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This time I want to share with you a little script that, thanks to the use of arrays, allows you to have interesting statistical and financial insights taken from the symbol on chart and compared to those of another symbol you desire (in this case the metrics taken from the perpetual future ETHUSDT are compared to those taken from the perpetual future BTCUSDT , used as a proxy for the direction of cryptocurrency market)

By enabling "prevent repainting", the data retrieved from the compared symbol won't be on real time but they will static since they will belong to the previous closed candle

Here are the metrics you can have by storing data from a variable period of candles (by default 51):

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**Variance**(of the symbol on chart in GREEN; of the compared symbol in WHITE)

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**Standard Deviation**(of the symbol on chart in OLIVE; of the compared symbol in SILVER )

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**Yelds**(of the symbol on chart in LIME; of the compared symbol in GRAY) → yelds are referred to the previous close, so they would be calculated as the the difference between the current close and the previous one all divided by the previous close

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**Covariance**of the two datasets (in BLUE)

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**Correlation coefficient**of the two datasets (in AQUA)

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**β**(in RED) → this insight is calculated in three alternative ways for educational purpose (don't worry, the output would be the same).

**WHAT IS BETA (β)?**

The BETA of an asset can be interpretated as the representation (in relative terms) of the systematic risk of an asset: in other terms, it allows you to understand how big is the risk (not eliminable with portfolio diversification) of an asset based on the volatilty of its yelds.

We say that this representation is made

*in relative terms*since it is expressed according to the market portfolio: this portfolio is

*hypothetically*the portfolio which maximizes the diversification effects in order to kill all the specific risk of that portfolio; in this way the standard deviation calculated from the yelds of this portfolio will represent just the not-eliminable risk (the systematic risk), without including the eliminable risk (the specific risk).

The BETA of an asset is calculated as the volatilty of this asset

*around*the volatilty of the market portfolio: being more precise, it is the covariance between the yelds of the current asset and those of the market portfolio all divided by the variance of the yelds of market portfolio.

Covariance is calculated as the product between correlation coefficient , standard deviation of the first dataset and standard deviation of the second asset.

So, as the correlation coefficient and the standard deviation of the yelds of our asset increase (it means that the yelds of our asset are very similiar to those of th market portfolio in terms of sign and intensity and that the volatility of these yelds is quite high), the value of BETA increases as well

According to the Capital Asset Pricing Model (CAPM) promoted by William Sharpe (the guy of the "Sharpe Ratio") and Harry Markowitz, in efficient markets the yeld of an asset can be calculated as the sum between the risk-free interest rate and the risk premium. The risk premium of the specific asset would be the risk premium of the market portfolio multiplied with the value of beta. It is simple: if the volatility of the yelds of an asset around the yelds of market protfolio are particularly high, investors would ask for a higher risk premium that would be translated in a higher yeld.

In this way the expected yeld of an asset would be calculated from the linear expression of the "Security Market Line": r_i = r_f + β*(r_m-r_f)

where:

r_i = expected yeld of the asset

r_f = risk free interest rate

β = beta

r_m = yeld of market portfolio

I know that considering Bitcoin as a proxy of the market portfolio involved in the calculation of Beta would be an inaccuracy since it doesn't have the property of maximum diversification (since it is a single asset), but there's no doubt that it's tying the prices of altcoins (upward and downward) thanks to the relevance of its dominance in the capitalization of cryptocurrency market. So, in the lack of a good index of cryptocurrencies (as the FTSE MIB for the italian stock market), and as long the dominance of Bitcoin will persist with this intensity, we can use Bitcoin as a proxy of the market portfolio

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