I like a diversified stock portfolio better as a hedge. Yes, there are situations where an entire portfolio could crash, but those tend to be the sort of situation where you want canned food instead of gold.
I’ve no answer to OP but the history of the gold/silver price ratio is interesting. Alexander Hamilton initially fixed the ratio at 15; it soon rose to match France’s 15.5 and, more than a century later (cf. William J. Bryan “Cross of Gold”) there was a strong movement to mint silver coins at a 16:1 ratio. (The market ratio was much higher then due to Comstock silver.) During the 19th century, France minted full-bodied coins of both gold and silver, with both circulating despite Gresham’s Law. Here’s a paper by Milton Friedman praising bimetallism as offering the potential for greater stability than monometallism.
The British gold sovereign, weighing about ¼ ounce (five Troy pennyweights) and worth 20 silver shillings may confuse … until you note that by 1601 England was on a “62 shilling standard” (one Troy pound of silver produced 62 shillings worth of silver pennies), with a silver penny thus having slightly less than ⅓ pennyweight of silver.
Sir Isaac Newton, who took his work at the Royal Mint very seriously, enters the story. Despite his efforts, England’s gold/silver price ratio was slightly higher than the world price, putting England on a de facto gold standard but forced to mint silver coins for foreigners. It is said that this huge silver imbalance led Britain to enter the opium business!
The amount of silver mined annually is about 9x that of gold so theoretically it should be one-ninth the value given their similar nature. In truth silver is used in more applications so it should be more valuable than the 1/9 x gold.
Theoretically
Much more copper is mined than zinc, yet the U.S. Treasury makes pennies out of zinc because it thinks it’s cheaper! Stupid bureaucrats.
And cadmium mining lags slightly behind silver mining; yet sells for 67¢ per kilogram. Maybe we should be buying cadmium futures!
… And let’s not get started on Beanie Babies, rarer than either silver or cadmium.
You’re mixing up cause and effect.
The amount of silver mined annually doesn’t determine of the price of silver.
The price of silver determines the amount that’s mined annually. If silver were worth more, we’d mine more of it!
What is the total estimated mass of Beanie Baby in the world? I did a little googling, but couldn’t find any numbers.
Maybe mass isn’t the way to measure this, though. Maybe 108 grams of silver corresponds to 6.02 x 10^23 Beanie Babies. 
When I was young and stupid(er) I took up an interest in commodity markets – not just silver. After a few months it occurred to me that every contract I bought or sold was sold or bought by someone who figured the market was going to go the other way than I did. End of studying.
This four-part history puts the blame on China, sucking all that Royal Mint silver out of the vaults for all that tea the Brits were drinking.
The question has mostly been well answered. I’d just elaborate on the difference between recent history and long past history as to the silver/gold ratio. Long ago silver and gold were both mainly money, and jewelry which tends to be related, a physical show of money. Also governments were more in the habit of and more successful in dictating monetary values and standards in the distant past. Not always successful obviously, but they’ve been progressively less inclined to even try as liberal (in the classical sense of the word) economic theories have gained dominance.
Plus nowadays silver prices in particular have a lot more to do with the demand to consume silver in industrial uses rather than hold it as money or jewelry. That’s not completely untrue of gold but less so.
The places trying to sell silver coins to retail often use predictions of higher than expected industrial demand for silver as a selling point, and other times the silver/gold ratio. But one argument actually tends to undercut the other. Any good financial predictor knows he or she will only make money being right slightly more often and/or to a slightly greater degree than being wrong. So if you predict industrial silver demand is going to be much more than the market predicts, you have to accept it’s almost as likely to be much less than you predict, even if you’re an exceptionally skilled forecaster. IOW a prediction of a likely big difference from what the market expects for industrial silver demand means a prediction that it’s highly uncertain, therefore undermining the idea of a natural ‘reversion to the mean’ of the ratio of silver to another commodity, gold, which can’t be directly substituted for silver in most industrial uses to the degree it could be for monetary uses.
It may be worth mentioning that it’s not just silver and gold whose prices fluctuate. The price of nickel fell 80% between 2007 and 2009. I don’t think nickel is special — that was just one of the graphs that presented when I did a quick Google just now. The prices of steel, cement, wheat, etc. all fluctuate wildly. Given this, it’s almost surprising that the average price of consumer goods, in terms of “fiat” dollars, is maintained as stably as it is.
Thus the fact that the economic might of France was able to maintain the gold/silver price ratio at 15.5 for an entire century is impressive. (Upthread I think I linked to a Friedman paper citing this and claiming that bimetallic money might be more stable than monometallism.)
That’s not actually true. Many of those buying or selling commodities aren’t necessarily assuming that prices will move in line with their contracts, but simply want to hedge just in case it does.
For example, suppose you’re in the energy business and stand to lose a lot of money if oil/gas drop in cost. You might buy put options in order to lock in current prices, even if you personally thought it’s more likely that prices will go up from here. This drives much of the trading in commodities and commodity futures (even some pretty exotic ones, e.g. utilities might hedge by buying weather futures).
Picking the house is easy. Just buy a dilapidated shithole in a nice neighborhood. The hard part is making the necessary repairs within budget and without incurring holding costs of having to pay the mortgage each month.
Which is why the “precious metals” portion of my investment portfolio is invested in mining companies. The price of their stock and their dividends tends to follow the prices of the metals they mine, but they are actually producing a product people want instead of warehousing it and charging for the right to own it.