Featured Numismatic Rarity vs Coin Value, my simple analysis

Numismatic Rarity vs Coin Value, my simple analysis
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I decide to take a few of my coins and look up their "Numismatic Rarity" according to PCGS. I then compared to the estimated retail value of each coin. I color-coded the rarity (green = not rare, red = rare) and the value (green = cheap, red = expensive). This is scaled based only on my coins I looked up, so the sample size is small, 44 coins total.

-PCGS

What I noticed is that there is less correlation between "Numismatic Rarity" and value than I was expecting. There are no coins that are RED for both value and rarity, and my most rare coin is also one of my least valuable. Obviously, popularity of series and a bunch of other factors come into play, but still, I am confused how a 1907 IHC can be a rarity 6.6 and only be worth ~$50.00. There are plenty of orange and yellow coin values that correspond well with rarity, and a few in the green zones.

Have a look, and tell me what you think.



- Matt

 

Matt -

You have discovered what has been posted about here many times. But quite frankly many refuse to listen because they don't want to believe that it is true. So even though they may have read about it numerous times they tend to forget it because they dismiss it as being inaccurate information.

That said, when discussing rarity all by itself, let alone discussing the relationship between rarity and value, there are several things that have to be considered. First and foremost, who is determining the rarity, and what are they basing that rarity on. The who is often easy, the what is somewhat more difficult.

For example, the what: when PCGS provides their rarity number does that number only take into account coins graded by PCGS, or does it take into account all coins known to exist ? Including those not graded and slabbed at all as well as all of those graded & slabbed by somebody else ?

The reason I am mentioning this is because quite often the published rarity of a given coin is, shall we say, misleading and often bit more than inaccurate. But the only way to determine that and prove it is by independent study. Of course very few are ever willing to do that given the amount of work it entails and so they tend to accept the information they are given, never questioning its accuracy. But it is not uncommon to find when ones does do the work that the rarity being reported by an acknowledged authority for a given coin is completely inaccurate. And sometimes wildly inaccurate.

In that paragraph you quoted above, notice how drastically the rarity can change depending on the grade of the given coin. For that 1881-S dollar it almost doubles from an overall rarity to that of one in 65. The same kind of thing happens with most coins, with some to a lesser degree and with others to a greater degree. And every now and then you will run across a given coin in a given grade where the rarity is extremely disparate with the value. But that can often be attributed to the fact that there are simply very few examples known in that particular given grade. There may well be many, many, more examples in grades above or below that specific grade, but because only a few are known in that specific grade, the rarity is skewed way out of proportion. So it is best not to read too much into it.

Also, published rarity numbers are often old, sometimes very old, and they are merely copied & repeated over and over again by each subsequent author reporting them. And they are accepted as being accurate by most even though those doing the accepting have no understanding of how those numbers were determined. Or if those numbers could have, even might have, changed over the years due to subsequent discoveries that were unknown when the original study was conducted.

So what is one to do if you cannot trust the published information ? Well the simple answer is you ignore it. And instead you watch and learn the coin market. The coin market is everything, all of the information you could ever want to know about any given coin, conveniently rolled up into a nice neat package for you. But the coin market is the big picture, so it must be viewed an open mind instead of a closed or biased mind. When you see something in the coin market that seemingly disproves what you previously believed to be true you must sit up and take notice instead of dismissing it because the coin market is rarely wrong. Yes it can be wrong at times, just not very often, because instead of one small group or even 1 individual disseminating information, you have the aggregate of all knowledgeable individuals providing their consensus.

But the thing about the coin market that you always have to remember is that it will reflect the value of a coin while often completely discounting the true rarity of that coin. And that is because rarity often has nothing to do with value. Value is often an emotionally driven function while rarity is a statistically driven function. And once you know that and realize it, well then you can finally begin to understand the coin market.

 

Here's a related philosophical question to further discussion about rarity . . .

How rare is Ayer's Rock if there is only one, but plenty for everone to share?

 

Yes, and while I was looking up my coins on PCGS CoinFacts (10 day free trial), I only have 3 levels to choose from on most coins: (1) All Grades (2) 60 or Better (3) 65 or Better. So for most of my coins, I chose the R-X.X number from the "All Grades" section, and in cases where it made sense, the "65 or better" category. So, these rarity levels are already quite broad, and not at all fine grained as you point out.

My overall goal was simply to find my "rarest coin" in the generic sense. Since I was so shocked to find it was the $50 1907 IHC, I figured I better share my little chart with the CT community and find out what the heck was going on. Fortunately, Peter decided to make my little post a Featured Topic (I'm very honored), so I am getting a lot of exposure to and insights from the best members of the site.

 

I love this part. Having spent years on financial blogs, forums, and reading every book I could find on Efficient Market Hypothesis (EMH) / Efficient Market Theory (EMT), I understand this concept well, but since Coins are a hobby to me, I haven't really thought of the "Coin Market" the same way I think of "Mr. Market" (allegory created by investor Benjamin Graham). I should have connected the two long ago, but then again I am not trying to make money in coins, just trying to purchase smartly. When I was checking for my rarest coin, it was purely out of curiosity. But you are correct, PCGS rarity scale is potentially flawed in many ways, and possibly should be totally ignored as you state.

A quick summary of EMT:

So, if I replace "stock market" with "rare coin market", lets see what we have:

So, in this sense, my rarest coin would be my most valuable coin, after perhaps accounting for base-metal value. The coin market factors things in such as current popularity, absolute rarity, conditional rarity, toning premium, and many other factors.

So, my rarest coin that I own according to ECMT would be my 1853 HALF DOLLAR - SEATED LIBERTY, ARROWS & RAYS PCGS MS 40 ARROWS & RAYS, CAC.

 

Nothing to do with CAC. Rarity as listed by PCGS on their CoinFacts site. I just happen to own mostly CAC approved coins. I have actually never looked at the CAC pop reports, but that is one of the things on my to-do list.

 

All good stuff, thanks Tom. I always thought of IHC are being very popular, and it was THE series that got me into coins at age 8. So, the coin in my CAC Type Set happens to be a coin I owned raw when I was younger than 10, and even if you take PCGS rarity levels with a very large dosage of salt, it is still probably my rarest coins in terms of numbers surviving. So if this series seems to be popular, can someone help me understand why this coin is so darn cheap? I don't think people would wildly overpay for my example, or wildly underpay based on the merits of my particular coin. Am I wrong about IHC being currently popular?

 

Another more detailed link for people following this thread who may not be familiar with PCGS CoinFacts site:

click for PCGS CoinFacts RARITY SCALE site


10.1 No Known Examples
10.0 Unique
9.0 to 9.9 Ultra Rare
8.0 to 8.9 Extremely Rare
7.0 to 7.9 Very Rare
5.0 to 6.9 Rare
3.0 to 4.9 Very Scarce
2.0 to 2.9 Scarce
1.1 to 1.9 Common
1.0 Very Common

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Thanks for the interesting post. This is totally random, but I thought I should point out that Gerry Fortin is a fellow Mainer. So proud of Maine right now, we're getting a lot of good representation on CT (although Gerry told me he does not have time for the forums yet).