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Investing in Rare Coins....a 62 year analysis.

"Over the last 62 years, this asset category has delivered an arithmetic mean annual return (before inflation) of 10.5 percent with a relatively low standard deviation of 12.3 percent. But the real benefit derived from this asset category lies in its diversification power. Some of its best relative performance is delivered during those periods when long-term bonds perform particularly poorly."

10.5% return before inflation...that seems pretty good to me.


The Financial Times....anyone ever heard of them?

This is a good article to read to your wife....after about 2 hours she should let you buy anything you want.

"Conclusions
As ANA's governor Barry S. Stuppler has suggested, the marketplace for numismatics is both broad and deep, having now reached an aggregate market value in the vicinity of $40 billion (and this figure does not include bullion-based gold and silver coins that would bring the total market value up considerably). It is an active market where single isolated auctions can experience transaction volume over $30 million. Professionalism and initial efforts towards institutionalization have been demonstrated by numismatic investment funds launched by Kidder Peabody and Merrill Lynch and by United Bank of Switzerland's UBS Gold & Numismatics professional consulting division.

Pricing data drawn from the last 62 years of history (1941–2003) suggest an attractive and potentially highly complementary asset category—particularly relative to fixed-income securities and as an offset to inflation. Over this period, rare coins, the S&P 500, and long-term U.S. Treasury bonds have delivered geometric mean returns of 5.52 percent, 7.86 percent, and 1.38 percent, respectively, after adjustment for inflation. But after reflecting their differential standard deviations, we find that rare coins, the S&P 500, and long-term U.S. Treasury bonds have delivered return-per-unit-of-risk of 0.46x, 0.46x, and 0.18x, respectively after inflation adjustment. Rare coins' greatest benefit may be one of diversification. The S&P 500 typically correlates with other common asset categories at a level of between 0.28 and 0.97 (inflation adjusted). In contrast, numismatic investments have delivered correlations across similar asset categories ranging from a far lower –0.21 to 0.29.

Robert A. Brown, Ph.D., CFA serves as Chairman-Investment Management Executive Committee and Chief Investment Officer for GE Private Asset Management, Inc., located in Encino, California."

Comments

  • RWBRWB Posts: 8,082
    Without knowing what coins they selected, it’s just a guess. However ---

    All of the stock aggregates listed performed much better than coins, according to their inflation adjusted analysis. They also omitted stock dividends – something coins do not pay.
  • They pay a different kind of dividend.
  • SonorandesertratSonorandesertrat Posts: 5,695 ✭✭✭✭✭
    So this goes back to ca. 1950. Back then, how many MS/PF 67 coins were there? There were fewer commonly used grades for MS coins. I suspect that much of the long-term price appreciation in rare coins (below five figures) is due to gradeflation.
    How did the average guy who bought MS65 generic Morgans, late-date Walkers, etc in the late 1970's do? These guys are buried in those coins. In today's market, the majority of the collector coins will go nowhere as investments.

    Coins are not fungible. Comparisons with other types of investments (aside from other types of collectibles, like fine art) are pointless. In a roaring stock market, small investors will make money without having to go to research heroics.
    In a bull coin market, most small investors/investor-collectors will lose money (because they didn't buy the right kinds of coins, they didn't buy coins that are nice for their grades, they didn't have a well-thought-out exit strategy, they
    buy at retail and sell at wholesale, etc.).
    Member: EAC, NBS, C4, CWTS, ANA

    RMR: 'Wer, wenn ich schriee, hörte mich denn aus der Engel Ordnungen?'

    CJ: 'No one!' [Ain't no angels in the coin biz]
  • I think you make some good points but as Q. David Bowers has said for decades, people who buy judiciously and know their series do very well over the long term.

    I think that is quite true. And, collector coins are usually defined as MS64 or lower; collector coins aren't usually investor coins.
  • coinguy1coinguy1 Posts: 13,484 ✭✭✭
    "All rare coin pricing data was provided by the following two sources: Handbook of United States Coins with Premium List (the Blue Book) for the annual copyrights 1942 through 1951, and A Guide Book Of United States Coins (Red Book) for 1950 through 2004.2"

    The above, alone, causes me to be skeptical of any published results. And, since I skimmed the article, I certainly might have missed it, but didn't see anything about transaction costs, buy-sell spreads, etc.

    And then there is the thorny issue of subjectivity in grading, shifts in grading standards, etc. And thus, investors buying at one grade, but having to sell at a different/lower one.

    Case in point, I just submitted a 1924 Saint to PCGS for a friend. He had bought it as an MS67 from a large, active dealer, roughly 30 years ago. I told him I thought it would grade MS64 and it came back 64+. And sadly, that is not an especially unusual situation, especially when dealing with uncertified coins.
  • adamlaneusadamlaneus Posts: 6,969 ✭✭✭
    You know? I don't want to derail this thread, but here's my thought on Collectors versus Investors.

    I define a Collector as someone who actually cares about the coins involved.

    I define an Investor as someone who has too much money and no idea what to do with it and is just looking to make more money. Doesn't give a whit about the coin as long as the valuation goes up.


    I define myself as a collector. With too much money.
  • MrEurekaMrEureka Posts: 24,198 ✭✭✭✭✭
    Even if this report is brilliantly compiled, I doubt it will be of much use to anyone but a coin salesman.
    Andy Lustig

    Doggedly collecting coins of the Central American Republic.

    Visit the Society of US Pattern Collectors at USPatterns.com.
  • SonorandesertratSonorandesertrat Posts: 5,695 ✭✭✭✭✭


    << <i>You know? I don't want to derail this thread, but here's my thought on Collectors versus Investors.

    I define a Collector as someone who actually cares about the coins involved.

    I define an Investor as someone who has too much money and no idea what to do with it and is just looking to make more money. Doesn't give a whit about the coin as long as the valuation goes up.


    I define myself as a collector. With too much money. >>





    I agree with this distinction between collectors and investors. But...just because a collector 'cares' about his/her coins doesn't mean that he/she will actually make a serious effort to acquire expertise in numismatics.
    It never ceases to amaze me that people think that they can learn how to grade by looking at images in books or on a computer monitor, or that they will (perhaps over10 years) spend $50,000 on coins but balk at the notion
    that assembling a modest, working numismatic literature collection will help them become more astute collectors.
    Member: EAC, NBS, C4, CWTS, ANA

    RMR: 'Wer, wenn ich schriee, hörte mich denn aus der Engel Ordnungen?'

    CJ: 'No one!' [Ain't no angels in the coin biz]
  • RWBRWB Posts: 8,082
    When you are talking about "investments" it is only about money - anything else is "hobby."


  • << <i>"All rare coin pricing data was provided by the following two sources: Handbook of United States Coins with Premium List (the Blue Book) for the annual copyrights 1942 through 1951, and A Guide Book Of United States Coins (Red Book) for 1950 through 2004.2"

    The above, alone, causes me to be skeptical of any published results. And, since I skimmed the article, I certainly might have missed it, but didn't see anything about transaction costs, buy-sell spreads, etc.

    And then there is the thorny issue of subjectivity in grading, shifts in grading standards, etc. And thus, investors buying at one grade, but having to sell at a different/lower one.

    Case in point, I just submitted a 1924 Saint to PCGS for a friend. He had bought it as an MS67 from a large, active dealer, roughly 30 years ago. I told him I thought it would grade MS64 and it came back 64+. And sadly, that is not an especially unusual situation, especially when dealing with uncertified coins. >>



    Did he buy from a PNG dealer who is still living?
  • 291fifth291fifth Posts: 24,284 ✭✭✭✭✭


    << <i>Even if this report is brilliantly compiled, I doubt it will be of much use to anyone but a coin salesman. >>



    image
    All glory is fleeting.
  • adamlaneusadamlaneus Posts: 6,969 ✭✭✭


    << <i>
    ...just because a collector 'cares' about his/her coins doesn't mean that he/she collector will actually make a serious effort to acquire expertise in numismatics.
    It never ceases to amaze me that people think that they can learn how to grade by looking at images in books or on a computer monitor, or that they will (perhaps over10 years) spend $50,000 on coins but balk at the notion
    that assembling a modest, working numismatic collection will help them become more astute collectors. >>



    I hear you. It is very easy to be lazy; and the internet makes it even easier.

    But it is a fine line for a collector that wants to keep it fun. Go too deep and it becomes work.
    I've had some dealers view me with derision when they discover the level at which I am interested in coin collecting. But I do not care because if I reaffirm the level at which I am happy with collecting, then that is all that matters.
    This forum has helped me understand the various depths of coin collecting and where I do and do not want to go.
    And I like the formatting too. It's easy to read.

  • RYKRYK Posts: 35,796 ✭✭✭✭✭


    << <i>Even if this report is brilliantly compiled, I doubt it will be of much use to anyone but a coin salesman. >>


    Actually, my investment advisor brought this article to my attention a couple years ago (and I did not have to pay him extra to do so in front of my wife).
  • au58au58 Posts: 1,288 ✭✭✭


    << <i>Did he buy from a PNG dealer who is still living? >>



    Can you expound on this, please? Is there some relevance?
  • ColonelJessupColonelJessup Posts: 6,442 ✭✭✭✭✭


    << <i>Even if this report is brilliantly compiled, I doubt it will be of much use to anyone but a coin salesman. >>



    Economists might consider this as the final confirmation of the Kondratieff long wave.
    "People sleep peaceably in their beds at night only because rough men stand ready to do violence on their behalf." - Geo. Orwell


  • << <i>You know? I don't want to derail this thread, but here's my thought on Collectors versus Investors.

    I define a Collector as someone who actually cares about the coins involved.

    I define an Investor as someone who has too much money and no idea what to do with it and is just looking to make more money. Doesn't give a whit about the coin as long as the valuation goes up.


    I define myself as a collector. With too much money. >>



    So then an investor can't be a person of somewhat average means who is looking to diversify his portfolio with no anticipation of making a windfall profit?
  • AMRCAMRC Posts: 4,266 ✭✭✭✭✭
    Let me pick the time slice and I can show ANYTHING to be a great investment. Tulips anyone?
    MLAeBayNumismatics: "The greatest hobby in the world!"
  • adamlaneusadamlaneus Posts: 6,969 ✭✭✭


    << <i>

    << <i>You know? I don't want to derail this thread, but here's my thought on Collectors versus Investors.

    I define a Collector as someone who actually cares about the coins involved.

    I define an Investor as someone who has too much money and no idea what to do with it and is just looking to make more money. Doesn't give a whit about the coin as long as the valuation goes up.


    I define myself as a collector. With too much money. >>



    So then an investor can't be a person of somewhat average means who is looking to diversify his portfolio with no anticipation of making a windfall profit? >>



    I'm not really saying who can and cannot be what. But my description of a coin investor is indeed a little strong. It's my reaction to the folks that are on the investment side of things. I tend to be on the collector side of things. Meaning that a loss isn't going to mean much to me.

    I'd say that this person is focused on diversifying their portfolio. And it's not about the coins. It's about wealth preservation. That is an investing concept.

    I would imagine that most folks are some blend of the two.
    A pure collector is collecting for the love of it and is entering into the purchase transaction with little notion of getting that money back later. Or just pulling stuff from circulation without any notion of expense; buying or selling.

    If I have to draw a line between the two, that's where i'll draw the line.

    There is a lot of talk on this forum relating to money, gains, undervalued coins, etc...
    I prefer the pictures, the numismatics, the history, the information.
  • HalfStrikeHalfStrike Posts: 2,202 ✭✭✭
    If you look at Graph 1 in that article, it seems to show that the return was very high from 1941 to about 1980, and from 1980 to 2003 when this article was written rare coins lost money when adjusted for inflation. I would imagine if this was updated to today you would see a strong rebound in the graph after 2003, however it does seem to show that 23 year span of dead money.
  • CoinosaurusCoinosaurus Posts: 9,623 ✭✭✭✭✭
    Can't use Redbook for this kind of study. As much as I like the Redbook guys.

    Have to use auction results for the exact *same* coin over many years. Then subtract commissions, insurance, SDB fees, etc.

    And not just pick out the winners......any dope can pick up the Pittman catalog and do that........

  • The same data was used to push investment coins during the bubble years when certification companies were new. Those folks that bought the pitch and were unlucky enough to buy near the top of the certified coin bubble, have lost 70% to 80% of their money, more like 95% when opportunity costs are factored in. Nice.

    Whenever the investment word comes up, I write the same thing. There is a small percentage of collectors that do well financially. They tend to share certain characteristics. The winners tend to have an excellent eye for grading, superior dealer connections, vast market knowledge gleaned from endless hours spent on a hobby they truly love. There is a much larger group of coin folks that do poorly financially. The losers tend to buy mostly for investment, perhaps after reading articles like the one linked. They usually don't know much about grading, usually don't want to learn. They often buy from a single source, often at above market prices, often from a sales person with a slick song and dance, peppered with half-truths like the ones cited in the article.

    I'm sure older folks can chime in with more examples. Whether it be rolls of 1950-D nickels in 1960, or common as dirt proof sets during the 1970s, or common MS65 certified coins in the 1980s when certification was relatively new, the average person chasing the hot story often ends up losing big. There has always been a segment of the industry pushing coins as investment. For the most part, the small fish, that don't know much, that actually believe the finely woven half truths posted at the article, get the short end of the stick and become food for the unscrupulous sharks that are always circling the hobby.
  • tradedollarnuttradedollarnut Posts: 20,162 ✭✭✭✭✭
    I once graphed prices realized of the ultra rarities and they all followed the same slope. And although you can pick out a loser here and there, for the most part they were fantastic investments over the years.
  • SonorandesertratSonorandesertrat Posts: 5,695 ✭✭✭✭✭


    << <i>I once graphed prices realized of the ultra rarities and they all followed the same slope. And although you can pick out a loser here and there, for the most part they were fantastic investments over the years. >>




    Absolutely, but the key phrase here is 'ultra rarities'. The average collector, who shops at local coin shops and who is extremely price conscious (to the extent that quality for the grade takes second place), will get skinned.
    Member: EAC, NBS, C4, CWTS, ANA

    RMR: 'Wer, wenn ich schriee, hörte mich denn aus der Engel Ordnungen?'

    CJ: 'No one!' [Ain't no angels in the coin biz]
  • roadrunnerroadrunner Posts: 28,303 ✭✭✭✭✭
    Most all of these gains are from inflation. It's fairly widespread across all tangible asset classes. The most important item here is what they used to remove the inflation component. If it was the CPI, then the gains are heavily skewed.

    roadrunner
    Barbarous Relic No More, LSCC -GoldSeek--shadow stats--SafeHaven--321gold
  • SonorandesertratSonorandesertrat Posts: 5,695 ✭✭✭✭✭


    << <i>I think you make some good points but as Q. David Bowers has said for decades, people who buy judiciously and know their series do very well over the long term.

    I think that is quite true. And, collector coins are usually defined as MS64 or lower; collector coins aren't usually investor coins. >>




    The key phrase is 'buy judiciously'. Most collectors don't do this---they buy coins without fully understanding what they are buying. There are numerous opportunities for a collector to buy coins that will be good investments
    without buying MS64 and up coins. For example, think about what has moved up during the last 20 years. Examples include AU Seated Liberty dollars, Ch.VF-XF-AU Barber halves, AU half cents, etc. I am sure that there will be further opportunities for
    collectors with modest budgets (i.e., all coins below ca. $2.5K). 3-4 decades ago, following my grandmother's advice (she was a coin collector), I put together a set of Barber halves in AU 50-55 (many would have been called 58 today)---
    I sold it 4 years ago for multiples of what I paid for the coins (and beat the effect of inflation). The problem is that 99+% of the collectors in the hobby today are too willing to sacrifice quality for quantity, they buy modern mint products, and get
    suckered by clever marketing (hence the PF70 craze).
    Member: EAC, NBS, C4, CWTS, ANA

    RMR: 'Wer, wenn ich schriee, hörte mich denn aus der Engel Ordnungen?'

    CJ: 'No one!' [Ain't no angels in the coin biz]
  • BaleyBaley Posts: 22,659 ✭✭✭✭✭
    some excellent points being made, some posters obviously understand the nuances around this subject.

    "coins as an investment" is a lot like "stocks for investment", "real estate for investment" and others...

    which coins (stocks, properties)? when, where, how, and how much purchased? when and how sold?

    is the asset class a "good investment"?

    Depends!

    Liberty: Parent of Science & Industry

  • bidaskbidask Posts: 14,011 ✭✭✭✭✭
    Why can't you have coins as an investment and enjoy looking at and owning them too?image
    I manage money. I earn money. I save money .
    I give away money. I collect money.
    I don’t love money . I do love the Lord God.




  • RollermanRollerman Posts: 1,865 ✭✭✭✭✭


    << <i>Why can't you have coins as an investment and enjoy looking at and owning them too?image >>



    Exactly! I had a CD that was only paying 1% that needed renewing. I decided that I could probably do as well AND have a lot more fun and enjoyment from some coin purchases and I was right! It's much more fun looking at coins than paper work!
    Pete
    "Ain't None of Them play like him (Bix Beiderbecke) Yet."
    Louis Armstrong
  • DHeathDHeath Posts: 8,472 ✭✭✭
    Were I making that analysis and claim, I'd develop a multivariate regression, or structural equation model if I believed the factors might not be independent, with ROI being the dependent variable. Independence might be an issue, for example, if investors moved cyclically between stocks and coins, or vice-versa. I would use established indexes to develop baskets of coins, such as the ones used by PCGS for the same purpose. I would select several grade ranges and metals (including precious metals). Grade range comparison would, of course, require one to successfully reconcile grading standards from 1942 (62 year study) to 2004. Lastly, were I to rely on a convenience sample, such as Redbook, for pricing data, I'd establish its' reliability (or unreliability) at the study's end-points, comparing Redbook prices to auction prices realized across my baskets in both 1942 and 2003. When reporting the results, I'd report the P values and std.errors from my factor analysis, along with a laundry-list of assumptions, such as continuity of Redbook pricing across several changes in ownership, and the strategy employed in the study to standardize grading across the years. Finally, I'd report the tax implications of converting each asset, as certain categories of investment have tax advantages not enjoyed by others.

    It is believed that the standard deviations are directly comparable across all of the asset classes appearing in Table 2, including rare coins, because each return series is based on actual transaction data as opposed to valuation estimates (as frequently occurs with private real estate).

    All rare coin pricing data was provided by the following two sources: Handbook of United States Coins with Premium List (the Blue Book) for the annual copyrights 1942 through 1951, and A Guide Book Of United States Coins (Red Book) for 1950 through 2004.2

    Are those statements congruous?

    Or, I'd read the report and be happy.
    Developing theory is what we are meant to do as academic researchers
    and it sets us apart from practitioners and consultants. Gregor
  • garrynotgarrynot Posts: 1,874 ✭✭✭


    << <i>Coins are not fungible. Comparisons with other types of investments (aside from other types of collectibles, like fine art) are pointless. In a roaring stock market, small investors will make money without having to go to research heroics.
    In a bull coin market, most small investors/investor-collectors will lose money (because they didn't buy the right kinds of coins, they didn't buy coins that are nice for their grades, they didn't have a well-thought-out exit strategy, they
    buy at retail and sell at wholesale, etc.). >>




    I have to agree. When I and many of us began collecting coins as a kid, investing was the furthest thing from our mind. Then when we get a little more money, and buy the key dates and upgrade, we are spending discretionary funds. This is still a hobby for me. It was a hobby for the big guys too. Eliasberg, Bass, Pittman. I never saw a word uttered by those gentlemen about investing in coins. Just because they died and their collections were worth millions is beside the point. The collections would have been worth millions just based on inflation. Investing in coins is just like investing in stocks and bonds, art, cars, furniture, etc. If you go into those markets with the goal to invest, then sometimes you will win, sometimes you will lose. If you go into those markets to collect, you will learn, enjoy and in the aggregate will probably do alright.

    Yet the constant obsession with quality, "top pop", condition census, sniffers, beans, is turning coin collecting from a hobby to an investment. New collectors and investors come to this hobby and hear a constant barage of information about the finest known and condition census and referring to everything else as fillers and dreck, and detailed descriptions of hairlines and reed marks and nicks and dings on coins. It's not good enough to have an example of something, we have to have a certified example of something, and it better be high end for the grade so you can crack it out a few times and get an upgrade. There is nothing written anymore about the fun of collecting anything.
  • mrearlygoldmrearlygold Posts: 17,858 ✭✭✭
    Back in the mid-late 90's I had purchased a 1799 Eagle in AU-58 from one of the fellows that is an integral part of my supply chain. I think I paid $5,000 for it. I know I bought another one shortly after that for 6K. Offering these coins to my then customer base fell on deaf ears. Oh that one guy was buying early dollars and a few others were buying early gold from me but I was buying quite a few of these early eagles ( including a really nice 1795 9 Leaf in MS-61 which is in the heritage archives )

    I thought that "some day" these coins would be worth $25 grand. So my goal was to set aside a number of these coins as part of my retirement "portfolio". That one day I might have a couple hundred thousand dollars invested in these coins, that I would not resell, and that would become 7 figures in my retirement years, allowing me to sell one here and there to support myself in my old age.

    I figured I had 20+ years before that happened. Ha!

    Happy Collecting image







  • DrPeteDrPete Posts: 1,497 ✭✭✭
    Some very good discussions above. What is interesting to me, is that the biggest gains (profits) made on coins by "collectors" tends to be made by those that had collecting as the main goal, not investing. Often the acutal collectors themselves did not see the profits, but rather their families that sold them after the collector died (Such as Eliasberg, Norweb, etc). I am really not aware of long-term primay investors in coins and how they have done compared to other investment strategies (and certainly such people would not wait until they are dead to sell). It seems to me that such individuals are actually few and many may have lost considerable sums. I know dealers have to buy and sell to make their living, and I have a healthy respect for those that do so while being fair to their trade partners. I have been to many coin shows and see how business is conducted, and it is an eye-opening experience; I am not about to quit my day job!

    I collect because I have that innate drive to collect, hold, study, value and share these coins with others. I would be lying if I said I was not hoping that my expensive coins would appreciate in value over a long period of time and that I could sell them and make a profit. I do not use my collecting of coins as my primary investment vehicle toward retirement, yet, when the time comes to sell my best coins, I hope they net me a good profit. To do so requires study of how coins are graded, valued, bought and sold, and what is good eye-appeal, etc. For me, focusing on a particular series I like and becoming as expert as possible also adds value to my experience. Holding the coins for 10 or more years and buying nice coins helps, and having a dealer (I use Harry Laibstain) to help you figure out what makes sense in the complex community of numismatics is critical. I try to emulate how the great collectors of the past have done things, and enjoy my coins and my collecting interests.
    Dr. Pete
  • renomedphysrenomedphys Posts: 3,599 ✭✭✭✭✭
    Any "collector" that says they don't care about profit is lying. There are degrees.

    Any "investor" that only cares about the grade on the plastic is stupid. There are also degrees.

    I prefer to think of myself as a "collector" that cares about the quality of his "investment."

    Right now, it's all about buying the best coins I can find in the best grades I can afford. But someday, I'm sure that to me or someone in my family, the money is all that will matter image
  • DeepCoinDeepCoin Posts: 2,781 ✭✭✭
    Coins are a GREAT hobby and less so as an investment vehicle IMHO. Contrary to the initial assertion, coins are a thin market. How are those proof 3CNs doing for you these days? Judicious collecting should provide a good return, but that is over extended periods of time and hopefully you have not bought into a bubble.

    Watch all the people buying the 5 ounce "coasters" get buried in 3 or 4 years. Too much hype in many areas. I do concur that buying quality early 19th century pieces is a good way to diversify, but I would never put more than 3% of my portfolio into coins. In fact, I occasionally realize how much I have tied up and then liquidate. It happens every few years, but then I am risk adverse.

    How many newbies have been burned by unscrupulous people when entering the hobby with an eye to "investment"?
    Retired United States Mint guy, now working on an Everyman Type Set.
  • sinin1sinin1 Posts: 7,500
    that sure does look like a brokerage hype article (not that I disagree with the general message)


    I had a first edition bluebook (recommended delaers buy prices) - and they had common date trade dollars at 80 cents

    also the early editions of both bluebook and redbook just had BU or UNC prices




    also if you just bought silver coinage at face in the early 60's you would be doing well
    but probably doing better if you bought some bads of BU Morgans
  • Results can also be skewed by the market at the sell point. I very much doubt those results would have been obtained by people who sold their coins from 1982 --> 1986, or during all of the 90's and very early 2000's.
  • MarkMark Posts: 3,533 ✭✭✭✭✭
    Aside from a large number of other comments about other problems, let me point out the largest flaw in the paper, namely its emphasis on the "arithmetic mean" as its measure of the return. Anyone with a PhD who uses that measure is clearly intent on deception. Here is an example: You own a coin (or coin portfolio) valued at $100. In year 1, it rises $100 to $200--a 100% return. In year 2 it falls $120 to $80--a -60% fall. The arithmetic mean return here is 20% (=[100% - 60%]/2); that is, the "mean return" was 20% per year. Obviously that 20% "mean return" is absolute nonsense because after 2 years the coin has actually lost value.

    I know of no reasonable use for the "arithmetic mean." There may well be one, but it's not one I know.
    Mark


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