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You have probably heard of the time value of money in the context of compounding.  The real value and amazing thing about investing over time is that returns really can add up quite nicely.  For example, if you are 25 years old and invest $10,000 in an S&P 500 index ETF that earns 8% per year you will end up with $49,610 at the end of 20 years.  That is the amount you will have if you do not invest any additional money.  What does this mean exactly?  If another person starts investing at age 45, and invests in the same increments as you do from then until retirement, they will need to have $49,610 to invest at the beginning to keep up with you.  The formula for calculated any terminal value for an investment, given a starting point, is as follows:  x = start($) * (1+ i)^t  where x is the terminal value, start($) is the amount of money to start with, i is the annual interest rate, and t is the amount of years.  As you can see from the equation, it is not linear.  This means that your money will grow to a certain amount after year 1 and then you get interest/capital gains on that year 1 amount.  The terminal value is not start($) * (1+i) * 2.  When you hear about the power of compounding, that is the normal way it is presented and will hold at all times.

The power of compounding is a double-edged sword though.  What do I mean by this?  Here is an example.  If you start out with $1,000 and the stock market goes down 10% in year 1 and up 10% in year 2, how much money do you have?  Well, you have $1,000, right?  That is not the correct answer but most common response given.  Let’s go through the math.  If you start with $1,000 and the stock market goes down 10%, you have $900 at the end of the year ($900 * (1+10%)^1).  If the stock market goes up 10% the next year, you have $990 ($900 * (1+10%)^1).  So at the end of year 2, your original investment of $1,000 has decreased by 1%.  Why?  Well, you must remember that the power of compounding is not a linear equation.  This fact means that you cannot just add the two returns together and divide by two.  When you are calculating investment returns in that manner, you are calculating what is referred to as the arithmetic return.  The arithmetic return for our aforementioned example is 0%.  Well, arithmetic returns are really used to think about what the expected return of the financial markets will be for any given time period.  However, you really care about how much money you will actually have in your brokerage account at the end of a given time period.  You can calculate this using the geometric return.  The geometric return will let you know your terminal value.  Your terminal value is a fancy way of saying ending balance.  At the end of the day, do you want to know your arithmetic return or your geometric return?  Personally, I want to know how much money I actually have.  Note that an arithmetic return will always differ from a geometric return whenever a negative return is encountered over the time period.

As you can see, the power of compounding really matters both in a positive sense and in a negative sense.  Think about the return of the S&P 500 back in 2008.  The S&P 500 was down roughly 40% in 2008.  Let’s use our math again.  If you had $1,000 on January 1, 2008, you would have $600 on December 31, 2008.  How much of a return would you need to get back to even?  Well, we already know that 40% is not the correct answer.  The correct answer is that you need to earn back $400 which is equivalent to 66.6%.  Now earning 66.6% in the financial markets in a single year is very rare.  Thus, your money will need to compound for a number of years to get back to even.  How long do you ask?  Well, the long-run average return of stocks is approximately 7.5%.  If we use are formula for terminal value, you will find that it will take a little bit longer than seven years.  This example illustrates one reason why Financial Advisors will recommend that you diversify your investment portfolio amongst many different type of investments.

Well, we can take that one step further though.  You will encounter some Financial Advisors that will explain how the S&P 500 example from 2008 works in the context of how losing principal can hurt you.  However, they forget one important item.  Remember that, when you are planning for your retirement or any other goal, you start with an assumption of how much you will earn from your investments.  Let’s say that your Financial Advisor tells you that he/she designed your portfolio such that it will earn 8% per year given your risk tolerance and the investments he/she recommends.  Why is that important?  Well, you should think back to our 2008 example.  If you started out with $1,000 at the beginning of 2008, you would expect to have $1,714 at the end of seven years if the stock market earned the assumed 8% figure per year.  Well, in our example above with a 40% loss in 2008, you would need to earn 7.5% per year just to get back to even over a number of years.  How much would you need to earn to get to $1,714 at the end of seven years?  You would need to earn 16.2% per year.  How long would it take you to get to $1,714, if you lost 40% in the first year, but earned 8% every year thereafter?  It would take you about 13.5 years.  Why is this important?  It is important because significant losses encountered in the stock market along the way will drastically affect your ability to reach your goals.  Additionally, they will test your “intestinal fortitude” (i.e. guts).  You may have been tempted to sell all your stocks at the end of 2008 and then missed out on the incredible gains from 2009 to the present day.  Now everyone says that they would never sell after a major decline, but that is just a hypothetical scenario.  What would you do if you had $1,000,000 in 2008 and wanted to retire in 2010?  In our scenario above, if you had invested all your money in an S&P 500 index mutual fund, you would have started out with $600,000 in 2009.  What would you do then?

When a Financial Advisor asks you about your risk tolerance and long-term goals, you must think about actual dollars and cents.  Move past a simple questionnaire and look into the mathematics of compounding now that you understand the formula.  Most Financial Advisors will prepare your portfolio recommendations based upon the arithmetic long-term returns of the financial markets in combination with your answers to the risk tolerance questionnaire.  Financial Advisors tend to ignore geometric returns.  Investors tend to overstate their risk tolerance.  Now that you know more about the “power” of compounding you should be able to better ask questions.  Remember you should not be fearful of investing.  Rather, I present this information to assist you in making better portfolio selections and more realistic assumptions regarding returns and assessment of your risk tolerance.