Calculating the BTC/USD Exchange Rate

[Threshold]

I want to determine how many bitcoins to charge someone for some goods.

What is the accepted, fair manner for determining the exchange rate?

For example, right now at mtgox it says:

Last Price: 18.55High:19.23Low: 16.375Volume: 56399

It doesn't really say a concrete exchange rate -- just the ranges from today's trading and the price of the last trade they processed.

Is there somewhere else I should look?

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[TiagoTiago]

To convert USD to BTC divide the USD value by one of those 3 values (18.55, 19.23 or 16.375), or a value between the min and max; to convert BTC to USD multiply the BTC value by the rate you choose.

Or you want somthing like the "official" exchange rate from 'Gox?

[Threshold]

I guess I was hoping that there was a community-accepted concept of a fair exchange rate.

Otherwise, as the buyer I'd want a big exchange rate and as a seller I'd want a small exchange rate.

I had hoped there was something "fair."

As you said, I could take the average of the high and low -- but that doesn't account for outliers -- atypical trades.  I suppose the median price would be fair -- but that'd be a lot of data mining to calculate.

[acamus]

use geometric mean of high and low

sqrt(high*low)

pretty common and about as 'fair' of a rate you're going to get. I think many merchants sell in another currency and accept btc as payment given market prices.

[hello_good_sir]

Keep an "average" price.  Every time a new price comes out average this price with the old price.  You will end up with a price that cuts fluctuations in half.  If you want to further reduce fluctuations make it a weighted average, with only 10% or even 1% coming from the latest price.

While writing this someone mentioned the geometric mean, I *love* the geometric mean.  I use it for situations where you are selling to a friend instead of a store.  It is a way for the savings to be proportional.

[Threshold]

It sounds like the geometric mean sounds like the winner.

[timmo11]

While writing this someone mentioned the geometric mean, I *love* the geometric mean.  I use it for situations where you are selling to a friend instead of a store.  It is a way for the savings to be proportional.

How come it is fairer than the arithmetic mean?

[TiagoTiago]

I would like to learn the pros and cons of each as well

[jerfelix]

The geometric mean is a reasonable simple solution to the problem.

If you want to be really analytical, you would look at the order book and determine how much it will cost you to convert bitcoins to USD (or whatever currency you are considering).

Two things worth noting - this method could actually be higher than the geometric mean (if the current price is close to the high of the day).  And the conversion rate really depends on how many Bitcoins you are converting.  Just consider this:  If it's 1 BTC,  you are going to get a higher in USD than if you are trying to convert 10,000 BTC.

So look at the order book chart linked above, and look up the number of coins you are trying to convert on the side (Y) axis.  Then slide your finger over to the orange line, and that will give you a minimum price.  And where the orange ends (to the right a little bit), that will give you a maximum price.  Look at the area that is contained in the graph of orange, between the minimum and maximum, and take the arithmetic mean of the minimum and the maximum.  And that's your answer. (of course, you can figure this out mathematically, and not just by eye-balling it.)

That is the price that you KNOW you can offload the coins for, at that moment in time.

[iya]

How come it is fairer than the arithmetic mean?

I would like to learn the pros and cons of each as well

The geometric mean is the "correct" mean for ratios, which prices are. It's the arithmetic mean on the log-scale:




Which chart looks more "correct"?

jerfelix is right of course: As a seller you're interested in the best "bid", and as a buyer you're interested in the best "ask". bitcoincharts.com has a calculator for larger orders, on the Market Depth page.