Why Lesson 2 is important
The power of compounding assumes its full glory (and your investments reach their full girth) as the i,or the rate of return, gets larger, and the n,or the length of time, gets longer. The andis important! Value investors look for a few more ipoints of return andto hold the productive investment for as many nyears as possible.
Because nis an exponent, it exerts the greatest power and influence on your investing portfolio. Time is an investor’s best friend. As Warren Buffett says,
“Time is the friend of the good business, and the enemy of the poor one.” No wonder value investors tend to be long-term investors! The upshot? Find the best possible iand then let nhappen.
Lesson 3: The Amazing Rule of 72
No investor in the history of the world understands, or has applied, the principle of compounding to a greater degree and with more success than Buffett. Yet he reportedly does most investing math without a calculator.
Does he possess a 2-gigahertz mind that’s able to grind out multiple power and exponential calculations faster than you can say Coca-Cola? Hardly.
Not to say that being the gifted individual that he is, he couldn’tperform so many rapid-fire calculations in his head. But he doesn’t.Instead, he uses one of the most useful general rules in investing, maybe in all mathematics, as a computational shortcut. It’s known as the Rule of 72.
How the Rule of 72 works
The Rule of 72 is based on compounding formula mathematics. With the Rule of 72, you can quickly estimate the rate of return or time period needed to doublea sum of money with compounding. If you know the rate of return, you can compute the time period and if you know the time period, you can compute the approximate rate of return. Here it is:
Number of years to double an investment at a given return rate:
= 72 divided by the rate of return (as an integer: the rate ×100) Return rate required to double an investment over a given number of years:
= 72 divided by the number of years
Here are some examples to make the concept clearer:
At 12 percent, it takes six years to double your money (72/12).
To double your money in eight years, you must earn a 9 percent rate of return (72/8).
At 10 percent, how many years does it take to quadruple your money?
Answer: It doubles in 7.2 years (72/10), so quadrupling would take twice that long, or 14.4 years.
If your best friend brags about having bought a house for $150,000 that’s now worth $600,000 and he’s had it for 10 years, what is the rate of return? Answer: It doubled twice ($150K to $300K to $600K) in 10 years, or once every 5 years. So (72/5) gives a 14.4 percent compounded rate of return. Not bad at all, but as a sharp investor you could well have beaten your friend in the stock market! Not to mention impressing him or her by doing this calculation in your head!
Return rates done right
Just what is the rate of return on an investment? It depends on how it’s calculated. Take a look at the example just presented for the Rule of 72. Your friend brags about buying a house for $150,000 and selling it 10 years later for $600,000. He may call that a 300 percent return and, because it occurred over 10 years, boasting of an average of 30 percent per year. On the surface, that’s correct.
But when evaluating the home purchase as an investment (compared to other investments), one must include the compounding effect to have an accurate, apples-to-apples comparison. If that $150,000 were invested 10 years ago in such a way as to allow returns to compound, what rate of return would have produced $600,000? As approximated using the Rule of 72, the compounded
rate of return is only 14.4 percent. Although not bad, 14.4 percent doesn’t make headlines, particularly compared to long-term stock market returns of 11 percent annually.
The compounded rate of return is sometimes called the geometricrate of return — in contrast to the straight average approach of simply dividing the total return by the number of years (as in 300 percent divided by 10 equals 30 percent annually). So, how do you calculate true compounded, or geometric, rates of return? There is a formula:
Compounded rate of return = [(Ending value/Beginning value)(1/n)]–1 where nequals the number of years.
In the example, $600,000/$150,000 is 4. Take 4 to the 1⁄10thpower (use your calculator) and get 1.149. Subtract 1, and get 14.9 percent, which is not exactly equal to the Rule of 72 result, but remember that the Rule of 72 is an approximation. You’ll have fun at cocktail parties telling people what they reallymade on their investments.
Why Lesson 3 is important
The Rule of 72 gives tremendous power to make fast calculations and deci- sions. It helps you to quickly compare investing alternatives and to speed up investing decisions. Not only that, it can help you figure out how long it will take to become a millionaire, and it’s pretty good for impressing your friends.
Lesson 4: The Frugal Investor, or How Being Cheap Really Pays
What investor hasn’t heard the advice “buy low and sell high”? The principle behind this cliché is so obvious that one can hardly write about it. But in the irrationally exuberant markets of 1999 and 2000, this old standard gradually gave way to “buy high, sell higher.” Traders (and novice investors experienc- ing the markets for the first time) bought stocks because they were going up, defying value investing logic.
What’s the problem? Well, simply, the higher a price you pay for a stock, the less likelyit is to achieve a high rate of return. Suppose that a stock has an intrinsic value of $75. If you pay $100 for it, you’re essentially betting that something good will happen to dramatically increase intrinsic value — or that some greater fool is out there to pay $110. True, it may happen, and it seemed to happen with regularity during the bubble years. You may get a 10 percent or 20 percent return on the investment.
But suppose that you were to buy the same stock at $50 as a value play, mean- ing that you think it’s undervalued. The chance for a 50 percent return — reverting to intrinsic value — is much higher than with the at-value or overvalued $100 stock.
Keep your “i” on the ball
Value investors always look for that opportunity to achieve superior i (think back to the formula in Lesson 1).You achieve superior iby buying a stock with good fundamentals, includinggrowth. So you get the growth rate — perhaps 6 percent, maybe 8 percent, or even 10 percent. But as a bonus, you also get the return to intrinsic value, which can turn 6 percent, 8 percent, and 10 percent returns effectively into 12 percent, 14 percent, 16 percent, and higher returns. The lower the price paid, the higher the likelihood of above- average returns. This idea comes straight from the teachings of Ben Graham and the practice of Warren Buffett.
Buffett always tries to find a pricing situation leading to an extra 2 percent or 3 percent or more for his investing return, or i.Remember Table 4-1? This is a very good thing.
How much does buying cheap help?
Take a look at Table 4-2. Note how long-term profits jump as the rate of return grows beyond the market average and time has an opportunity to work its magic. An investor consistently beating the market by 2 percent would achieve 20 percent greater return in 10 years ($3,106/$2,594), 43 per- cent in 20 years, and 72 percent in 30 years. An investor beating the market