growing at a rate of roughly 3% per year.

The examples above are in reference to a single person. In reality, there are millions of individuals buying shares of publicly-held corporations. In a short period of time the value of these portfolios growing at 8% annually will equal and then exceed the output of the U.S. economy. This highlights a key problem with measuring returns via growth in the market value of a portfolio.

A first step in understanding this problem is to develop an appreciation for the variables being used. We will use the following definitions in this work:

  • Equities -- a share of stock representing shared ownership in publicly-held companies.
  • Earnings -- the net after-tax income of a company.
  • Retained Earnings -- Earnings not paid out to equity-holders as dividends
  • Dividends -- Cash payments to equity-holders drawn from earnings.
  • A Stock Variable -- a variable measured at a point in time.
  • A Flow Variable -- a variable measured per-unit of time.
The last two definition are important to add clarity in our thinking. The market value of a portfolio of equities is a stock variable. When we look at historical growth rates, we are measuring the growth rate of a stock variable. Earnings, Retained Earnings, Dividends paid; as well as interest payments on bonds; or rental income on properties are all flow variables. Real GDP is also a flow variable.

This distinction between stocks and flows can help us understand the difference between growth rates and yields/rates of return. For example the rate of return on a bond (more accurately known as the current yield) is expressed as the annual (semi-annual) interest payment 'R' divided by the price paid 'P' for that bond. In effect this yield 'Ψ' is derived as the ratio between a flow variable 'R' and a stock variable 'P'. Price-earnings 'PE' ratios are intended to capture the same type of information such that a 'PE' of 20 would imply a yield of 5% -- annual earnings per share are 5% of the price of each share.

In efficient financial markets different financial assets are competing for the savings (a flow variable) and wealth (a stock variable) of the household sector based on their rate of return, associated risk, and other characteristics (maturity / liquidity) that match the investment goals of these savers. These savers should ultimately be motivated by the stream of income generated by these assets -- new income that is matched by growth in the output of the economy. Assets that do offer higher returns in a given time period are offering compensation for higher levels of risk. Higher returns this year to offset lower or zero returns in some future period. Thus we would expect that equities with unpredictable earnings/dividends and market prices would likely offer higher yields in a given time period relative to corporate bonds (with a well defined stream of interest payments and some risk of default), or Treasurys (with a stream of interest an no risk of default). However, over the long term the yields on all assets would converge to represent a reasonable claim on the growth in real economic output. That is:

Ψi,long term = %ΔRGDPlong term

To focus on growth rates in stock variables can be misleading. According to Ibbotson and Associates (2000), $1 invested in 1929 in a portfolio of S&P 500 stocks would be worth roughly $229 in real terms in the year 2000 [ $1(1.0762)74 = $229]. This $229 represents a claim on the future earnings potential of the companies included in that portfolio. Now with well-functioning secondary equities markets a single investor could liquidate the portfolio and purchase/acquire $229 worth of goods and services. However, if all investors were to liquidate, asset prices would plunge. The value of these shares is preserved as long as most people are willing to hold on to their equity portfolios.

Currently, the New York Stock Exchange allows for the trading of equities for 2,784 different companies. There are 351 billion shares outstanding (a stock variable) and on any given day 1.435 billion shares (a flow variable) change hands. In these secondary market transactions, one person is selling equities and buying cash, another person is buying equities and selling cash. In a given year there is a 104% turnover of these 351 billion shares (source: The New York Stock Exchange www.nyse.com -- October 15, 2002). However, it is the market-clearing price of the 1.435 billion shares changing hands on a given day that determines the market value of the outstanding 351 billion shares -- value that would not be sustained if all equity-holders attempted to convert these financial assets into cash with the desire to convert the cash into real goods and services.

This then is an argument for acquiring equities for the flow of income they generate rather than capital gains. This income flow will be in the form of earnings if the investor finds utility in being part owner of the physical assets of a growing company and dividends if the investor seeks a source of income to support the purchase of goods and services as one might do in their retirement. The proper metric is the periodic yield on shares not the rate of growth of share prices.

Advocates for holding equities in individual portfolios should emphasize the yield on these shares relative to other income producing assets. Although the 8% real rate of growth in the S&P 500 is a matter if historical fact, this should not be the rational for buying equities. This growth rate in equity prices has been driven, in large part, by demographics and financial innovation (like mutual funds) where the flow of new buyers into secondary markets exceeds the flow of sellers in those same markets. These share prices will rise as the companies behind them become more profitable and thus generate more earnings income -- earnings leading to higher yields that make equities all the more attractive to hold. As shown above, it is impossible for every investor to realize an eight percent return on their portfolio in an economy growing by 3% per year. Additionally, individual investors must realize that gains in-excess of the rate of real economic growth can be realized by a few at a point in time but never by all.

Thus, individuals who have realized an eight-percent or better real return in the purchase and near-term sale of equities (capital gains) have done so, due in part, to transfers of wealth within the economy rather than sharing in the wealth created by a growing economy. These transfers will be from those who guessed wrong in investment game to those who guessed right. This is part of the riskiness of buying equities -- risks that must be clearly identified and acknowledged by all buyers and potential buyers of financial assets.

Sustainable rates of return in the absence of these transfers implies that the value of portfolios grow at a rate close to the rate of real economic growth. A notion that should be stressed to all potential investors.