Where Logarithmic Scales Lead To Exponential Returns
In a recent exercise we undertook to find a secure pricing algorithm for a new asset, we came across something very interesting in a time-atrophied logarithmic moving average data set that we manipulated with the average bias moving away from the present to the year-ago point.
By plotting data points two months apart, and shifting the moving average calculations cumulatively shorter towards the year-ago point in time (with the shortest “average” being the single first entry year-ago price point and the longest average being the present one which included all the previous 6 data points) we were able to create a more robust, alpha coefficient variation of CoinMarketCap’s price Index by quite a wide margin:
What we did specifically was that we compared the annual composite CoinMarketCap (CMC) Index on a bi-monthly basis to the annual logarithmic moving average of CMC’s Top 10 coins and we found that on average volatility was 70% higher in the case of the CMC composite index numbers than in the logarithmic moving average numbers. In terms of absolute performance, logarithmic moving average numbers were up an average of 3.5% per two-month period versus 5.4% per two-month period in the case of the composite returns. Once you account for the drag that volatility takes out of the composite numbers, that’s roughly a whole percentage point of additional alpha outperformance that the logarithmic moving average scale has over the unadjusted scale recalculating for a monthly timeline.
This result appears to correlate much more with the logarithmic moving average versus pure composite / Top 10 variation, since the Beta (volatility measurement) of the Top 10 index was even higher, with an overall 20% lower performance month on month (on average) between the Top 10 and the entire index in absolute terms (alpha). Therefore, our conclusion is that one of the most preferential and robust (volatility-neutralised) pricing mechanisms for any sort of cryptocurrency asset is the annual logarithmic moving average Top 10 CMC price index. If an asset were priced according to the annualised T10 L.M.A. in dollar averaged terms then the pricing guideline for an asset would look like this:
It’s like the best of a stablecoin with a bit of the best of market momentum thrown in there, in other words. In a year notable for roughly a 75% decline in overall market prices, such a stable average variation resulting in an average gross increase of 1.5% per month (21% on the year) is a blinding result, especially as those returns are 100% volatility neutralised (i.e. factoring out all the risk relative to the risk of the overall market).
What this illustrates is how we tend to standardise far too many trading and pricing algorithms still when it comes to Blockchain assets, which basically means that we forget to calculate to factor in quite a significant variable given the relative innovation trajectory of the space. That variable that we forget to factor in is none other than market growth itself.