Table of Contents
INTRODUCING WILEY INVESTMENT CLASSICS
Title Page
Copyright Page
Foreword
Preface to the 1993 Edition
Preface to the 2006 Edition
Introduction
Chapter 1 - Market Risk, Timing, and Formula Strategies
RISK AND MARKET RETURNS
MARKET TIMING AND FORMULA STRATEGIES
ENDNOTES
2006 NOTE
Chapter 2 - Dollar Cost Averaging Revisited
DOLLAR COST AVERAGING: AN EXAMPLE
SHORT-TERM PERFORMANCE
LONG-TERM PROBLEMS WITH DOLLAR COST AVERAGING
SUMMARY
ENDNOTES
Chapter 3 - Value Averaging
VALUE AVERAGING: AN INTRODUCTION
SHORT-TERM PERFORMANCE
LONG-TERM PERFORMANCE AND VALUE AVERAGING
SUMMARY
ENDNOTES
2006 NOTE
Chapter 4 - Investment Goals with Dollar Cost Averaging
BACKGROUND
READJUSTING THE INVESTMENT PLAN
GROWTH-ADJUSTED DOLLAR COST AVERAGING
SUMMARY
ENDNOTES
Chapter 5 - Establishing the Value Path
VALUE AVERAGING VALUE PATHS
SUMMARY
ENDNOTES
Chapter 6 - Avoiding Taxes and Transaction Costs
TAX CONSIDERATIONS WITH VALUE AVERAGING
REDUCING TRANSACTION COSTS
SUMMARY
ENDNOTES
Chapter 7 - Playing Simulation Games
WHY SIMULATIONS?
WHAT AND HOW?
CONSTRUCTING THE SIMULATION
ENDNOTES
2006 NOTE
ENDNOTES TO APPENDIX TO CHAPTER 7
2006 NOTE
Chapter 8 - Comparing the Strategies
FIVE-YEAR SIMULATION RESULTS
TWENTY-YEAR SIMULATION RESULTS
SUMMARY
ENDNOTES
Chapter 9 - Profiting from Overreaction
TIRING OF A RANDOM WALK
WHY DOES THIS MATTER?
ENDNOTES
2006 NOTE
Chapter 10 - Details: Getting Started
USING MUTUAL FUNDS
WORKING OUT THE DETAILS
2006 NOTE
NOTES FOR FINANCIAL PLANNERS
SUMMARY
ENDNOTES
2006 NOTE
Chapter 11 - Examples: Strategies at Work
THE GOAL AND INVESTMENT ENVIRONMENT
INVESTMENT RETURN & TAXES
IMPLEMENTING DOLLAR COST AVERAGING
IMPLEMENTING VALUE AVERAGING
SUMMARY
ENDNOTES
Chapter 12 - A Final Word
Index
INTRODUCING WILEY INVESTMENT CLASSICS
There are certain books that have redefined the way we see the worlds of finance and investing—books that deserve a place on every investor’s shelf. Wiley Investment Classics will introduce you to these memorable books, which are just as relevant and vital today as when they were first published. Open a Wiley Investment Classic and rediscover the proven strategies, market philosophies, and definitive techniques that continue to stand the test of time.
Foreword
Since its first printing in 1991, the cachet of Value Averaging has steadily grown to cult-classic status. So reluctant are its readers to part with the two original editions that these humble volumes have turned out to be highly profitable investments in and of themselves. The closure of the book’s original producer, International Publishing Company, was followed by the exhaustion soon thereafter of the planet’s last remaining supplies at a redistributor in, of all places, Cave Junction, Oregon; prices for used copies thereupon sailed into territory more typically seen with F. Scott Fitzgerald first editions.
Why, for the past several years, have investors been willing to pay hundreds of dollars for one thin paperback? The reputation of an investment classic usually issues in no small part from its literary qualities: the velvety logic of Benjamin Graham’s The Intelligent Investor, the good humor and powerful exposition of Burton Malkiel’s A Random Walk Down Wall Street, the moral thunder of John Bogle’s Common Sense on Mutual Funds, or the narrative elegance of Edward Chancellor’s Devil Take the Hindmost. While Mike Edleson’s Value Averaging is nothing if not well written, it qualifies as essential investment reading for an entirely different reason. Simply put, Mike Edleson’s book is the single best guide on the mechanics of deploying a steady stream of cash into a portfolio. I’ll go one step further: It is the only book that fully describes how any investor, from the smallest 401 (k) participant to the largest pension fund manager, can fully harness this powerful discipline.
The power of the value averaging method derives from its marriage of two proven but heretofore separate techniques: dollar cost averaging and portfolio rebalancing. The mathematical imperative of dollar cost averaging, the time-honored purchase of equal, periodic amounts of stocks, forces investors to buy more shares of stock or mutual funds when prices are low than when they are high, increasing overall returns, on average. Rebalancing, on the other hand, is most often applied to mature portfolios and mandates the periodic adjustment of portfolio allocations back to a set policy, forcing a strong element of “buy-low/sell-high” discipline into an investor’s trading decision making.
Mike’s special genius lay in realizing that these two techniques could be combined in the accumulation phase of a portfolio; not only are more shares bought when prices are low and fewer shares when prices are high, as with dollar cost averaging, but more money is deployed into stocks when prices are low and less when prices are high, producing yet more salutary long-term results.
Any investor fortunate enough to have come across Value Averaging during the 1990s and absorb its message was amply rewarded; prices defied both logic and gravity as that fateful decade wore on, and the technique told its practitioners to invest progressively less money on high-priced equity. Then, as prices plunged between 2000 and 2002, the hoards of capital accumulated during the previous several years was used to purchase shares at bargain-basement prices.
No investment technique, of course, works 100 percent of the time. Regular portfolio rebalancing, for example, usually increases portfolio returns, but it does not always do so. When markets move strongly up or down for a long period of time, such as occurred during the 1990s in the United States (up) and in Japan (down), rebalancing can hurt portfolio returns by the continuous purchases of a falling asset or the continuous sales of a rising asset. The same is also true of value averaging into an asset class over a period of relatively few years in a generally rising market, in which case the investor would have been better off purchasing a single lump sum.
Most investors, of course, will be adding to their portfolios for many decades. Here, the risks of a “bad draw” are far less, but still not zero, and are mainly the result of misjudging the long-term market return, one of the technique’s central inputs. Grossly overestimating this value will result in the purchase of too much stock, possibly exceeding the saving capacity of the investor, whereas grossly underestimating this value will result in too little stock being purchased.
The past few decades have seen a tectonic shift in the retirement landscape, with the replacement of the traditional definedbenefit retirement plan with a slew of defined-contribution schemes, prime among which is the 401 (k) account. The net effect of this radical alteration of the retirement savings paradigm has been the conscription of tens of millions of employees into becoming their own unwilling portfolio managers—in essence, a vast and unprecedented experiment in social engineering. For the vast majority of participants, untrained in basic finance and provided with mediocre investment vehicles, it will end badly. The few who will do well will be those who have read and absorbed the messages of the volumes listed at the beginning of this foreword, and in the order listed. Value Averaging is, if you will, the essential chocolate-sauce-and-cherry topping on the parfait, providing, in normal circumstances, an additional reward in excess to that obtained by assembling a disciplined, low-cost, diversified portfolio.
An investment strategy is much like the blueprint for a skyscraper. It is one thing to understand how the steel and concrete elements are assembled, and it is quite another to be welding rivets on an exposed girder 60 stories above a city street. While Value Averaging is a necessary and essential element in the assembly of a sound portfolio, it is most certainly not sufficient. First, you must actually be able to save. Perhaps you can pick securities as well as Warren Buffett, but if you are unable to put away a substantial percentage of your income, you are doomed.
Second, and just as important, you must be able to execute. The discipline of value averaging mandates that when everyone around you has panicked, not only must you keep your head and continue to purchase stocks, you must do so in far larger amounts than in more normal times. This will be particularly true if you are well along in the process, as the large amount of stock assets already in your portfolio will leverage up the amount of necessary purchases in the event of a bear market. As the old cliché goes, no balls, no blue chips: Some will have the knowledge, but not all will have the moxie.
At the risk of overburdening the reader with too many metaphors, the investment process can be likened to a sporadic, interminable war against both the markets and the “enemy in the mirror”—one’s own emotions. While Dr. Edleson cannot supply you with the courage necessary to confront these frightful adversaries, he can at least provide you with the training, weapons, and body armor with which to do battle in the capital markets.
—William J. Bernstein
Preface to the 1993 Edition
This book evolved out of an article I wrote titled “Value Averaging: A New Approach to Accumulation,” published in the AAII Journal X, no. 7 (August 1988). That article introduced an effective formula investment strategy that was a bit more complex than dollar cost averaging (constant dollar investing) but provided higher returns and other potential advantages. Over time, over a thousand investors called or wrote me with several questions, comments, enhancements, or other ideas. So this book was written with investors in mind—investors who want a clean and easy system for accumulating and moving their wealth through time to achieve their financial goals. It’s not for investors who want to get rich quick; getting rich slow is a noble enough financial goal to achieve.
After trying the latest gimmicks and following the current gurus in a futile quest to outwit and beat the market, some investors are actually satisfied with a fair return for the risk taken with their investment dollar. And, as you’ll see in Chapter 1, the stock market really does provide a good return over time; there just doesn’t seem to be much guidance for the intelligent individual investor on how to achieve these reasonable investment goals effectively. In this book, I attempt to provide and analyze some reasonable and effective ways to build up wealth over time. As opposed to haphazardly jumping from one fad to another, I recommend some disciplined, systematic approaches that allow you to build wealth in a consistent manner and generate good returns without undue risk. Using a systematic approach that is mechanical and nearly automatic relieves the investor of any need for market-timing skills, stock-picking skills, and the emotional involvement in the market that so often turns would-be investors into speculators.
If this all sounds a bit boring, then so be it. Perhaps you will miss the excitement and peril of second-guessing every trade and timing decision you make. Or you might become bored with deciding what to do with the hundreds of dollars you save on newsletters and stock guides, or how to spend all the hours you’ll free up.
The book is designed to first give you an overview of the market and a few basic formula strategies for investing in it. Chapter 1 delves into stock market risk and return, so that you are familiar with the investment terrain. Chapters 2 and 3 (respectively) summarize dollar cost averaging and value averaging, two basic formula strategies. The remainder of the book is oriented toward helping you decide on and tailoring an investment strategy that meets your needs, so that you can easily map out and immediately start your investment plan. Chapters 4 and 5 provide the methods and give examples of how to set and adjust the amount you invest over time to achieve your investment goals. There are some new formulas and procedures in these chapters that will allow you to respond to inflation, market growth, and many of the uncertainties you will face as your goals and investment performance change over time. Chapter 6 analyzes several important enhancements to these formula strategies and discusses how to deal with taxes and other transaction costs.
Up to this point, all of the data analysis is based on more than six decades of actual historical market data. Chapter 7 introduces you to market simulations, used to “game” how a strategy might perform in a wide range of potential future markets. Chapter 8 uses both market simulations and historical data to compare the performance of the two formula strategies and their many variations. Chapter 9 focuses on the tendency for market price movements to overreact. This tendency provides an additional rationale for formula investing; it also highlights the role of formula strategies in taking advantage of excessive price movements, instead of letting them take advantage of you. Chapter 10 provides some usable guidelines and nitty-gritty details for investors and financial planners on how best to use the strategies to meet their individual needs. Chapter 11 follows an investor through a 10-year case study of investing with these two strategies. Real world problems like dealing with inflation, taxes, market surprises, and changing rates of return are examined in detail. Chapter 12 summarizes.
Value Averaging: The Safe and Easy Strategy for Higher Investment Returns provides enough complexity for those readers who really want to “dig into” the material; but most of the tough parts can be skimmed or skipped by casual readers without affecting their ability to construct a reasonable, workable investment strategy. A calculator (especially an inexpensive financial calculator) will come in handy in working through some of the material. And although a computer isn’t necessary, readers who have facility with spreadsheet software (e.g., Lotus 1-2-3, Quattro Pro, Excel, etc.) will probably want to experiment on their own with a few of the ideas and perhaps even customize their own plan on their computer. Appendixes following Chapters 4, 5, and 7 provide specific examples and instructions for using spreadsheets to help with your calculations.
The historical stock market data used in many of the analyses in this book are market index data from the University of Chicago’s Center for Research in Securities Prices (CRSP). The data used are composed of the daily or monthly return (coming from both dividends and price changes) on the combined listed stocks of the NYSE and AMEX markets, all weighted by their total value, or market capitalization. The monthly figures are end-of-month data from December 1925 to December 1991. The daily figures are from July 2, 1962, to December 31, 1991.
I would like to acknowledge the valued contributions of: Bruce Cohen, Barbara Craig, Jerry Edgerton, Carole Gould, Phil Hamilton, Ronald J. Liszkowski, Alicia Lowe, Vita Nelson, and Maria Scott. My apologies to others whom I should have included. I mention, also, Chris Edleson, because he likes to see his name in print. Special thanks are due to Larry Dillard and Manny Contreras, who provided valuable research assistance. Finally, I dedicate this book to Jan, who, for all of her support, has still not read the book.
Preface to the 2006 Edition
It’s been 16 years since I wrote the original Value Averaging (1991) and 14 years since the revised edition (1993) came out. The classic edition being republished is the 1993 edition. The intervening period has been anything but boring for investors. As the markets alternated between exciting and exasperating, fortunes were made and lost and made again.
As we roll the clock forward from the original book, let’s take a look at modern markets and value averaging to see whether the strategy is as strong today as it was then. First, let’s get a historical perspective by comparing the market of the past decade (1996-2005) to similar market action from 70 years earlier (1926-1935). While you probably weren’t around for that earlier period of our history, you’re likely aware of the market insanity of the 1920s and 1930s, with the speculative bubble of the Roaring Twenties, the Great Crash of 1929, the unprecedented drawdown of market wealth that occurred over the succeeding few years, and the Great Depression of the 1930s. In the graph in Figure P-1, this wild historical decade is contrasted to the current decade (since 1995), exactly 70 years apart, but scaled to the same starting point. It’s an interesting comparison, as the early gentle run-up, the spike skyward, the crash and near-immediate rebound, the more painful and extensive second crash, and the steady climb out of the gutter after about three years, bear an uncanny resemblance across 70 years of time.
Oh, did I forget to label the lines on the graph? How careless of me. The 1926-1935 market series, Great Crash of 1929 and all, is represented by the darker, lower line on the graph. The lighter line that spikes to nearly the top of the graph before crashing shows the NASDAQ 100 index over the decade we’ve just lived through, 1996-2005. While not making light of the enormous travails our grandparents endured, the financial roller-coaster risk we’ve survived recently is truly hair-raising.
Figure P-1 THE ROARING TWENTIES OR THE NASDAQ NINETIES?
The data and analysis in the original book stopped at 1991. At a few critical points in this 2006 edition, I’ve added some analysis and advice to bring you up-to-date. Here is a look at the modern market action for a few of the indices used in updating. The NASDAQ 100, the S&P 500, and the broad-based Russell 3000 have their total return levels compared on the graph shown in Figure P-2 from the end of 1991 through 2005. For an amount of money invested in each of these indices at the end of 1991 ($100 is shown), you would have quadrupled your money in the S&P and Russell, and more than quintupled your money in the NASDAQ, if you survived the ride.
How would the formula strategies discussed in this book have fared over this 14-year period? The good news is that the approaches, especially value averaging, continue to “do their thing” and provide good returns over time. The better news is that value averaging did extremely well relative to every one of the indices shown.
Figure P-2 U.S. STOCK MARKET PERFORMANCE (SINCE THE PUBLICATION OF THE ORIGINAL BOOK)
Table P-1 presents the resulting internal rate of return (IRR) from applying the investment strategies monthly since December 1991, picking up where the original book left off. For all indices, value averaging (VA) continued to produce higher returns than dollar cost averaging. Value averaging did especially well for investments in the NASDAQ index, providing over 5½% additional return over the period—over 50% better than dollar cost averaging (DCA).
A few additional updates are provided after selected chapters in this edition to confirm whether the strategy still works—and how it might be implemented differently in today’s markets. Following five of the chapters, you will find a brief “
2006 Note,” in which I supplement the original material with comments on the investment strategies or advice on their implementation. In a nutshell, you will learn the following:
• The market (barring NASDAQ) performed about as we had expected and predicted.
• Future expected stock market returns, though, are likely to be considerably lower than the original book predicted. Use lower growth rates when implementing value averaging today.
• While dollar cost averaging still works well, value averaging continues to outperform by producing generally higher returns.
• Be careful with the Lotus 1-2-3 spreadsheet instructions in the appendices; since Excel works differently, you can’t just type them in verbatim. More on the spreadsheets below...
• Markets don’t seem to have overreacted statistically in the past two decades as much as they had historically.
• I still recommend employing value averaging using quarterly (or similar) investment periods.
• Dramatic changes in the investment landscape have provided you with substantially improved opportunities to pursue accumulation strategies. More, better, and cheaper tools now provide flexibility you could only dream of when I first wrote this book 16 years ago.
TABLE P-1 Performance of Strategies, End of 1991-2005
Starting $100 Monthly Investment, Growing to ~$50,000 Investment Target
Index | Rate of Return DCA | Rate of Return VA |
---|
S&P 500 | 8.3% | 9.0% |
Russell 3000 | 8.6% | 9.5% |
NASDAQ 100 | 9.6% | 15.2% |
I need to offer a brief clarifying comment on data. Unlike in the original book, I didn’t use CRSP NYSE/Amex data for the updates, the obvious problem being that the important NASDAQ data would have been excluded. I worked with basic historical daily data on the major stock indices here, including two (Russell 3000 and Wilshire 5000) that are broad-based and roughly comparable to the original CRSP data—but include NASDAQ stocks as well. The analysis presumes reinvestment of dividends (total return analysis), although I re-ran all analyses on price-only index returns and got essentially the same results.
Finally, a couple of notes for those of you who want to get deeper into this investment arena. An academic study by Professor Paul S. Marshall on value averaging was published a few years ago (JFSD Vol. 13, No.1, Spring 2000). If interested, I suggest Googling “Marshall value averaging” to find a copy of the paper and some of his related works.
John Wiley & Sons is making available to you a few of my Excel spreadsheets as a supplement to this book on its Web site through 2007. With these, you will be able to do some simple back-testing analysis, run simulations, and set up simple implementation spreadsheets to get you started investing with the strategies.
These files are provided as-is, with no warranty, no license to redistribute, and no support of any kind; but we hope some of you will find them a helpful tool. Simply go to the John Wiley & Sons Web site: www.wiley.com/go/valueaveraging. The password for readers to gain access to the files consists of the following nine characters: 1991-2006.
While there are many people to whom I am grateful, I’d like to especially thank Dr. William Bernstein, a superb author, for his support and continual prodding to republish this book, and Bill Falloon, who had the vision to make it happen. I’m also thankful for my wonderful and supportive wife Jan, and for Tom, David, Ken, David, Shane, and Dan (along with my other fine colleagues), who each make every day more interesting than the last.
—Mike Edleson
May 2006
Introduction
“Buy low, sell high!” Or so we’ve been told. Lots of investors have this incredible knack (which they invariably deny) for “buying high” and “selling low.” It’s easy to get trapped into following the psychology of the market, what with all the excitement generated by the media and the market itself. It takes a lot of guts to buy into the stock market when it’s at the very bottom—first of all because you never know when you’ve arrived at its bottom and second because just about everything you read at the end of a bear market is full of despair and doom. On the other hand, most investors have found out through painful experience that the easiest (and worst!) time to buy stocks is when everyone is euphorically proclaiming the immortality of a soon-to-be-ended bull market.
Market timers and fundamental analysts have their own methods of trying to make this investment dictum come true. Even so, the rest of us who are too busy or too realistic to try calling turns in the market have not been totally left out in the cold. Although we can join in their “beat the market” games, we are far less experienced, informed, and capitalized than they are. We can buy their assistance, but often at a price that may exceed its actual value, if any. Or we can strike out on our own, despite the rough terrain of emotional hills and valleys implied above. Formula strategies are the pack mules that can help you in this journey.
A formula strategy is any predetermined plan that will “mechanically” guide your investing. One very naive such formula, for example, is to buy one share of stock every week (not recommended!). The best-known formula plan, discussed in Chapter 2, is dollar cost averaging, whereby you invest the same amount of money in an asset each regular investment period, regardless of its price.
A flexible variation of this is value averaging, a strategy I devised in 1988. The basic formula of value averaging, discussed more fully in Chapter 3, is to invest whatever is needed to make the value of your asset holdings increase by some preset amount each investment period.
Other formula strategies call for rebalancing your holdings among asset types; for example, constant-ratio plans dictate that a fixed percentage of your wealth should be held in stocks. Some more active versions of formula strategies are really more like market timing; for example, variable-ratio plans change the proportion in each asset type based on some fundamental or technical indicator (e.g., dividends, P/E ratios, short interest, etc.). Asset allocation strategies generally fall into this category. We will focus on the more passive formula strategies—dollar cost and value averaging—which are simpler and less chancey for the investor.
The first three chapters provide some basic information on formula plans, particularly dollar cost averaging and value averaging. The basic notions to grasp are that formula plans help you avoid the herd mentality and its arbitrary and often ill-timed investment shifts; they also help guide you in the general direction of buying lower and possibly selling higher. Dollar cost averaging helps a bit on the “buy low” side, but it provides no guidelines for selling. Value averaging has the effect of exaggerating purchases when the market moves lower, but buying less and sometimes even selling shares when the market moves higher. The latter is a bit more complex but well worth considering, given the added flexibility and generally higher returns. All of these issues will be analyzed at length in the chapters to follow.
1
Market Risk, Timing, and Formula Strategies
Whether you call it investing or playing the market, buying and selling stocks is risky business—risky but lucrative. In choosing to read this book, you have likely decided to build an investment portfolio that may include some of those risky stocks in order to garner some of those lucrative rewards. Before making investment decisions, you should have a reasonable idea of the typical risks you will face in the stock market and the likely rewards you might expect to earn. This chapter provides an introduction to these issues and familiarizes you with some historical data on market performance.
RISK AND MARKET RETURNS
First we will look at the investment returns that have been earned in the stock market in the past. Later in this section we discuss the risk inherent in these returns. Together, this information will provide you with a realistic sense of your opportunities in the stock market.
Market Returns over Time
When any wise market prognosticator is asked the inevitable question: Is the stock market going to move up or down?, the unsatisfying but correct answer is: Yes, it will. Day-to-day movements are anyone’s guess, but over time the market has risen substantially. Stock price movements for the past 66 years are shown in Figure 1-1.1
Figure 1-1 MONTHLY STOCK PRICE LEVELS, 1926-1991
Note that a $1.00 investment on the last day of 1925 would have been worth $533.64 by the end of 1991. That’s a 9.98% compounded annual return over a period where inflation averaged 3.2%. Of course, you could have invested $2.54 prior to the October 1929 stock market crash and despaired as it went as low as $0.41 by mid-1932, losing over five-sixths of its value. Even though there has been only one such period in the past century, this scenario still highlights the magnitude of the potential risks faced when investing in the stock market.
Figure 1-2 MONTHLY STOCK RETURNS, 1926-1991
If you (or more likely an ancestor) had invested $100 in the overall market each month during 1926-1991, your investment would have grown to $11,386,000, more than 140 times the total number of dollars you would have invested. Now admittedly, $100 a month was a lot of money back in the 1930s (worth about $800 in today’s dollars), but so is $11 million today. Let’s take a closer look at the type of risk entailed in attaining these investment rewards.
Figure 1-2 shows the total return (capital gains plus dividends) for each individual month in the 66-year period. Although it is extremely unusual for the market to move more than 20% in a given month, you can see that it has happened about ten times. The average market return for one month is slightly under +1.0% (0.95% monthly), or 12% annualized.2 (See “Returns and Compounding” in the box on page 7.)
Figure 1-3 portrays similar data, but for years instead of months. Here it is easier to see that the market generally goes up, but that there is still random variability with no apparent pattern. The range of returns is from a − 44% loss to a +58% gain, although since World War II they fall in a tighter range of −28% to +51%. Individual stocks, of course, exhibit much more variability than the market as a whole, so avoid confusing typical market returns with what might happen to a single stock.
Figure 1-3 ANNUAL STOCK RETURNS, 1926-1991
RETURNS and COMPOUNDING
A return on investment (e.g., 8%) must be connected with a period of time (e.g., a year). Annual terms are commonly used, but not always. When we shift our concern from one time period to a different one, we must “translate” the return figure as well.
Suppose the total return on a 2-year investment was 21%. A natural way of stating this would be to convert the 2-year return into an annual figure—a 1-year return. But simply dividing the 21% by 2, yielding an annual return figure of 10.50%, would be incorrect. Simple “averaging” of a return ignores compounding. Suppose you had a $100 two-year investment, and made a 10.50% return on it in the first year. That gives you $110.50. With another 10.50% return in the second year, you end up with $122.10 (10.50% of $110.50 is $11.60). This is a 2-year return of 22.10%, not just 21 %. Actually, a 21% two-year return is equivalent to a 10% annual return ($100 + 10% = $110; $110 + 10% = $121, a 21 % total return).
If
a is the annual return, then this formula will give you the compound return for
n-years:
(1 + a)n = 1 + n-year return
In the example above,
a =
10% and
n =
2, so:
(1 + 0.10)2 = 1.21 = 1 + n-year return
0.21 = 21 % = 2-year return
The process works in reverse, too, to find the annual return given a longerperiod return. Taking the
n-th root (on a calculator, that’s raising something to the
1/n power), the formula is:
1 + a = n-th root(1 + n-year return)
or,
1 + a = (1 + n-year return)1/n
EXAMPLE: What annual rate gets you a 50% return over five years?
1 + a = 5-th root(1 + 0.50) = (1.50).2 = 1.0845
a = 8.45% annual return
This process can also be used for calculating compound returns for periods that are less than a year in length. Using the top formula, what is the monthly compound return if you get a 12% annual return? HINT: One month is 1/12 of one year.
(1 + 0.12)1/12 = 1.0095 = 1 + monthly return
0.0095 = 0.95% = monthly return
A more general way to write the formula is helpful in translating monthly rates into annual. Suppose that your
long time period is
n times as long as your
short time period. Then the per period compound returns are related as follows:
(1 + short period return)n = 1 + long period return
Suppose you could earn 1.0% each month on an investment. What is the annual return? Here, the short period return is 0.01, and
n = 12:
(1.01)12 = 1.1268 = 1 + long (annual) return
0.1268 = 12.68% = annual return
This is the proper method of converting between monthly and annual return figures, and it is used throughout this book.
Even though the market is indeed risky, there is some truth to the statement Time heals all wounds. This is evident in Figure 1-4a, where instead of looking at one-year investments, we look at four-year periods. Only the worst period (the Great Depression) shows a loss. The annualized return over longer time periods is less variable, because the randomness of the returns causes them to “average out.”
Figure 1-4a ANNUALIZED STOCK RETURNS, 1926-1989
We could also look at the most recent 64 years, sliced into 4-year periods beginning in 1928. This similar analysis is shown in Figure 1-4b; the results differ slightly. While still less variable than single-year returns, these 4-year returns show a different pattern with more losses.
Figure 1-4b ANNUALIZED STOCK RETURNS, 1928-1991
Distribution of Market Returns
The risky nature of the stock market causes many people to mistakenly view it as a form of gambling. Yes, the outcome is uncertain and, as in a casino, you can lose your money. But in the stock market, the “house” doesn’t take a cut (although your broker or management company certainly will). On average, you will lose money in a casino; on average, you will win money or earn some positive return in the stock market (e.g., the +12% average noted above). In either case, the longer you “play,” the more certain these outcomes are. Also, unlike the potentially disappearing bankroll you take into the casino, there is no way the value of your diversified stock portfolio or fund will ever go to zero (even though any individual stock might).
Let’s have a look at the historical data on market gains and losses—it is quite interesting and instructive. There were 792 months of market return data between 1926 and 1991; also, daily data were analyzed from the period July 1962 to December 1991. The results are tabulated in Table 1-1. Almost 55% of the daily returns were positive—in a typical 22-day month, the market would have had 12 up days and 10 down days. For longer periods, note the increasing probability of a gain in the market over that period.
The market tends to rise over time. Over just a brief instant of “market time,” this trend is indiscernible. Over a full day, you can see the tendency, but the random “bounce” around the trend still causes a large number (45½%) of down periods. But as we allow more time, the upward trend compounds, while at the same time the random bounces average each other out. So as time increases, we are more assured of getting a positive return out of the market. This characteristic of the market explains the typical advice from investment advisors to put into the stock market only your “five-year-andout” funds. That is, if you might need access to your funds within the next five years or sooner, it may not all still be there (if invested in the stock market) due to risk of loss; but funds invested for longer periods are less likely to experience a loss.
TABLE 1-1 Counting the Stock Market’s Ups and Downs
We can also look at the actual distribution of returns over various time periods to develop a better sense of the risk of the marketplace. A histogram, or bar chart, of annual returns is shown in Figure 1-5, which has a different format from the previous ones; now the annual return is shown along the horizontal axis. The number of times that a particular return occurs is on the vertical axis. The annual returns are grouped into ranges of five percentage points. Reading from left to right, we see that there was one year during which the return was below −40%, one year when it was between −35% and −30%, and two years when it fell by −30% to −25%. You can verify this by looking again at the time series of annual returns in Figure 1-3expectexpectationon aver age