The expected return on your investments could dictate some pivotal spending choices you’ll need to make with your money. At some point, for instance, you may be faced with the dilemma of whether to use money in excess of your fixed expenses to pay down debt or to put it towards your investments for potentially greater long-term financial gains.

Unfortunately for investors desirous of order and predictability, past performance does not guarantee future results. Given their volatility and inconsistency between various time frames, the market’s historical returns should only be a minor consideration for an investor.

Driving that point home, a chart published by the New York Times illustrating the average annual real return of the S&P 500 index during every year between 1920 and 2009, demonstrates the great inconsistencies and volatility of market returns throughout history; averages vary widely based on their starting and ending points.

With that major caveat, historical annualized total returns may be a useful indicator to gauge likely returns (particularly when comparing among different investments).

When it comes to quantifying an investment or portfolio of investments’ return, how you go about it can give you considerably different results.

There’s the simple average, or arithmetic mean, determined by adding each year in the series’ growth or loss and dividing it by the number of years, but for our purposes this approach is inaccurate for a couple reasons: One, it assumes that the returns from each year are independent from one another—but if you lose money during one year you’ll have less money to invest in the next year and vice versa; each year’s net loss or profit affects the ensuing year’s potential returns. For instance, losing all of your capital in one year prevents you from earning returns on it during the next. Two, it fails to consider the effects of compounding.

#### Compounding

Compounding occurs when an asset generates earnings from previous earnings. Interest-bearing bank accounts are prime examples; accrued interest is added to the principal (original amount), then becoming the new basis from which future interest is calculated. Compound growth takes place in investments as well, as in the case of dividend-paying stocks—when you choose to reinvest their dividends to purchase additional stock shares, you’re inciting the magic of compounding.

For a more accurate picture, we’ll need to use the “geometric average,” also termed “annualized total return” or “compounded annual growth rate (CAGR),” which is the average return of investments over a certain period of time assuming reinvestment of any dividends. This value is usually a percent or two lower than the arithmetic mean/simple average.

To calculate it you’ll need to know two variables: the returns for a given period of time and the time frame during which the investment was held. To run the calculation, add one to each number (to avoid any problems with negative percentages), then multiply all the numbers together and raise the product to the power of one divided by the quantity of numbers in the series. Subtract one from the result, and you’ve got the annualized total return.

“Annualized returns” are simply investment returns held for a period other than one year, scaled to one year. Unlike annualized total return, their calculation doesn’t factor in the reinvestment of dividends (leaving them out altogether). These are particularly useful for comparing the returns of different assets held for varying amounts of time. Sometimes annualized return is used synonymously with annualized total return, but note the distinction between the two.

Note that conventional individually purchased bonds do not offer compounding; they generally pay coupons (interest) at set intervals and return the principal upon maturity. Some types of bonds (series I and EE savings bonds, as well as zero-coupon bonds) do have a compounding feature, in which the coupon value is added to the principal from which future coupon payments are calculated. When investing through a bond fund, however, you’ll have the option to reinvest bond interest—in that case, fund managers use your interest to purchase additional bonds, producing a similar outcome.

#### Average Inflation

The Federal Reserve Bank of Cleveland reports that its latest estimate of 10-year expected inflation is 1.90%. However, it was at about 3% throughout the 1900s, and a Morningstar article reports it as having averaged 3.4% between 1914 and 2012. The 12-month inflation rate averaged over the last 12 months leading up to February 2017 was 2.7%. It’s more prudent to err on the side of caution when it comes to planning; consider using a more conservative estimate of at least 3% when factoring in inflation into a calculation of expected returns.

#### Fees

The 2016 Investment Company Institute Factbook states the average mutual (including both actively and passively managed) fund fee is 0.68%.

According to Vanguard, the industry average ETF expense ratio is 0.53%, while Vanguard’s is 77% lower, at 0.12%, as of December 2015.

A 2016 Motley Fool article provides that the average expense ratio of index funds is 0.11%, and 0.84% for actively managed funds.

#### Taxes

Capital gains (profits over the original price of an investment, or its “cost basis”) are taxed at either the short- or long-term capital gains tax rate. Trading shares held for one year or less incurs the short-term capital gains tax rate, which is simply your ordinary income tax and higher than long-term capital gains tax rate, which applies to investments held for more than a year. Your taxation will depend not only on how long you hold the investment, but on the type of investment (some bonds are exempt from state and/or federal taxes, for instance), whether you’re investing from a tax-sheltered retirement or other account, and your individual tax situation (income, whether you’re married, etc.).

The “nominal rate of return” is that before taxes, inflation, and fees are adjusted for.

The “real rate of return” considers inflation and is thus provides a more realistic picture. To calculate it, use the following equation:

real rate of return = (1+ nominal rate) / (1+ inflation rate) – 1

Or just subtract the current inflation rate from the nominal rate of return for an approximation.

The real rate of return, however, does not include taxes; the “after-tax rate of return” is a separate component. However, there’s also the “after-tax real rate of return,” meaning (as you probably can guess) the return after both inflation and taxes. You should also subtract fees, which can take a substantial bite out of your investment returns.

#### Current Yield of Bonds

It’s nearly impossible to make an accurate prediction of bond returns in less than a year. If interest rates skyrocket, the resale value of bonds plummets due to the inverse relationship between interest rates and bond prices.

But if you’re planning to hold bonds for a longer period of time, their current yield is a good indicator of their returns, according to Vanguard founder John Bogle, who said that since 1926 “the entry yield on the 10-year Treasury explains 92% of the annualized return an investor would have earned over the subsequent decade had he or she held the bond to maturity and reinvested the coupon payments at prevailing rates.” Similarly, 90% of the Barclays U.S. Aggregate Bond index’s 10-year returns from 1976 to 2012 is explained by entry yield, according to the Pacific Management Company.

“Current yield” refers to a bond’s annual earnings divided by its current market price.

#### Historical Performance of Stocks

Between 1926 and 2015, stocks returned 10.1% (that’s the CAGR) before inflation (as well as taxes and fees), based on data from several bond indexes. Inflation averaged about 2.96% between those years, making the real return (inflation adjusted) about 7.14% (note that’s before taxes and fees).

Similarly, Christine Benz, director of personal finance at Morningstar, reports the average annualized return of the S&P 500 index over the 1915–2015 time frame as having been 10% (before inflation), and that the 20-year period preceding 2015 experienced similar returns.

Moneychimp provides a calculator for CAGR of the S&P 500 stock index that employs data from Nobel Prize winning economist Robert Shiller and Yahoo! Finance. Using the tool, I found that, over the past 20 years (between 2006 and 2016), the S&P’s CAGR (before inflation, fees, and taxes) was 7.7%. With inflation, it was 5.72%. From 1950 through 2016, the before-inflation CAGR was 11.92%, and 9.65% after inflation. From 1871 through 2016, the before-inflation CAGR was 9.07%, and 6.88% after inflation.

#### Historical Performance of Bonds

Between 1926 and 2015, bonds returned 5.4% before inflation (as well as taxes and fees), based on data from several bond indexes. Inflation averaged about 2.96% between those years, making the real return (inflation adjusted) about 2.44% (note that’s before taxes and investment fees).

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