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Invest Today For A Better Tomorrow

The Miracle of Compound Interest

Why Most Investors Fail to Achieve This Ideal

Seeing the miracle of compound interest propel Jill, with a very middle-class wage and modest savings level, to millionaire status by the time of her retirement, we might wonder why so many retirees are struggling. This question brings us to the second reason Jill is sipping piña coladas on a beach while Average Joe lives from Social Security check to Social Security check. The dirty little secret of the investing world is that even diligent savers like Average Joe largely fail to realize the ideal of returns that compound at the rate of the overall stock market.

Although a portfolio invested in the broad stock market would have increased at a 10% average rate over the last century, the average equity, or stock, investor has seen returns that significantly lag this rate. Over the past 20 years, data from DALBAR, a financial research company, indicate that the average equity investor’s return was about 4%, more than 5% below the return of the overall stock market. That’s less than half!

There are two reasons why the returns of the average investor fall far short of the market:

1. Fees. Whereas Jill paid relatively few fees, some 2% of Average Joe’s assets disappeared into the hands of a financial advisor, investment manager, broker, or some combination thereof every year. Without these fees, Average Joe’s portfolio would have been worth $432,000 instead of $309,000 at retirement, even with his late start.

2. Poor investment decisions. Historically, investors have been carried away by optimism when times are good and by pessimism when times are bad. The result is herd behavior, with money moving into stocks just in time to capture a market crash, and money moving out just in time to miss the start of a bull market. For instance, in 2000, investors added $325 billion to equity mutual funds, or bought into the market, at a time when the S&P 500 (an index that serves as a benchmark indicator of the overall U.S. stock market condition) was high, with an index level in the range of 1400 to 1500. In 2002, investors sold a net of $12 billion when the S&P 500 was low, in the range of 820 to 1170. If he had made fewer investment mistakes, Average Joe’s portfolio would have been worth $623,000 at the time of his retirement, even with his late start.

Each of these factors can really be attributed to one thing: financial illiteracy. Simply put, the average investor lacks the confidence to manage money on his or her own and lacks the ability to achieve even market-level returns. To put the cost of financial illiteracy into perspective, think of the result of the parable above. Jill and Average Joe were both alike except that Jill took the time to become financially literate at a young age, and Joe did not, pushing off savings until he was at a stage where he could hire an advisor. To Average Joe, financial illiteracy seemed to “cost” only 2% a year — far less than he was making on his investments. But over the course of his lifetime, his ignorance would cost him some $500,000 in lost wealth. Figure 3 concludes this chapter by looking at the dramatic effect that financial illiteracy can have on a retirement portfolio.

Figure 3 – Joe’s refusal to save during his 20s and investment mistakes throughout his life left him with about 1/3 of the retirement wealth of average Jill, despite their similarities

A Note About the Return Figures Used

In several places in this book, examples with numbers are provided to illustrate a point. These numbers should not be taken literally. Where possible, I have based them on real historical data – for instance the stock market really has returned an average of 10% a year over the last 150 years. Nobody can argue with that – it is simply a fact.

However, for the sake of illustrating the relevant point and not getting bogged down in complexity, I often assume that a return is constant, when, as you can see in Figure 2, returns can vary greatly from year to year and even decade to decade, and nothing is certain in the stock market. An example showing a constant 8% return that is used to show the power of a tax-free account should not, for instance, be taken to mean that you can get constant 8% returns anywhere – you clearly cannot in 2013.

Similarly, the point of this chapter is not to argue that you should be able to double your money every seven years like clockwork, but to point out that because of the amazing properties of compound interest, a seemingly small annual return can really add up over time. The crux of this chapter is true whether returns average 4%, 6%, 8% or 20% in the future – I chose 10% because it is the data-point that we actually have from history.

Further Reading

• Predictably Irrational, by Dan Ariely, talks about the psychology behind many of our poor investment decisions in a manner that is friendly for the layperson.
• Stocks for the Long Run by Jeremy Siegel and Triumph of the Optimists by Elroy Dimson both discuss historical stock market returns in detail.

At its most basic level, an investment represents an exchange between two parties – one who needs money now in order to build something that will generate money in later years, and another who has money now but would like to postpone using it until the future. Stocks and bonds represent two different ways of structuring this kind of across-time agreement. Secondary markets like the New York Stock Exchange allow investors to “trade” their initial investments to others in exchange for cash. The intrinsic value of any investment is just the future income stream that it will produce, discounted back to the present to account for the time value of money.

What an Investment Really Is

In a modern world complete with a litany of complicated investment options, it is easy to lose sight of what an investment in the financial markets actually represents. It can be instructive to imagine what things would have been like in a simpler time and place – an ancient town where “Ted” and “Bill” are two farmers and neighbors.

In our scenario, Ted’s farm is in the land of plenty. He has had several good farming years and has more food stockpiled than his family will be able to eat. He would like to be able to exchange food today for food in the future, when he might not be as lucky in his harvest, or as able to work.

Bill is just starting out, and would like to spend time working on enlarging the farm and building a new barn so that he can expand his operation in future years in order to be more like Ted. However, if he spends his time enlarging the farm he will not be able to harvest his crops this year. This would not make Bill’s hungry wife and kids very happy.

Since Bill needs to obtain extra food now in order to produce more food later, and Ted has extra food now and would like to get more food later, it seems that a mutually beneficial trade should be possible. But the problems in structuring this trade are significant, since it is taking place across time. Ted wants to be sure that he will get as much or more food in the future as he is giving up now. Otherwise he could grind or dry his corn, put it into storage, and lock it away from Bill’s hungry children. Ted also naturally worries that Bill will just run off with the extra food and never deliver on his end of the deal. Finally, Ted wonders whether there are other farmers like Bill, in towns far away, who might give him a better deal.

For all their complexity, the modern financial markets evolved to solve precisely these kinds of age-old problems. In the next section, we will look at how stocks and bonds represent two different ways that Bill and Ted could have structured a mutually beneficial agreement.

Explaining Stocks and Bonds

The first way that Ted and Bill might have decided to structure their arrangement is a simple “pay you back later” agreement, equivalent to saying “Can I borrow your car? I promise I will bring it back in two hours.” To make the deal attractive for Ted, Bill might offer to give him an additional three bushels of corn at the end of every year until the debt has been paid off ( “Can I borrow your car? I’ll fill it up with gas before I bring it back”). So Ted would receive yearly corn payments in addition to the return of his initial investment at the end of the loan term.

If Ted and Bill had structured the arrangement in this way, they would have created something similar to a bond. Today, bonds are a type of debt that represents an IOU from a user of money (the “debtor”) such as a company or government, to a provider of money (the “creditor”) such as an investor. In exchange for immediate use of the creditor’s money, the debtor agrees to make a periodic interest payment, as well as to return the full amount owed at the end of a fixed term. Creditors can make a positive return over the course of the investment because they get their initial investment back at the end of the term, and they receive interest payments in the mean time. For our example of Bill and Ted, let’s say the term is three years. Table 1 shows the two farmers’ actions over that time.

Ted and Bill could have also structured their arrangement another way. Ted could provide Bill with 100 bushels of corn in exchange for a portion of the ownership of the new farm, say 10%. This way, Ted would be entitled to 10% of the future production of Bill’s farm. If the improvements to the farm were successful, Ted could receive much more corn than he initially gave up, earning a positive return on his investment. If the improvements were unsuccessful, he might end up receiving less than he initially gave Bill. This kind of arrangement allows Ted and Bill to share in the risk of the project, and is similar to a stock. Table 2 shows each man’s actions in a stock-like agreement, where Ted is investing in Bill’s “company.”

There are a couple reasons Bill and Ted might prefer the “stock” arrangement to the “bond” arrangement. If the farm improvements Bill was planning were relatively risky – for instance, if he was building a new kind of production machinery and there was a chance it would not work as planned – he might prefer the stock arrangement since the payments he would have to make to Bill would vary with the success of the project, eliminating his personal risk of not being able to make a payment. For his part, Ted might also prefer the stock arrangement since it gives him the potential for a greater return if the project goes well. With the bond, Ted had the security of knowing that he would at least get his money back (we will assume for now that Bill will not default on the loan) plus some small interest payments, but with the stock arrangement he has the upside potential of earning much more corn than he invested.

Today, stocks are certificates issued by companies when they do not have the cash on hand to build a new factory, launch a new product, or otherwise invest in their business. In exchange for providing needed money, investors receive partial ownership of the company. If the company makes profits in the future, it will give a portion of its earnings to its owners in annual or quarterly payments known as dividends. By purchasing a stock, an investor has the opportunity to make a positive return over the course of the investment if the total dividends received from the company are greater than the value of his or her initial investment (this is assuming the investment is held forever; we will get to secondary markets in a bit).

Thus far, we have assumed that the circumstances for Ted and Bill do not change between the time they enter into the agreement and the time the agreement is complete. But imagine that shortly after giving his surplus food to Bill, Ted’s farm is overrun by corn-eating locusts. He could try to get his food back from his neighbor, but Bill has already held his fields fallow for a year, and there is not enough to feed both families. A solution to this problem could be for Ted to sell his contract with Bill to a third farmer, “Jane,” who also has a surplus of corn. Jane would give Ted corn now in exchange for receiving future corn payments from Bill.

The modern equivalent of this kind of re-selling of contracts takes place in secondary markets like the New York Stock Exchange. Secondary markets for financial contracts let an individual who initially invested in a stock or bond sell it to another individual that would like to take it over. The prices for stocks and bonds that are frequently quoted in newspapers and on the Internet are simply the most recent price at which these secondary exchanges between individuals are taking place.

One downside of both stocks and bonds is that many individual investors do not have enough money or time to manage a very large portfolio of them. Mutual funds arose as a solution to this problem. A mutual fund pools together money from many different investors and invests this larger pool in a portfolio of stocks. Each investor in the mutual fund owns a portion of this portfolio and receives a portion of any income or investment gains. Mutual funds are managed by a professional investor who is usually employed by a company like Fidelity or T. Rowe Price.

Where the “Value” of an Investment Comes From

Often, commentators will talk about a stock or bond as being particularly “overvalued” or “undervalued.” Such a description poses the question of how to define “fair value.”

The theory of intrinsic value says that an investment’s price should equal the value it would have to a buyer who planned to hold it forever (even though, with the advent of secondary markets, most investors do not actually do so). Investors who plan to hold a stock or bond forever are not concerned about what the asset is trading for on secondary markets, they are simply concerned with the value that they will receive from the annual or semi-annual interest, or dividend payments. Thus the value of a stock that is correctly priced today should be the present value of its future dividends.

The idea that a string of dividends going forever into the future has a “present value” seems a bit strange at first. But it makes complete sense in the context of what economists call the time value of money. The basic idea is that receiving $1 today is worth more than receiving $1 five years from now. You can think about this in three different ways:

1. If you had a dollar today you could invest it in a guaranteed bank account or certificate of deposit (CD).
2. You can buy more things with a dollar today than you will be able to with a dollar five years from now. This is because of inflation, the slow rise in the cost of living over time. For instance, a dollar in 1970 bought four loaves of bread; today it will not even get you half a loaf.
3. If you are human, you probably would prefer to spend a dollar today, even if it could be used to buy the same things five years from now. Most of us prefer immediate gratification to delayed gratification. Given the choice of eating cake now or eating cake one week from now, we choose now. Which is not to mention that many of us have to spend money today for things like eating, which cannot be delayed indefinitely.

Because dividend payments received in the future are worth less than those received today, we need to apply a discount rate to them in order to express what they are worth to a rational investor today.

If we know or can observe what the time value of money is, than we can place a dollar value today on the promise of $1 five years from now. In doing so, we are “discounting it back to the present.” And if we can place a current dollar value on the promise of $1 five years from now, then there is no reason we cannot place a current dollar value on any stream of future dividends or interest payments.

This is precisely what is needed to value a stock, bond, or any other kind of investment – estimate the income the investment will provide at each year in the future, and discount it back to the present at an appropriate time value of money.

A good estimate for the time value of money today is the interest rate on a very safe investment, such as U.S. Treasury bonds (IOUs from the U.S. government). There is a kind of Treasury bond known as a zero-coupon bond. If you purchase a zero-coupon bond, such as a U.S. savings bond, you receive a guaranteed amount of money at a specified time in the future, but you do not receive any interest payments until then. Because of this, the price of a zero-coupon bond that will pay us $1 ten years from now will be much less than $1 today, and this price is just the time value of money. For instance, if a ten year zero-coupon bond that pays $100 at maturity is selling for $60 today, then that means that $100 ten years from now is equivalent to 60 of today’s dollars.

In the Bill and Ted example, the intrinsic value of Ted’s investment will always be his best guess on how many bushels of corn Bill will give him in the future. This would vary with the probability of success of the project and/or Bill’s credit worthiness. In today’s markets, intrinsic value equates to the estimated future dividend or income stream of a company, discounted back to the present to reflect the time value of money and the riskiness of the investment.

Why the Markets Move Around So Much More Than You Would Think

It may seem difficult to explain the wild gyrations of the stock market in the context of a theory that says stock prices should, in principle, never diverge from their intrinsic value. Large market volatility can be a result of three factors.

First, it is exceedingly difficult to estimate what the intrinsic value of a company is, since this rests on estimating profits forever into the future and discounting them back to current dollars at an equally uncertain time value of money. Estimates can change dramatically based on changes in technology, competition, the regulatory environment, geopolitics, the economy, estimates of future inflation, and the individual preference for money now vs. later. Since we live in a dynamic world where all of these are changing on a daily basis, rational estimates of intrinsic value are certain to change with time.

Second, the markets are composed of human participants and may not be immune to emotional factors such as fear and greed. Human emotions may have a particularly large role today because the average holding period of a stock has shrunk to only four months according to the Economist. This short holding period creates an incentive for market participants to play what prominent economist John Maynard Keynes referred to as a “beauty contest.” This tendency is an especial temptation for professional fund managers and others who are judged by short-term measures such as the performance of their fund over the past quarter. The idea is that the markets can, in periods of intense speculation, come to resemble a game where the objective is not so much to figure out which companies are the most valuable, but instead to figure out which companies most investors will think are the most valuable. Rational investors may buy into shares trading at prices that are much higher than any reasonable estimate of their intrinsic value if they think that others will be willing in the future to purchase those shares at even higher prices still. This kind of dynamic can create market volatility independent of changes in the fundamentals of a business or the economy. Of course, perception can sometimes become reality…

On that note, the third important piece of the volatility puzzle may come from what billionaire hedge-fund speculator George Soros describes as reflexivity. The idea is that movements in stock prices do not just reflect estimates of the future, but they can, in fact, directly impact the future. A recent example of this phenomenon is the 2008 financial crisis. Falling prices on investments like stocks at first reflected lower intrinsic value of assets as a result of deteriorations in the real economy. But falling prices then caused even further deteriorations in the economy because households and businesses looked at the lower values of their stocks, bonds, and houses, realized they were not as wealthy as they once had thought, and cut spending. When everyone cut spending at once, the economy deteriorated further, causing even more pressure on investment prices. Reflexivity can create markets that are susceptible to wild jumps from one extreme to the other.

Further Reading

• Investopedia.com has a nice tutorial on the time value of money for those confused by the explanation in this guide.
• For those interested in learning more about the intrinsic value concept, Professor of Finance at the Stern School of Business at New York University Aswath Damodaran has posted slides on the subject.