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Gold-silver update, April 5 2018

Today there is a bit of divergence in gold and silver – gold is down a bit, at 1325.20, silver up a bit, at 16.37.  This perhaps reflects what the talking heads are saying, that silver, having underperformed gold,  is due for a rise.  Indeed some serious commentators are suggesting that silver could return to its 2016 highs, within months rather than years.  As for the gold-silver ratio, it is still sky-high.  Yesterday, at 81.75, it was the highest it has been for two years.  Today it’s down to around 80.95.  Of course a falling gold-silver ratio isn’t necessarily bullish for silver – it might just mean that silver is falling less than gold.  Yet there is historical evidence to suggest that when the gold-silver ratio spikes, a rise in the silver price soon follows.  This is because silver tends to follow gold, and when gold makes its move, without silver following, the ratio can temporarily hit very high levels.

We should also remember that silver is a hybrid metal.  It is a precious metal with many industrial uses.  Today’s small rise in silver may just reflect what is going on with the base metals.  Copper, for example, is up over 1%, at $3.08 a pound.


What should a Bitmain L3+ Litecoin miner cost?

Cryptocurrencies are getting smashed, and those involved in their mining are feeling the pinch. I suppose a lot of people must have bought mining equipment from Bitmain in the last few months, hoping for a quick profit. One machine that was heavily bought was Bitmain’s L3+ Litecoin miner, which can mine a variety of scrypt coins, including Litecoin, Dogecoin, and Verge. Plus a few exotics, such as Leafcoin, Lindacoin, and Sexcoin.

The L3+ Litecoin miner does around 504 megahashes a second, which in ordinary language is half a billion random numbers a second. Bitmain are currently selling it for $855, thought a couple of months ago the price was over $1500. You also have to pay for a power unit, which is over $100, not to mention shipping and customs. So the price you’re paying, right now, is around $1250. Not bad for a money machine. You plug it into your router, sign up to a mining pool like prohashing.com, and your sleepless machine is making you money 24 hours a day.

If only things were that simple. If you’re running a miner, there are three things to consider. Firstly, the cost of electricity, secondly the dollar price of the coins you’re mining, and thirdly, and most importantly, the coin’s difficulty. Electricity is easy to calculate. Where I am, in the State of Washington, electricity costs eight cents a kilowatt, which by global standards is cheap. If I run the 800W machine for a day, it will cost me $1.54, so if I am making less than this, the mining is no longer profitable, and I turn the machine off.

Mining Litecoin has become increasingly difficult, with difficulty being a metric of mining effort. It is currently measured in millions, with difficulty approaching 7 million:

The opposite of difficulty is earnings per day.  As difficulty increases, you earn less and less.  With an L3+, you were earning something like 0.07 Litecoins a day at the beginning of 2018.  The figure now is just over half that, at around .037.  The earnings graph paints a sorry picture:

We can now start thinking about what an L3+ should cost.  Right now, the earnings graph of Litecoin is linear, and if we assign 1 to January 1, 91 to April 1, and so on, we can create a crude equation, with time (t) as the independent variable:

Daily earnings = .07052 – .0003562t

This equation is not entirely realistic, because earnings cannot fall below zero, and in reality we are talking about exponential decay.  Put another way, as earnings approach zero, people will be turning their miners off, and difficulty will start to stabilize.

Nonetheless, the equation is saying that on the 197th day of 2018, Litecoin earnings will fall to zero.  That’s the end of July.  So one should not count on earning any Litecoin of any consequence from late July onwards.  Using a bit of calculus, that means, in theory, that there are only 2.04 Litecoins left to earn.  In practice it is more, because the machine will always be earning something, but at this rate the amounts will soon be nominal.  Litecoin is currently $120.2, so that’s $245 earned by late July.  We then have to take into account electricity.  There are 106 days left of non-nominal earnings, which at $1.54 a day will cost $163.24.  Subtract that from $245, and you get $81.76.

Actually, things aren’t quite that bad, if you turn your L3+ off the moment you’re not covering your electricity.  Assuming $120 Litecoin, this is when the daily earnings drop to .0128 Litecoin, when is on day 162, or June 11.  That will yield 1.808 Litcoin, or $217, assuming Litcoin is at $120.  The electricity cost for those 71 days is $109.34, leaving you with $108.

This means that if you want to buy an L3+, you should pay no more than $108 – and that includes the shipping cost.  The power supply is a different matter, because it can be used on other machines.  But what if Litecoin goes up?  It might.  But it might also go down.  Besides, if Litcoin does go up, you are almost certainly going to be better off buying it from an exchange.

If you do decide to buy the L3+ directly from China, for $855, and you ignore the other costs, then to make a profit you need Litcoin to be well over $400 by the end of July.  Indeed much more than that, because the machine takes a week or two to ship, losing you valuable time at the profitable end of the earnings curve.  But if Litcoin really gets to $450 by the end of July, you would be thousands of dollars better off if you had bought the Litecoin rather than the Litecoin miner.

All this emphasizes the point that right now anyone entering the Litcoin-mining sphere is playing a no-win game.

Finally, my analysis is probably worst-case, assuming that the Litcoin price doesn’t fall substantially below $120.  As L3+ miners start getting turned off at the end of May and beginning of June, the difficulty profile of Litecoin may dramatically improve.  We can then have another look at the economics of the situation.

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Choosing a high school: does it really matter?

My thirteen year-old son is just finishing middle school and it’s time to think about high school.  There are three choices in the School District, or four if you count home-schooling.  Clover Park High School is the default school for where we live.  It’s a prison-like building, which puts a high premium on sports.  Indeed it’s the home of the Warriors, and every week I can hear the Star Spangled Banner blasting from their stadium.   Another high school is Lakes.  It’s the school that all my son’s friends are going to, and they teach rudimentary German and Japanese there.  Finally there’s Harrison Preparatory School, Harrison Prep for short.  Its big advantage is that they don’t do sports, but they do have a waiting list.  The school claims that they prepare students for college, and they are very proud of their International Baccalaureate program.

So how do we make our choice?  One method is to use test results.  Every year the State of Washington gives children a standardized test, called the Smarter Balanced Assessment, SBA for short.  The tests are in English Language Arts (ELA), mathematics, and science, and they are designed to test whether children have reached state standards for their grade level.

The State have published statistics for 2016-2017, on the website of the Office of Superintendent of Public Instruction.  You can look up all the School Districts in the state, and you can then compare the good, the bad, and the ugly.  The SBA has four levels, 1 to 4.  Level 4 is Advanced and Level 3 is proficient.  In other words, the kid with a 3 or 4 has met the state standards.  Levels 2 (Basic) and 1 (Below Basic) are below standard.

Let’s look at some examples.  In the Tacoma School District there is a school called the Science and Math Institute.  It’s a great shame we don’t live in Tacoma, because that would be just the school I’d want my son to go to.  Nonetheless, I’ll check the SBA scores.  For ELA it’s not too bad, with 73.2% of 11th Graders reaching the standard, with a 3 or a 4.  And one has to remember that it’s a science and math institute, so the kids are going to be more focused on numbers than words.  Turning to the math scores… and 25 eleventh graders out of 80 at the Science and Math Institute have met the state standards.  That’s 31.3%, or 35.2% if you count previous sittings of the test.  That’s weird… either the students need more practice taking tests or the school needs a name-change.  Another example is the International School, in Bellevue School District.  Bellevue is where the money and the tech companies are, and this is reflected in the school’s SBA scores.  Of the 11th graders that took the math SBA, 93.6% reached or exceeded state standards.

We now have to consider my son’s School District.  I created a table, listing the number of 11th graders in Clover Park, Lakes, and Harrison Prep who were above and below state standards in math:

There are real differences between the three schools, and if one does a Χtest one gets a significant result.  However, are the results enough to show that Harrison Prep is the better school, at least for mathematics?  They suggest that for the student of average ability it probably is.  For children who are markedly above or below average, the situation isn’t so clear.  Both Clover Park and Lakes have a lot of students who are above standard – indeed enough to fill two whole class rooms, in each school.  And From the Washington figures we have no way of knowing how well these above-standard students are catered for.

As a final thought, we can estimate the effect size of Χ2. We divide Χ2 by the total number of students in the table, and square-root the answer.  Χ is 40.775, and when we divide this by 486 we get .084.  And the square root of .084 is .2897.  We can therefore say that differences between the three schools explain 28.97% of the differences between the math scores.  This leaves us with an unexplained 71.03%.  So maybe it doesn’t really matter which high school my son goes to.  Or maybe he should be home-schooled?


Will Donald Trump die for his country?

Presidential assassinations are rare events.  Since 1789, when George Washington became president, only four US presidents have been assassinated.  Abraham Lincoln in 1865,  James Garfield in 1881, William McKinley in 1901 and John F Kennedy in 1963.  This doesn’t change the fact that from an occupational point of view, being US President is a dangerous job – there have been 44 different men who have served in this office, meaning that over 9% of them have been assassinated.  Admittedly the job of US President is safer than being a British solider in World War War I, where the death rate was 11.5%,  but far more dangerous than being a US serviceman in Vietnam between 1964 and 1975, with a death rate of less than 1%.  So we shouldn’t condemn Clinton, Bush Junior and Trump for skipping the draft, because their willingness to go to the White House shows that they were ready and willing to lay down their lives for their country.

We then have to ask whether or not the four presidential assassinations are telling us anything about future likelihood.  One could argue that three of the four assassinations happened over a short period of time – between 1865 and 1901 – and they won’t happen again.  These three assassinations involved handguns.  Maybe those charged with protecting presidents hadn’t fully appreciated the dangers posed by high quality weapons, which were easy to conceal.  After McKinley’s assassination, there were no more assassinations with handguns, and it took a sniper’s rifle in 1963 to kill John F. Kennedy.  Yet in 1975 there were two assassination attempts on Gerald Ford, both with handguns, which could easily have succeeded.  And in 1981 Ronald Reagan was wounded by a bullet fired from a revolver.

If we want to use the past four assassinations to assess the likelihood of futures ones we have to assume that the chances of assassination are the same, across the whole 229 year period.  Perhaps we could say that the protection given to presidents is balanced by increasing desires and opportunities to assassinate.  Maybe George Washington, as the first US President, had very little protection, but very few people had an inclination to kill him.  As protection increased, presumably after the assassination of Abraham Lincoln, so did the population of the US, as well as the number of guns in circulation.  In other words, there remained one president, but an increasing pool of people who might want to attack him.

There is also the question of independence.  I am assuming that all four assassinations were independent events, not influenced by one another.  James Garfield was assassinated only 16 years after Abraham Lincoln, so the memory of the event was still fresh in the national consciousness.  Under these circumstances, one might argue that one should treat the three Nineteenth Century assassinations as a single event.  In which case we can regard there as only being two independent assassinations since 1789.

Assuming that each assassination was an independent event, and that the probability of an assassination has been constant since George Washington became president, we can say that each year there is a 1.75% chance of the President being assassinated.  We can see the four assassinations in one graph:

We can now make a crude estimate of what the chances of Donald Trump being assassinated are, by end of his term on January 20, 2021.  Remember, I am talking about assassination.  A president doesn’t have to be assassinated to die in office, and since 1789 there have been four who have died of natural causes.  Donald Trump, as a 71 year-old male, has a 2.5% chance of dying over the course of a year.  OK, it’s probably lower than that, because currently he’s in good physical shape and he also has access to the best healthcare in the world.

In terms of assassination, we have to consider when the next event will occur.  Assuming America continues to have presidents, it is unlikely that that there won’t be another assassination.  Even if presidents and other leaders cut themselves off from the unwashed masses, they can still be assassinated.  For example by security guards, like Indira Gandhi, or by supposed colleagues, like Julius Caesar.

Now for some mathematics.  If we want to calculate a crude probability of a presidential assassination, within a particular time period, we can use the cumulative density function of the exponential distribution:

The letter e is log natural (2.718), λ is the mean number of assassinations per year, and t is time.  There are 0.0175 assassinations per year (4 divided by 229) and let’s take 20 years as time.   This means that the probability of a president being assassinated sometime between now and 2038 is 0.2949, or 29.49%.  However if you want a 50% chance, then you would have to go out 39.68 years.  In other words, we can say that there is a 50% change that a US president will be assassinated in the next 40 years.  Below is the probability graph of the next 100 years, with the red line pinpointing the 50% chance at 40 years.  The green line hits 80% after 100 years, indicating an 80% chance of an assassination between now and 2118.

What about Trump?  Today is March 29 2018.  On April 30 1789, 83,608 days ago, George Washington became US president.  So right now, the chances of a president getting assassinated in a one-day period are 1 in 20,902.  Moving forward, there are 1028 days left before Trump’s term of office ends.  We can then create a new graph, which zeros in on the remainder of his term:

Looking at these 1028 days, on Thursday March 29 2018, we see that the chance of him being assassinated by the end of 2018 is 1.29%.  Looking  forward to the end of his first term, on January 20 2021, and it’s 4.78%.  A chance that’s small but not insignificant.

One final point.  These probabilities only hold for the day you calculate them  If it is January 1 2019, and Trump is still alive and tweeting, you’d have to do the calculations all over again.  You would find that the chances of an assassination between that date and the end of the first term would be only 3.51%.


Silver: Is it a breakout or a breakdown?

Silver is a dreadful investment.  The price moves within a tight range, and whenever you think it’s going to breakout to the upside, the price gets smashed.  It works the other way.  The moment it starts falling into the abyss, it gets magically lifted.  This means that there is no opportunity to make serious money with silver.  You have to trade it nimbly, or else gather pennies by selling out of the money options.  However I am not convinced that the situation will go on for much longer.

Let’s look at the price of silver, since January 1 2015.  The minimum price was around $13.50, the maximum just short of $21, the 25th percentile $15.83, the median $16.67, the 75th percentile $17.33.  As you can see, from January 1 2015 the range is very tight, and it’s getting tighter:

The three horizontal red lines represent the 75th percentile, the median and the 25th percentile.  So for approximately 75% of the time, from 2015 onwards, the silver price was between $15.83 and $17.33.  The white lines show support and resistance.  As time progresses the price is bouncing with a narrow and narrower range, and in the late summer the white lines will cross.  I would therefore expect that over the next few months the silver price will breakout or break down, as it makes a sharp move out of its trading range.

If there is a breakout rather than a break down, we might expect it to happen on the median point, and to encompass the whole range from minimum to maximum.  The range in price since January 2015 is around $7.13, so adding that onto the median gives us a breakout target of $23.80, by the end of 2018.  A breakdown target, by contrast, would be $9.54, but my bias is for a breakout, not a breakdown.