On the value of US coins

Some say that money is only worth the paper it's printed on.  It's not my place to agree or disagree with that, but given that the paper is not worth all that much, I was wondering how much US coins are worth.  For my analysis, I looked only on coins from one cent to a quarter, ignoring the discontinued half dollar and the new dollar coins, as they rarely if ever find their way into my pocket.  For value, I referenced the metal spot prices (in dollars) at the London Metal Exchange.

A few words about the materials the coins are produced from.  Until 1981 (and partially 1982), 1 cent coins were produced from copper.  Since then, they were switched to zinc, whose value is negligible in our calculation.  Dimes and quarters were made of silver and heavier than today until 1964.  Since then they consist of copper core and copper/zinc plating.  If you were prepared to break the law and saw a quarter in half, you'd see that its inside color is very much like the one of a new cent.  Five cent coins have always been manufactured from a copper/zinc alloy.

Using the unscientific method of counting the coins in my pocket (actually, in my coin jar with well over 1000 coins and thus with sample results having a relatively low margin of error), I found that for each $100 worth of coins you'd have 1080 coins.  441 of them will be one cent coins, 139 five cents, 241 dimes and 258 quarters.  That, assuming, that you're like me and don't spend any of your coins in wending machines or laundromats.  On their face value, they may be worth $100, but their real (metal) value is only about $17.40.  The follwing chart shows this distribution.



You may notice that copper cents are suddenly woth more than before, but the value of other coins took a dive.  Based on my count, about one in ten one cent coins you'd get is still copper, and currently the value of copper is about 2.16 cents, more than double the coins face value.  In other coins, the copper content amount for less, compared to face value.  The following table shows the relative value of the coins.



So what to conclude from this?  Not much.  Currently, we have laws against defacing currency, which will prevent you from melting the one cent coins and making some money.  Not only it would be illegal, but also would require enormous amount of coins to make it worthwhile.  Still, if the price of the US dollar keeps falling, one day the coins may be worth much more.  Until then, though, I'll keep looking for the silver dimes and quarters that occassionally happen - they are worth roughly ten times their face value right now.

Liberty Dollar and the inflation-proof currency

On November 15, the FBI has raided the offices of Liberty Dollar and seized all its assets. Up to that point, the Liberty Dollar was the best known alternative currency in the US, a currency that cold be used by those who didn't want to pay or receive payments in US dollars. The main reason for not using US dollars was stated as the fact that US dollars are not inflation-proof. Liberty Dollar has solved this issue by linking its currency with precious metals. Its coins contain an amount of precious metals, mainly silver and gold, valued at the coins' face value. Its notes (deposit certificated) were fully backed by precious metals, including two tons of gold, which were seized in the raid.

It is not my goal to explore the legalities of using Liberty Dollars or government theft; other blogs have covered it already. I was more interested in the claim that Liberty Dollars or other precious metals-backed currencies were inflation proof. The currency's Web site is prominently featuring a well-known chart showing the decline in the value of US dollar. I recreated the chart using government inflation data:


What the chart does not address, though, is the growth in prices and wages. Inflation causes harm primarily if the growth in personal income is lower than the rate of inflation. The following chart shows the level of disposable (after-tax) personal income. Note that to normalize this number and account for differences in industry-specific wages and number of household members, I averaged the total personal income by the number of people in the US. This chart shows income in current dollars, not adjusted for inflation.


The graph seems to grow faster than the decline in dollar value. This is not an illusion - translated into 1914 dollars, the average disposable personal income grew from $400 to $1600, a four-fold increase. This despite the fact that the average tax burden grew from 2% to 12%, a six-fold increase. In other words, if the US dollar didn't change its value, we'd earn four times as much today as nearly 90 years ago.


In fact, it seems that wages have almost always outpaced inflation in the US. The following chart shows the inflation-adjusted change in wages, as well as the price in two staples that haven't changed much for the past century: a gallin of milk and housing costs. As can be see, we not only earned more in real wages, but we spent less on housing and food. The reason we don't feel much richer is that we find new things to spend our money on.


In fact, we are not saving much at all. Gone are the Jimmy Carter days of nearly 10% saving rates; for the past two years we saved less than 1% of our disposable income. Given that all my savings (with the exception of a small sum in the bank I need for liquidity) go into gold, I was wondering how well gold would hold up against the dollar. The following chart shows two things: the number of gold the average American could purchase with his savings every year, and the total profit or loss generated by holding onto the gold, given the gold spot prices.


As can be seen, if a person started purchasing gold since the abandonment of the Breton Woods System (given that that's when the price of dollar began floating against gold), by 2001, 30 years later, that person would lose money. That despite the fact that at that time the person would accumulate over 25 pounds of gold. Only thanks to the most recent fall in the price of dollar the value of gold holdings would yield a profit. Thanks to this, the current return on investment averages 7.74% annually for the past 36 years. That is still less than putting all savings into a Dow Jones index fund, which would at this point yield around 8.67% annually and increase the total gain in savings from $140,400 for investing in gold to $177,300.

I believe that historical inflation data doesn't support the claims than precious metals based currency was safer than US dollars. That doesn't mean it will be true for the future, though. As the past few years show, the US dollar may be on the verge in a long-term slide, and with no clearly dominating currency in the next few decades, gold may be the safest investment. I'm betting on it.

Terry Goodkind's Grace

I'm in the process of reading Terry Goodkind's Sword of Truth series of fantasy books. Towards the beginning of the fourth book, Goodkind described a magical symbol he called The Grace. From what I could learn on-line, The Grace plays a certain role in the books, but I was more intrigued by Goodkind's description of the symbol. In his Appendix of Terms, Goodkind describes the symbol as follows:

A grace is a magic symbol representing all of existence. A grace consists of a small circle, inside a square, with one apex of the circle touching the middle of one side of the square. Each of the square's four points touch a point on the larger circle, which the square is inside. Inside the smaller circle is an eight pointed star. Lines radiating from the star's points pierce all the way through both circles, and the square, with each line bisecting a corner of the square. A grace is always drawn starting with the outer circle

In the book he also mentions that the Grace is a symbol that's drawn by hand, on any medium. The first grace the main characters encounter is drawn in dirt; later it is explained that wizards often drew it almost subconsciously.

To my knowledge, however, a Grace has not been published by the author of the books, and so only guesses of how the symbol looks currently exist. Wikipedia has one such symbol, which shows the most literal interpretation of the Grace. However, when I tried to visualize the Grace, I was a little more liberal in putting words into drawings. First, I abandoned the idea of radiating lines escaping the outer circle. While this could be permissible in drawings, it could become very awkward in other symbols, which require some kind of framing, and the outer circle does offer such a frame. Windows, for example, could be designed into a self-containing Grace. In fact, Goodkind seems to have been inspired by cathedral windows, such as the Rose Window of the Cathedral of St. John the Divine in New York City, which contains elements of an eight-pointed star in two concentric circles. This window, like many other similar windows, also has lines radiating from the center, where Jesus (an equivalent to Goodkind's Creator) is placed.

After a little experimentation, I came up with a design that abandoned another element of the definition, the radiating lines crossing the corners of the square. I find this design to be very fascinating, and currently I'm working on a stained glass version.

Then, however, I decided to take a step back and redesign the Grace to allow for the easiest free-hand drawing. After all, people were drawing it subconsciously, and I wanted to come up with something that's easier to create, especially with the added constraint that the drawing begins on the outside. The second design is thus a step back, placing the radiating lines as they should be. Eight pointed star is not as easy to draw as a five- or six-pointed star, but techniques for each of the latter can be used. I often draw an eight pointed star when I'm doodling, using the same technique as in a five-pointed star: an uninterrupted line. Instead of skipping over one point, however, I skip over two. The other method, which mimics the six-pointed star technique, is even simpler, just instead of two opposing triangles two squares are drawn. This is the technique I used for the second drawing. Given that one square must be aligned with the larger square, I found this method to be the most simple and precise for drawing a grace.

As can be seen, though, I still took certain liberties. First, in both images I had the radiating lines cross inside the star, which makes them look more like a grid than rays. Second, in both cases I filled the inner circle with the star. This element is not addressed in the definition, but I fould the inner circle to be the perfect guide to draw a precise star.

Neither design explains one big question I have, however. Goodkind describes characters as tracing some of the radiating lines and identifying them as lines they represent, such as the line of magic. Given that the Grace has no identifying marks for top or bottom, though, I don't understand how any of the radiating lines can be identified.

The Oil Prices Fallacy

With oil closing to $100 per barrel, I explored the history of oil prices and their correlation to a few items. My results are summarized in the chart below; click for a full-sized version.

First thing I found was that oil prices are nowhere near their peak of 4.54 grams of gold (AUG) per barrel. Today, Nov. 6, the price is at 3.6g AUG per barrel, or nearly a quarter lower than their peak. The price that changed was the price of the US dollar, not the price of oil (of course, prices are relative, but given the relatively low volatility of oil prices and higher volatility of the price of dollar I'd blame the dollar in this case).

Second, I'd like to point out to the longest run in oil price increase, which began with two mega mergers of oil companies and ended with another merger and the first electoral victory of G.W. Bush. Given the fact that during the same run there appeared to be a deficit in oil supply, possibly caused by increased refinery capacity (these two resulted in a decreased refinery utilization), I assume that the oil processing industry entered a time period of reduced competitiveness with two large conglomerates and four smaller companies. Once other companies merged to offer adequate competition to Exxon Mobil and BP, the price stabilized. Bush's election victory over Gore was also seen as a positive development, as the industry observers hoped that it would open access to new drilling areas, such as expanding oil production in Alaska.

One last observation, which is not apparent from the charts, is that the oil prices are highly correlated with refinery utilization (85%), and there seems to be a positive relationship between the two (regression with p=0.0004). Why this is so is anybody's guess; my assumption is that there is no shortage of refinery capacity in the US, and thus seasonal changes in demand for gas affect both the refinery utilization and oil prices.

Be it as it is, for me the most important finding was that oil is still far from its record price, and that it's unlikely it'll get there anytime soon. Unlike the US dollar, whose price keeps tanking.

Most influential Americans in politics

The Daily Telegraph has recently published the list of most influential Liberal and Conservative Americans. I've had some fun with the lists, and here are the results:

The grid is as follows: top-left position shows the most influential person, bottom-right the least of the top 100. Actually, top 101, as both lists had one field populated by two people; in the Liberals case with a man and a woman, thus the half-shaded gender box. The patterns tell part of the story: Conservatives are much more homogeneous, consisting primarily of white males. However, they also tend to be younger on top of the list, which came as somewhat of a surprise to me. As much as I'd like to see the "lame ducks" who most likely die before the mess they create can play out itself, I also understand that the longer a person is in the top echelons of a political system, the more influential that person is likely to become. The fact that so many Conservatives in the top 20 are below 50 indicates a possible lack of confidence in the older generation (a possible proof of this is the fact that G.W.Bush placed 21st).

One thing the pattern doesn't show is that there are virtually no Asians in the list. The only two Asian Americans are both conservatives, one of Indian and one of Filipino heritage. Also, it is important to realize that as with any such list, it is certainly not definitive. In fact, I'm expecting similar lists from other publications to differ from this one a great deal.

So who made it to the list? Here are all of them:

Liberals

Conservatives