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Should you melt down your pennies?
My much-beloved Financial Times gets one wrong:
It could soon be worth Americans melting down their pennies for scrap, if zinc and copper prices continue their current rate of increase.
Copper prices have risen 30 per cent so far this year, and zinc is up 55 per cent - a rise of about $550 a tonne in a little more than three weeks.
A rise by the same magnitude would make the metal content in the US one cent coin worth more than its face value.
The weight of 160 pennies - also known as a one cent coin - comes to a pound, worth a face value of $1.60. But - with each penny made of 97.5 per cent zinc and 2.5 per cent copper - based on current prices, the metal value is worth about $1.36. Therefore another 25 cents-a-pound rise in zinc, or about $551 a tonne, would see the metal value of the US penny worth more than the monetary value.
We all know, of course, that you should not exercise an option before its expiration. The longer time runs, the greater the chance for price to bounce around. Once you are "out of the money," further drops in price don't hurt you any. But "in the money," you gain from price movements in your favor. So hold onto those pennies and wait. Yes there are complications (what is the stochastic process governing these prices?) but most likely the standard result holds up.
Posted by Tyler Cowen on April 13, 2006 at 07:27 AM in Economics | Permalink
Comments
That's because when an option's value rises, it's replacement cost rises also. Here the replacement cost (of pennies) is fixed. So if the metal is worth more than the face value, you should sell it as metal - then change the proceeds into pennies and repeat until uneconomical?
Posted by: nick at Apr 13, 2006 7:39:01 AM
Nick raises an excellent point. But if cross-denominational arbitrage is working in perfect-market mode, movements in the price level change the replacement cost of pennies and other forms of currency. Their prices are fixed in nominal terms only. If arbitrage costs lead to some slack in thie ability of the real value of currency to change, I think you are at best indifferent to exercising the option as opposed to holding it. Plus those same arbitrage costs will discourage you from changing your proceeds into pennies and starting all over again, as suggested in comment #1.
Or so it seems to me.
Tyler
Posted by: Tyler Cowen at Apr 13, 2006 8:01:41 AM
You should not exercise a call on a non-dividend-paying asset before its expiration -- this is not true for every option. (Consider the option to refinance your mortgage.)
In this case, by exercising earlier, you can sooner reinvest the proceeds of the sale, so it may truly be optional.
Posted by: sammler at Apr 13, 2006 8:14:59 AM
Erm, s/optional/optimal.
Posted by: sammler at Apr 13, 2006 8:16:49 AM
you have a basically unlimited supply of pennies available. if you can easily sell the copper, there is no point in maintaining the optionality of the pennies you have - you can easily use the proceeds to buy MORE of teh options you started out with. this should not be viewed as an option, but simply as a pure arbitrage.
Posted by: ridiculous at Apr 13, 2006 8:27:05 AM
I've met people who did exactly this with quarters when the price of silver went up in the '60's-'70's. Expect the copper/zinc to be removed from pennies if the arbitrage keeps growing.
And there are _is_ a good reason to exercise your penny options: pennies have large carrying costs. Do you have enough glass jars to hold _tons_ of pennies? Or do you have to rent mini-storage, or tell your wife not to park in the garage until the price of copper falls? These carrying costs are mathematically equivalent to a dividend on the underlying asset, if the dividend is a fixed amount instead of an assumed-constant yield.
The largest carry cost might be the cost of the capital invested in the pennies -- if they're sitting in your garage, they are not earning the same return as the same money would earn in a bank. Yes, you might expect the value of copper to rise at the risk-free rate, but, your option doesn't have a delta of one. And your options are risky; your CFO will charge you a higher internal interest rate on the capital he allocates to your penny strategy.
p.s. Your mortgage, BTW, does _not_ disprove the optimal exercise rule. Refinancing an mortgage is not an option; it is a series of options, one for each monthly payment for 15-30 years. Thus, you are _always_ facing an option expiry if you have a mortgage.
Posted by: DK at Apr 13, 2006 9:18:45 AM
Or, you could hoard pennies with the intention of making your own set of copper cooking pans.
Also: the current (mostly zinc) composition of pennies was established in 1983. Pre-1983 pennies were almost entirely made copper.
Posted by: Independent George at Apr 13, 2006 9:56:27 AM
If you weren't already aware, one of the neater resources for tracking the rise in value of the base metal of U.S. coins is the Coinflation web site.
Doing some back of the envelope math, U.S. pennies minted beginning in 1982 will be worth the face value of the coin when the market price of zinc reaches $1.767 per pound. The "melt-worthy" price is somewhat higher given the costs of storage, transportation, smelting, etc.
Meanwhile, older pennies (copper) have already attained meltworthiness.
Posted by: Ironman at Apr 13, 2006 10:28:07 AM
When exactly does this particular option expire?
And doesn't the "don't exercise before expiration" rule only apply to options that are readily marketable, so that sale of the option is more lucrative than exercise?
Posted by: Bernard Yomtov at Apr 13, 2006 11:22:59 AM
If we take Mr. Cowen's initial idea literally, we should imagine the holder of pennies (and thus of a long option position in the price of zinc) could safely sell calls on zinc futures, covering any possible payout by melying the pennies. (Or, alternatively, could buy zinc futures on a drop and sell on a rise, covering a sustained rise by melting pennies -- but this requires more expertise.)
In practice, this would monetize some part of the pennies' excess value, but need not be optimal (which is the meat of this discussion).
Ridiculous: good point, but we are somewhat concerned with the difficulty of obtaining more pennies to melt.
DK: thanks for the concrete illustration. But I'm not sure the mortgage case (pay current rate for one more month, or refinance) is so different from the penny case (pay storage for one more month, or melt).
Posted by: sammler at Apr 13, 2006 11:46:59 AM
Does collectabilty become the vehicle through which the "time value" of the premium is expressed? If enough people melt their zinc/copper pennies and they become rare, and a floor is established at melt value then does the rarity become the option premium? If not that then I'm in agreement with the others, that the storage costs probably greatly exceed any potential time value in the options.
Is there some way to fix the text box slipping behind the ads as soon as one starts to type?
Posted by: nelsonal at Apr 13, 2006 12:02:26 PM
The penny was debased in 1982 when the price of copper appeared to be likely to remain higher than one cent per penny's-worth of copper, partially because the mint has to pay for the copper, so even if it's uneconomical to melt pennies for their copper, it was uneconomical to make pennies from copper.
The question for the Mint is how long to wait before debasing the penny (to what, aluminum?), given the costs of switching, the likelihood of fluctuations in the price of zinc back below the breakeven point, and the time required for Congress to authorize debasing the penny.
The coinflation site shows that 5-cent pieces are closer to reacing that point than are pennies.
Posted by: Anthony at Apr 13, 2006 12:52:59 PM
Anthony: Probably copper-plated steel, like Canadian pennies since 2001.
(By the way, the Canadian penny was 98% copper until 1997! So don't be upset if you get one in your change...)
Posted by: Anonymous at Apr 13, 2006 1:46:37 PM
The mortgage refinance option is a put option, not a call. (Insurance policies are generally also put options.)
Posted by: Anon at Apr 13, 2006 3:28:53 PM
I really like Sammler's idea -- but I think the way to do it is to short OPTIONS on zinc & copper, not the futures. This turns the transaction into a "covered call." If the price ends up above the strike price, melt 'em and deliver (or suffer a loss on your short call and then a gain on the physical sale, if they're cash-settled contracts rather than physical-delivery contracts.
The key to the strategy is that, with some probability p, the closing price will not exceed the strike price. It's silly to sink the cost c of converting pennies to the zinc/copper mixture unless you know you're forced to do so. By using options rather than futures, you save an expected cost of pc. This probabilistic cost savings would make it attractive to be "bolder", selling calls with lower strike prices.
So we shouldn't be melting down the pennies, but we should be planning (and contracting now) now to get paid to exercise our real option to melt down the pennies in the future. This way, we can get paid whether we melt 'em or not.
An added benefit: the metals market may not yet have factored in the price-dampening effect of extra supply, which will come on the market when melting becomes profitable. Thus, the price should hit a ceiling when melting pennies becomes profitable, but the option prices won't reflect the fact that a big move ABOVE that level is a long shot.
Posted by: ModalHubby at Apr 13, 2006 4:18:40 PM
Well, this topic doesn't come up very often... An article on arbitrage, coinage, and value of the underlying metal:
http://research.stlouisfed.org/publications/review/92/09/Faces_Sep_Oct1992.pdf
Posted by: M Flood at Apr 13, 2006 5:08:56 PM
Anon: How is a mortgage a put? Taking out a $100K 5% mortgage is equivalent to selling the bank a $100K 5% amortizing bond, but retaining the option to call the bond back in whole or in part.
Sammler and Anon: I agree with you that it is similar to the pennies with storage costs. But he real (highly technical) issue that makes mortgages different is that interest rates tend to revert to the mean over time, while stock and other asset prices tend to go up. You also have reinvestment risk and a lot of other wrinkles that don't apply to stocks.
Posted by: DK at Apr 13, 2006 5:53:07 PM
Nice! Somewhat useless but very interesting facts - that's totally my kind of information! Thanks!
:P
Posted by: Aaron at Apr 13, 2006 6:11:19 PM
We haven't heard from a metallugist yet. Don't count the higher value of the copper until you know how to separate it and the cost of that. But the question for the metallugist is: if you don't separate it out how will 2.5% copper effect the use of the things zinc is used for?
Posted by: lee at Apr 13, 2006 6:12:18 PM
Back in 2003, I bought $100 in pennies from the bank and sorted them out. Just over 20% of the pennies where from 1981 and before, and comparing the number of pennies of each date to the actual production figures from the mint, I was able to guesstimate that about 4% of all pennies are removed from circulation each year (i.e. lost, stored away in jars, damaged, etc). So, now in 2006, I estimate that about 17-18% (20% x 0.96^3) of pennies currently in circulation are from 1981 and before (95% copper). Roughly, 1 in 6.
Means you gotta sort through a whole lot of pennies to get to that copper. I did a rough calculation in my head a day or two ago, and figured out that at the current price of copper, you could make a gross profit of about $300-$350 in copper if you sorted through *ONE TON* of pennies from circulation. And that's just the profit from the intrinsic value of the metal minus the face value of the coins -- it does not take into consideration the cost of obtaining the coins, storage, transportation, SORTING, melting the copper, labor costs, etc. Even though a pre-1982 penny is worth 1.9 cents in copper, it seems like we sure got a long way to go before it is really cost effective to melt copper out of pocket change.
Me, I'm keeping a closer eye on the price of zinc and nickel. Once zinc hits about $1.75-$1.80 per pound (which it very well may do later this year), then post-1982 pennies are worth more in melt value than face value. At that point, you no longer have to sort out the pre-1982 and post-1982 pennies -- just melt them together and sell both copper and zinc. And nickel is hovering around the $8 per pound range, if it rises close to $9-10 a pound, then the nickel coin (which is 75% copper and 25% nickel) is worth more in melt value than face value. I suspect we could see nickels disappearing from our change before pennies do.
Finally, just want to ditto a recommendation that someone else who mentioned www.coinflation.com -- a nice little site to keep track of this sort of thing.
Posted by: M High at Apr 13, 2006 6:33:18 PM
I’m not a metallurgist but I have dealt in scrap metal: including coins. A decade and more ago we bought 36 tonnes (two entire truckloads) of nickel silver (which is actually doesn’t contain silver at all) coins in Russia. The huge inflation of the early 90s (thousands of percent a year) had made the meltable value hugely higher than the face value.
We didn’t make a huge profit, as above, most of that went to the people who did the collecting and sorting but it was worth trucking it all from the Urals into a European refinery.
Not all that important I know, I just like the fact that I did once buy two truckloads of coins.
Posted by: Tim Worstall at Apr 14, 2006 5:58:12 AM
"We all know, of course, that you should not exercise an option before its expiration."
Um, no. You should never prematurely exercise a CALL option; it can be perfectly rational to prematurely exercise a PUT option, since you can earn a risk-free return on the proceeds during the time to expiration.
And I hope we all know, "of course," that options can only be prematurely exercised in U.S. securities markets. In Europe options cannot be exercised until the day of expiration, making the whole question moot.
Posted by: KipEsquire at Apr 14, 2006 9:36:11 AM
And while we're on the subject, we should also make clear that the phrase "you should never prematurely exercise a call option" is only true as opposed to selling it. Exercising as opposed to selling simply destroys the option's time value, or "theta," which can never be rational.
But if there no secondary market in which you could sell the call option (e.g., employee stock options), then it could be perfectly rational to exercise it prematurely.
Posted by: KipEsquire at Apr 14, 2006 9:46:40 AM
Thank you, KipEsquire.
Posted by: Bernard Yomtov at Apr 14, 2006 11:31:25 AM
Why do U.S. "Pennies" exist at all now ??
Who needs them ?
Today's 'penny' is worth about one-tenth that of a year-1950 penny, in inflation-adjusted purchasing power.
Today's U.S. 'dime' is the equivalent of a 1950 penny.
Americans in 1950 surely did not need or use
'Tenth-of-a-Penny' coins. They don't need them now either.
Abolish both the current U.S. penny & nickel.
And with standard U.S. Government inflation rates, dimes & quarters will also soon be unnecessary to the citizenry.
Probably the only reason our penney & nickel are still official currency ... is because the Feds don't want to highlight their erosion of American fiat currency.
Posted by: Demming at Apr 14, 2006 11:44:47 AM
