Investment Math Question

[DeletedUser394]

I'm having trouble figuring this out.

Let's say the CAD and the USD are at parity, 1:1

You buy an asset in CAD for $10,000. The asset in question is independent of currency, and you can buy/sell it in any currency you want (I'm basically talking about precious metals.. or bitcoins, or anything really).

Now you have this asset worth $10,000 CAD but then the CAD loses 10% of its value compared to the USD and now the currency ratio is 0.90:1.

The underlying value of the asset hasn't changed and is still worth $10,000 CAD, but the CAD is worth less compared to other currencies.

If you elect to sell in USD and then convert back to CAD do you actually make a profit when the value of the asset hasn't changed, or is that already priced into the asset? I think so, but for some reason I'm having trouble seeing it.

Is there an equation that would explain the above situation?

Thanks!

 

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[socaldude]

Just like options, it would be a zero sum game. Depending on who is selling or who is buying, someone's gain would someone elses loss.

To explain this in mathematics it would probably be a parity equation; one price relative to another. If there is no parity then there is an arbitrage opportunity.

But for non-institution investors, this is rare.

 

[DeletedUser394]

Let's say you were a rich guy in Zimbabwe pre-hyperinflation.

You bought 100 oz of gold with your good Zimbabwe dollars and kept it in a safe deposit box.

Then a few years later the Zimbabwe dollar collapses and is almost worthless, so you sell that 100 oz of gold for USD. If I understand what you're saying, then if you were to convert that USD back to the almost worthless Zimbabwe dollars it wouldn't make a difference because the value of the Zimbabwe dollar was already priced in to account for the hyperinflation.

So whether you were to sell your gold back for Zimbabwe dollars or USD the outcome is the same.

So the purpose of the asset (in this case gold) was to hedge against your own currency collapse, the Zimbabwe dollar? The value of the asset when compared to more stable currencies didn't change. It was just your currency that collapsed.

 

[socaldude]

No it would not be the same outcome. If you accurately predicted the collapse of the Zimbabwe dollar and bought gold, a hard asset or commodities then yes you saved your A$$. But remember somebody else had to take your Zimbabwe dollars and give you gold, somebody got stuck with the currency. This is what happens during hyperinflation, you do not want to hold the currency that is going to zero, you spend it as fast you can and therefore prices skyrocket and currency values plunge, nobody wants the now worthless currency. But because you converted your dollars to another asset before hand you avoided the panic. Other asset values should stay the same(in theory).

always think of it in terms of a buyer and a seller each with a different thing to trade.

 

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[DeletedUser394]

Ah yes, I neglected to think of the other party involved in the transaction.

In the case of a modest 10% drop (like the CAD vs USD that occurred recently), in that situation the outcome would be the same (CAD to GOLD then back to either CAD or USD), as obviously you can find a buyer for CAD or USD.