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Guessing the silver price

There’s an old game, where you fill a glass jar with sweets, or candies, and everyone guesses how many are there.  The winner keeps the lot.  And if you take the average of all guesses, you’ll get a good approximation of the actual amount.  I think it’s called the Wisdom of Crowds.  The same principle might apply to the markets.  If I ask 30 people what the price of silver is going to be on July 31 2020, I just have to take the average guess and position myself accordingly.

Unfortunately, this assumes that the players in the game are neutral.  If you own an asset, the situation is different.  I saw this at work over the Summer.  On the ADVFN financial bulletin board, there’s a thread called “The Really Useful Silver Thread”.  It’s not actually that useful, and many of the posts are about conspiracy theories.  Yes, people who invest in the precious metals are suckers for conspiracies, and they believe that markets are manipulated by malevolent forces.  Not to mention Goldman Sachs and J.P. Morgan.

Larry Williams, in his book Trade Stocks and Commodities with the Insiders, summed it up succinctly: “The bullish camp, those looking for wildly higher prices, has made a mantra and religion out of silver.  To them the world is going to hell and the sooner the better” (p.38).

Still, there is a certain community spirit on the board, and also an annual competition.  The prize is two ounces of silver, and you have to guess the silver price by Christmas, with the closest guess being the winner.  If my memory serves me correctly, the silver price at the time the competition was open was around $18.  The guesses, in dollars, were as follows:

73.29, 55.23, 45.00, 36.37, 27.50, 25.75, 24.00, 23.56, 23.08, 23.05, 22.22, 21.77, 21.75, 21.42, 21.10, 21.00, 20.90, 20.80, 20.50, 20.20, 19.87, 19.85, 19.80, 19.48, 19.20, 19.05, 18.52, 18.30, 18.05, 17.90, 17.55, 17.45, 16.50, 11.95

As the histogram at the top of this post demonstrates, the distribution was far from normal, with the lowest guess of $11.95 being 1.03 standard deviations below the mean, the highest guess, $73.29, being 4.14 standard deviations above.

I suppose the biggest problem with these guesses was personal stake.  With the sweet jar one’s guess is neutral.  One doesn’t really care how many sweets there are.  With silver, there is often total commitment to the cause.  The price is manipulated, and one day the manipulation will end.  The true price of silver is $50, $75, $100, take your pick.  You’re therefore tempted to go for some crazy number.  This means, from a rational perspective, that guesses over $27.50 should be discounted.  Commodities don’t double in value in the space of a few months, unless there is a global shock.

The mean guess, at $24.16, doesn’t tell us much, because it is heavily influenced by the crazy guesses.  The median guess, at 20.85 is more reasonable.  If the precious metals market had recovered its steam, after the Autumn correction, we might have reached this price.

Alternatively, we could look at the 95% confidence interval.  The high value is 28.31, the low value 20.04.  So even the lower bound is totally out of whack, given that today, six days before Christmas,  the price of silver is $17.04.

From a rational point of view, if you own silver, it would have made sense to put in a low-ball guess.  It would be a possible way of hedging your long silver position.  If your longs are underwater, you at least have the consolation of having a real chance of getting $34  of silver, from a competion that costs you nothing to enter.

For myself, I guessed $16.50.  The next highest guess is $17.45. I saw a youtube video a few years ago, where someone said that silver below $16.50 is cheap, above $16.50 expensive.  It seemed a reasonable estimate.  I therefore need silver to close below $16.975 to win my two ounces.

Does the story have a moral?  Don’t listen to bulletin boards.  And remember that wishful thinking can’t move the markets.


Box plots for tracking volatility in silver prices

In the social sciences, the box plot is a popular graph.  It’s because it contains so much information.  It is based on two metrics, the median and the interquartile range (IQR).  The median is the central data point.  So let’s take daily silver prices for 2018.  My data isn’t perfect, but I get a median of 16.6 – half the data points are above 16.6, half below.  The IQR is the distance between the 25th and 75th percentiles.  The 25th percentile is 16.46, the 75th percentile 17.04.  This is the box on the box plot – the solid rectangle between the 25th and 75th percentiles.  The median is the line which cuts the box horizontally.  The box then has whispers which extend up to one and a half times the length of the box.  Any data point which goes beyond this limit is marked individually, as an outlier.

The box plot then gives a graphic description of the data and its range.  We can then create a graph of box plots, to show how the range of data has changed over time.  For example, we can assign one box plot for each year:

The data for 2007 and 2018 are incomplete, but one gets the picture.  Note the outliers in 2007, 2010, and 2017. In the last few years the range of silver prices, and therefore the volatility, has been collapsing.  In 2018 the range has been constrained to a range of about a $1.50.  Could this be a coiled spring?  Could it uncoil one way or both ways?


The Dollar and Gold – a dubious correlation

Gold is priced in dollars, so when the US Dollar goes up, gold goes down, right?  This relationship between gold and the Dollar is much talked about, and there is a view that as the Dollar rises, so gold falls.  In other words, a rising Dollar is toxic for the gold price.  The same logic follows for other commodities, such as silver and copper.

The relationship between two things can be measured as a correlation, where two things that move in exactly the same way have a correlation of 1.  By contrast, two things that move in perfectly opposite directions have a correlation of -1.  In the case of gold, one might expect its correlation with the dollar index to be very negative.  But does this negative relationship actually exist?

If one looks at the data since 2007, without making allowances for the autocorrelation of time series data, there is no correlation between gold and the Dollar Index.  To be precise, it’s -.02.  Very slightly negative, but not statistically significant.  If one allows for autocorrelation, the correlation does become significant, at -.28.  This means that changes in the Dollar Index account for just under 8% of changes in the gold price.  In other words, 92% of gold’s movement is unexplained by the Dollar Index.

I suppose one of the main reasons that so-called pundits are currently obsessing about the strength of the gold-dollar relationship is recent history.  At the moment, in the first half of 2018, there is a strong negative relationship between gold and the Dollar:

As you can see, the relationship between gold and the Dollar Index is savage, and any rise in the dollar is going to be met with a smashing of gold.  The unadjusted correlation is -.72, meaning that over half the variance is shared.

Yet nothing lasts for ever, and the moment a highly correlated relationship seems set in stone, it breaks up.  Here’s the graph of the 30-day correlation between gold and the dollar, since the beginning of 2016:

Right now the correlation between gold and the dollar is at an extreme low, of -.92.  It’s therefore got nowhere to go but up.  This has consequences for anyone who is both long the Dollar and long gold.  At the moment it’s a hedged trade, but for how long will it stay that way?


Guns, suicide, and population density

It’s probably not the right time for a Brit to comment on Americans and guns.  Over the last few months there has been a wave of knife-murders in London, giving it a higher murder rate than New York.  Perhaps if more Londoners had guns, the murder rate would be lower.  If I lived alone, I would certainly buy a gun.  Not because it would make me safer, but out of curiosity.  From a British perspective, having a gun in your own home is so weird, you’ve just got to try it, unless your wife says otherwise.  There may also be a societal obligation to own a gun.  Burglary rates are lower in the US than in the UK, and one reason may be the deterrence of unregistered gun ownership.  If you’re a burglar, you don’t know whether your intended victim is a gun owner.  Even a bed-ridden 95-year old woman could have a Gloch under her pillow.  This means that those of us who don’t own guns are parasites, relying on gun owners for their passive protection.  If people stopped owning guns, burglary rates might start rising.  It’s a similar situation with vaccinations.  If you don’t vaccinate your kids against measles, you’re relying on other families to vaccinate their children.  Why should I risk my children getting a bad reaction to the vaccine?  Let other children take the risk, and let my child get the benefit.  Yet if vaccination rates fall below a certain threshold, the benefits of public vaccination programs start declining.

Guns might protect you against burglary, but what about other things?  Suicide for example.  The 2016 suicide statistics have been out for some time, and inevitably they are used as a foil against gun ownership.  It would seem that states with the highest rates of gun ownership have the highest suicide rates.  Of course gun ownership is a difficult thing to work out, as there is no obligation to register your weapons.  There are also bad statistics that get passed around the internet.  For example, the rate of gun ownership in Hawaii.  I have seen reputable sources claim that it is 45.1%, one of the highest in the nation.  I have seen other sources reporting 6.7%, which seems more plausible.

Anyway, the standard statistical approach is to create a scatter plot, comparing suicides per 100,000 with gun ownership, by state.  You get a graph like this:

The scatter plot clearly shows that as gun ownership increases, so does suicide.  The green dot at the bottom is New Jersey, with the lowest suicide rate in the Union, of 7.2 per 100,000.  It also has the second lowest gun ownership rate, of 12.3%.  At the other end of the spectrum, you can see two green dots on the top right, representing Alaska and Montana.  They have suicide rates of respectively 25.8 and 25.9, well over three times that of New Jersey.  They also have very high rates of gun ownership, approaching 60%.

However we have to be careful.  States with high suicide rates may have particular futures, which attract gun ownership.  Such as a low population density.  Alaska has a density of 0.43 people per square kilometer, compared with New Jersey, with a density of 400.  Here is a histogram of the population densities of the 50 states:

As you can see, it is a rather skewed distribution, so we’ll transform it, using the 4th root:

We can then create a scatter plot comparing suicide with the transformed data:

A beautiful, inverse relationship, with a correlation of -0.85.  We also find that gun ownership and the transformed density have a correlation of 0.79.  So the higher the population density, the the lower the suicide rate and the lower the rate of gun ownership.  We can then do a hierarchical regression, trying to predict the suicide rate per 100,000:

When we try to predict the suicide rate just with the transformed density, we have an R-squared of .72, meaning we can account for 72% of the variance.  The addition of gun ownership to the model raises R-squared to .73.  It’s a miserably low increase, which is miles away from being statistically significant.  This means that on a state level, one should be careful about arguing that there is a relationship between gun ownership and suicide.  What matters is population density.

One can speculate about the reasons for this relationship.  In a state like Alaska or Wyoming there may not be easy access to mental health facilities.  The isolated environment may also be attractive to people who are ruggedly independent, who don’t believe in asking for help until it’s too late.  And of course if you live in such states, you’re more likely to have a gun, either for hunting or for personal protection.

For me, the main takeaway is that the beauty of the great American wilderness conceals a dark shadow.  It’s OK to live in the Montana outback if you’re happy and well-balanced, but if you have any doubts about your mental health, you should forget your rural dreams and consider moving to a city.  Newark, New Jersey, for example.


Precious metals round-up: Saturday April 7 2018

Friday was non-farm payrolls.  The figures weren’t great, with 103,000 jobs created in March, well short of expectations.  The US economy is not quite as buoyant as some had hoped, and the dollar lost some ground.  The precious metals hardly moved, silver closing the week down a fraction at $16.36, gold up a fraction at $1,333.  The gold-silver ratio, at 81.45, remains in outlier territory, in the top percentile for the 21st Century.

At the same time, the commitment of traders (COT) report was bullish.  The commercials had increased their longs in both gold and both gold and silver, and reduced their shorts.  Managed money has done the opposite.  The commercials represent the large players, and they tend to be on the winning side of the trade.  Managed money, which includes hedge funds, are supposedly the perennial losers.

However, it seems unlikely that the precious metals can go up significantly without a fall in the dollar.  Since late January the dollar index has been trading within a tight range, close to the 90 mark.  Precious metal bulls needs the dollar index to go much lower, at least down to 85.  At that stage a break-out in gold and silver prices becomes distinctly possible.