The Problem

After Bitcoin stops going up every year, it will assume a kind of yo-yo pattern where it goes up and down around a value rather than continuously going up like a space rocket.

We don't know when this will happen or whether it already has. Some say they do. If you think Bitcoin's price will double every year forever, you have another thing coming.

On Vaultoro, you can trade Bitcoin, Dash, Ether and Gold and Silver. To capture gains that happen in Bitcoin and save them to silver or gold you can create an equation as follows:

Definitions

Let A_BTC,i represent the initial amount of BTC in the account.
Let A_BTC,f represent thefinal amount of BTC in the account.
Let A_Au,i represent the initial amount of gold in the account.
Let A_Au,f represent thefinal amount of gold in the account.
Let a be the amount of bitcoin to spend on the metal
Let p be the price.

Initial Equations

A_{BTC, f} = A_{Au, f} * p

This will be true if there is an equal amount of value of both the comodities.

To get to A_BTC,i to A_BTC,f as follows.

A_BTC,f = A_BTC,i - a

A_Au,f = A_Au,i + a/p * 0.995

The front-ends do not handle MathML so here is a JPG of the rest.

Equation Solution

The same equations work when balancing Bitcoin and Silver or Bitcoin and Ethereum on the same exchange.

An Example

Now we plug in values for Gold or we can apply it to silver instead:
Suppose we have $10,000 of silver and bitcoin on the Vaultoro exchange. And we have $3000 of silver and $7,000 of bitcoin. Now these prices are not in dollars in Vaultoro, they are in BTC. You cannot even have dollars on Vaultoro.

So instead we are talking about 0.123,7 BTC and 3571 g of silver.

The amount to buy is
1000 * ( 0.123,7 - 3571 g * 0.000,0161 BTC/g) / 1995

Sell 0.0338 BTC for silver at 0.000,016 BTC/g. But you will have to wait, maybe you wont sell because nobody is buying at that rate. You have to buy at

This leaves you with 0.090 BTC and 5656 g of silver.

Now, if silver should go up in value, your BTC bags will increase, and yes, you will lose in Bitcoin terms should the Bitcoin price keep climbing but suppose the price of silver takes a random walk and ends up back to where it is now?

grams of silver	total bitcoin	amount of BTC to spend on silver	price of silver g/BTC	Total value in BTC
3 571	0.123 7	0.033 37	0.000 016	0.180 8
5 656	0.090 3	-0.011 42	0.000 02	0.203 5
5 085	0.101 8	0.010 22	0.000 016	0.183 1
5 724	0.091 5	0.005 71	0.000 014	0.171 7
6 132	0.085 8	-0.012 31	0.000 018	0.196 2
5 448	0.098 1	0.013 69	0.000 013	0.169 0
6 501	0.084 4	-0.009 81	0.000 016	0.188 5
5 888	0.094 3	-0.011 78	0.000 02	0.212 0
5 299	0.106 0	0.010 65	0.000 016	0.190 8

As you see when the Bitcoin price finally becomes stable or duringtemporary bear market, a balanced portfolio can pay off.

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