Is there a term that better describes a compound annual growth rate (CAGR) when it is negative?
"Not sure why CAGR is a problem for both directions. I used to be a physicist, and, when I taught classes in graduate school, students always wanted to use the terms ""accelerate"" and ""decelerate"" to describe ""speeding up"" and ""slowing down"". But acceleration is just a vector with magnitude and direction. There's nothing special about slowing down that it needs a special name. It's just acceleration in a direction opposite to the direction of motion. I think the same thing applies here. There's nothing special about negative growth rates that they need a special name. Just stick a minus sign in front of the number and you convey the required information." "My experience is in economics, so it may differ from an accounting or personal finance perspective somewhat; that being said, I find it perfectly acceptable to use a term like CAGR when the rate is positive or negative. Economists talk about negative growth rates all the time, and it's universally assumed that growth rates can be positive or negative.1 Ideally, the actual magnitude and sign of the value should be specified by the value itself. The term, whether it's ""growth rate"", some modified version of it like CAGR, or any label in a table or on a graph, should describe the calculation or source used obtain the value. I shouldn't need the name to indicate the sign of the number if the number is present; the name is only there to help me understand the value. Unfortunately, I don't know of any specific term that represents the geometric averaging nature of CAGR and also eliminates the minor potential for semantic confusion. However, I think the minor problem of semantics needs to be balanced against the tradeoff of using a different term that isn't as common, if one were to exist. CAGR is a standard, well-known term that a) allows someone who is familiar with the term to instantly understand the procedure you're using, and b) allow someone who isn't familiar with it to quickly search and find an explanation, since searching for CAGR will numerous simple explanations of how it's calculated. 1. This is different from the concept of economic growth, which is usually assumed to be positive in informal discussions. In economic modeling, many of the first steps in creating a model are symbolic anyway, so ""growth rate,"", ""change in output"", and ""economic growth"" are used interchangeably to describe changes in GDP because the values either aren't known, irrelevant until later in the project, or pulled from data that describes it using one or several of the previously stated terms." Same question had popped up in our office,and we got an answer from one of the senior colleague. He said that we can call it CARC (Compounded Annual Rate of Change).
This is only a rule of thumb. Peter Lynch popularized it; the ratio PE/growth is often called the Lynch Ratio. At best it's a very rough guideline. I could fill up this page with other caveats. I'm not saying that it's wrong, only that it's grossly incomplete. For a 10 second eyeball valuation of growth stocks, it's fine. But that's the extent of its usefulness. Perhaps something else comes with the bond so it is a convertible security. Buffett's Negative-Interest Issues Sell Well from 2002 would be an example from more than a decade ago: Warren E. Buffett's new negative-interest bonds sold rapidly   yesterday, even after the size of the offering was increased to $400   million from $250 million, with a possible offering of another $100   million to cover overallotments. The new Berkshire Hathaway securities, which were underwritten by   Goldman, Sachs at the suggestion of Mr. Buffett, Berkshire's chairman   and chief executive, pay 3 percent annual interest. But they are   coupled with five-year warrants to buy Berkshire stock at $89,585, a   15 percent premium to Berkshire's stock price Tuesday of $77,900. To   maintain the warrant, an investor is required to pay 3.75 percent each   year. That provides a net negative rate of 0.75 percent. In the equity markets, the P/E is usually somewhere around 15.  The P/E can be viewed as the inverse of the rate of a perpetuity. Since the average is 15, and the E/P of that would be 6.7%, r should be 6.7% on average. If your business is growing, the growth rate can be incorporated like so: As you can see, a high g would make the price negative, in essence the seller should actually pay someone to take the business, but in reality, r is determined from the p and an estimated g. For a business of any growth rate, it's best to compare the multiple to the market, so for the average business in the market with your business's growth rate and industry, that P/E would be best applied to your company's income. "The S&P 500 index from 1974 to present certainly looks exponential to me (1974 is the earliest data Google has).  If you read Jeremy Siegel's book there are 200 year stock graphs and the exponential nature of returns on stocks is even more evident.  This graph only shows the index value and does not include the dividends that the index has been paying all these years.  There is no doubt stocks have grown exponentially (aka have grown with compound interest) for the past several decades and compounded returns is definitely not a ""myth"".  The CAGR on the S&P 500 index from 1974 to present has been 7.54%: (1,783 / 97.27) ^ (1 / 40) - 1 Here is another way to think about compounded investment growth: when you use cash flow from investments (dividends, capital gains) to purchase more investments with a positive growth rate, the investment portfolio will grow exponentially.  If you own a $100 stock that pays 10% dividends per year and spend the dividends every year without reinvesting them, then the investment portfolio will still be worth $100 after 40 years.  If the dividends are reinvested, the investment portfolio will be worth $4,525 after 40 years from the many years of exponential growth: 100*(1 + 10%)^40" I would use neither method.  Taking a short example first, with just three compounding periods, with interest rate 10%.  The start value y0 is 1. So after three years the value is 1.331, the same as y0 (1 + 0.1)^3. Depreciating (like inflation) by 10% (to demonstrate) gets us back to y0 = 1 Appreciating and depreciating by 10% cancels out: Appreciating by 10% interest and depreciating by 3% inflation: This is the same as y0 (1 + 0.1)^3 (1 + 0.03)^-3 = 1.21805 So for 50 years the result is y0 (1 + 0.1)^50 (1 + 0.03)^-50 = 26.7777 Note You can of course use subtraction but the not using the inflation figure directly.  E.g. (edit: This appears to be the Fisher equation.) 2nd Note Further to comments, here is a chart to illustrate how much the relative performance improves when inflation is accounted for.  The first fund's return is 6% and the second fund's return varies from 3% to 6%.  Inflation is 3%. Assuming cell A1 contains the number of trades: will price up to A1=100 at 17 each, and the rest at 14 each. The key is the MAX and MIN. They keep an item from being counted twice. If X would end up negative, MAX(0,x) clamps it to 0. By extension, if X-100 would be negative, MAX(0, X-100) would be 0 -- ie: that number doesn't increase til X>100. When A1=99, MIN(a1,100) == 99, and MAX(0,a1-100) == 0. When A1=100, MIN(a1,100) == 100, and MAX(0,a1-100) == 0. When A1=101, MIN(a1,100) == 100, and MAX(0,a1-100) == 1. Of course, if the 100th item should be $14, then change the 100s to 99s. PE can be misleading when theres a good risk the company simply goes out of business in a few years. For this reason some people use PEG, which incorporates growth into the equation. "In double-entry bookkeeping, no transaction is ever negative. You only deal in positive numbers. We ""simulate"" negative numbers by calling numbers debits and credits, where one is the negative of the other. Only a balance can be negative. In this case, Income is a credit account. That means that things that increase your balance are credits and things that reduce your balance are debits. So a gift from grandma is a credit. It's a positive number, and you write it in the credit column. You pretty much never subtract from Income except to correct a mistake. Assets, like a checking account, are debit accounts. Increases are debits and decreases are credits. You routinely have both debits and credits on a checking account, i.e. you put money in and you take money out. Every transaction affects (at least) two accounts: one with a debit and one with a credit. So in this case, the gift from grandma credits income and debits checking. Buying food credits checking and debits expenses." Set your xirr formula to a very tall column, leaving lots of empty rows for future additions. In column C, instead of hardcoding the value, use a formula that tests if it's the current bottom entry, like this: =IF(ISBLANK(A7),-C6, C6) If the next row has no date entered (yet), then this is the latest value, and make it negative. Now, to digress a bit, there are several ways to measure returns. I feel XIRR is good for individual positions, like holding a stock, maybe buying more via DRIP, etc. For the whole portfolio it stinks. XIRR is greatly affected by timing of cash flows. Steady deposits and no withdrawals dramatically skew the return lower. And the opposite is true for steady withdrawals. I prefer to use TWRR (aka TWIRR). Time Weighted Rate of Return. The word 'time' is confusing, because it's the opposite. TWRR is agnostic to timing of cashflows. I have a sample Excel spreadsheet that you're welcome to steal from: http://moosiefinance.com/static/models/spreadsheets.html (it's the top entry in the list). Some people prefer XIRR. TWRR allows an apples-to-apples comparison with indexes and funds. Imagine twin brothers. They both invest in the exact same ideas, but the amount of cash deployed into these ideas is different, solely because one brother gets his salary bonus annually, in January, and the other brother gets no bonus, but has a higher bi-weekly salary to compensate. With TWRR, their percent returns will be identical. With XIRR they will be very different. TWRR separates out investing acumen from the happenstance timing of when you get your money to deposit, and when you retire, when you choose to take withdrawals. Something to think about, if you like. You might find this website interesting, too: http://www.dailyvest.com/ Here is an article that explains this: http://finance.ninemsn.com.au/pfproperty/investing/8123730/negative-gearing-explained. In essence, it is an investment set up to produce near-term losses for tax purposes by means of borrowing without positive cash flow. The investor hopes that despite operating at a loss, the property will appreciate in the long run (and long-term capital appreciation is typically taxed at a lower rate than current income). You cannot use continuous compounding for returns less than or equal to 100% because a natural logarithm can only be taken for a positive amount.  This answer includes the accurate way to ascertain r, for which many people use an approximation. For example, using -20% monthly return for 12 months:- -0.2 -0.223144 0.0687195 Checking: 0.0687195 True Now trying -100% monthly return:- -1. Indeterminate Why?  Because a natural logarithm can only be taken for a positive amount.  So the latter calculation can not be done using (logarithmic) continuous compounding. Of course, the calculation can still be done using regular compounding.  For -100% the results go to zero in the first month, but -150% produces a more interesting result: -1.5 -11920.9 If your question is truly just  What is good growth? Is there a target return that's accepted as good?   I assumed 8% (plus transaction fees). Then I'd have to point out that the S&P has offered a CAGR of 9.77% since 1900. You can buy an S&P ETF for .05%/yr expense. If your goal is to lag the S&P by 1.7%/yr over the long term, you can use a 85/15 mix of S&P and cash, sleep well at night, and avoid wasting any time picking stocks. "Thanks!  Do you know how to calculate the coefficients from this part?:  ""The difference between the one-year rate and the spread coefficients represents the response to a change in the one-year rate. As a result, the coefficient on the one-year rate and the difference in the coefficients on the one-year rate and spread should be positive if community banks, on average, are asset sensitive and negative if they are liability sensitive. The coefficient on the spread should be positive because an increase in long-term rates should increase net interest income for both asset-sensitive and liability-sensitive banks.""  The one-year treasury yield is 1.38% and the ten-year rate is 2.30%.  I would greatly appreciate it if you have the time!" "Not to state the obvious, but whenever an investment is being made, the ""nuts and bolts"" is your return on investment.  Analyzing the rate of return on an investment is the primary factor in any decision.  Ideally, once the actual mechanics of investment and side ""benefits"" are factored out, the goal is to be able to analyze the pure financial return. Usually the biggest problem faced in analyzing various investments is comparing the Present Value of an investment to a series of payments that may be made or received in the future.  When considering the purchase of a large equity, for example, you might be looking at what series of payments are required to purchase the asset.  You can also reverse this and ask, ""What amount of money is equivalent to this series of payments?"" Ultimately, the Present Value of an Annuity is the way to make these comparisons equal.   Fundamentally, the Present Value of an annuity is an amount of money that should, in theory, be equivalent to a series of payments.  There is, for example, technically no difference between $1064.94 today and $100 a month for a year, at an interest rate of 1% per month.  Grant you, most people would be happier with the money now, but that is what interest does - it compensates you for waiting on your money.   You can fire up a spreadsheet and calculate the Present Value as long as you have the monthly payment, interest rate, and number of periods.  Alternatively, you can calculate any one of those missing four variables - and the key is usually to understand what that rate would be in order to compare the investments. Finally, the taxable implication is really just an adjustment to the rate of return. Imagine the following three scenarios: (Obviously the rates are fictional - the goal is to show they are the same). Scenarios 1 & 2 are really just two sides of the same coin.  Using the Future Value formula in Excel = FV(0.5%, 12, -100), you get $1233.56.  In scenario 1, you would have $1233.56 in your bank account.  In scenario 2, your bank would have $1233.56 from you, and you would have $100 less debt per month.  They are equivalent transactions.   Scenario 3 is really just a variation on scenario 2, localized to the United States.  Because the interest is tax deductible, however, the rate of 6% isn't really accurate.  Assuming you had a 25% tax bracket, you'd actually be getting back one quarter of your interest.  Put another way, 7.5% mortgage interest costs you as much as 6% credit card debt. This is how you compare apples and organges - just turn everything into an annuity or a lump sum, using Present Value calculations.   Finally, quick rule of thumb - if you owe taxes in both Canada and the US, your Canadian taxes are probably higher than your American ones.  As such, any tax incentives will be concomitantly higher.  If you only can only use Canadian tax incentives, then look to those incentives, other things being equal." &gt; According to pretty well accepted corporate finance principles.  What are the names of those principles and where can I read more about them and how they apply to huge tech companies?  I'd like more than your word on something as huge as you are claiming. That all my stocks are holding way too much cash and are run by finance morons.