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Statistical and Financial MetricsGood morning traders!
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):
✓ Variance (of the symbol on chart in GREEN; of the compared symbol in WHITE)
✓ Standard Deviation (of the symbol on chart in OLIVE; of the compared symbol in SILVER)
✓ 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
✓ Covariance of the two datasets (in BLUE)
✓ Correlation coefficient of the two datasets (in AQUA)
✓ 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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Risk Metrics: beta 'β', correl 'ρxy', stdev 'σ', variance 'σ²'Portfolio Risk Metrics (Part I):
beta 'β'
The beta coefficient can be interpreted as follows:
β =1 exactly as volatile as the market
β >1 more volatile than the market
β <1>0 less volatile than the market
β =0 uncorrelated to the market
β <0 negatively correlated to the market
excerpt from the Corporate Finance Institute
correlation coefficient 'ρxy'
The correlation coefficient is a value that indicates the strength of the relationship between variables.
The coefficient can take any values from -1 to 1. The interpretations of the values are:
-1: Perfect negative correlation. The variables tend to move in opposite directions
(i.e., when one variable increases, the other variable decreases).
0: No correlation. The variables do not have a relationship with each other.
1: Perfect positive correlation. The variables tend to move in the same direction
(i.e., when one variable increases, the other variable also increases).
excerpt from the Corporate Finance Institute
standard deviation 'σ'
68% of returns will fall within 1 standard deviation of the arithmetic mean
95% of returns will fall within 2 standard deviations of the arithmetic mean
99% of returns will fall within 3 standard deviations of the arithmetic mean
excerpt from Corporate Finance Institute
variance 'σ²'
In investing, variance is used to compare the relative performance of each asset in a portfolio.
Because the results can be difficult to analyze, standard deviation is often used instead of variance.
In either case, the goal for the investor is to improve asset allocation.
excerpt from Investopedia
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Alpha & BetaAlpha & Beta Indicators for Portfolio Performance
β = Σ Correlation (RP, RM) * (σP/σM)
α P = E(RP) –
Where,
RP = Portfolio Return (or Investment Return)
RM = Market Return (or Benchmark Index)
RF = Risk-Free Rate
How to use the Indicator
RM = SPX (Default)
The Market Return for the indicator has the options of $SPX, $NDX, or $DJI (S&P 500, Nasdaq 100, Dow 30)
RF = FRED: DTB3
The Risk-Free Rate in the Indicator is set to the 3-Month Treasury Bill: Secondary Market Rate
The Default Timeframe is 1260 or 5-Years (252 Trading Days in One Year)
RP = The symbol you enter
HOWEVER , you can determine your portfolio value by following the following directions below.
Note: I am currently working on an indicator that will allow you to insert the weights of your positions.
Complete Portfolio Analysis Directions
You will first need...
a) spreadsheet application - Google Sheets is Free, but Microsoft Excel will convert ticker symbols to Stocks and Retrieve Data.
b) your current stock tickers, quantity of shares, and last price information
In the spreadsheet,
In the first column list the stock tickers...
AMZN
AAPL
TSLA
In the second column list the quantity of shares you own...
5
10
0.20
In the third column insert the last price
Excel: Three tickers will automatically give you the option to "Convert to Stocks",
after conversion, click once on cell and click the small tab in the upper right-hand of the highlighted cell.
Click the tab and a menu pops up
Find "Price", "Price Extended-Hours", or "Previous Close"...
$3,284.72
$497.48
$2,049.98
Next, multiply the number of shares by the price (Stock Market Value)
Excel: in fourth column type "=(B1*C1)", "=(B2*C2)", "=(B3*C3)"...
= $16,423.60
= $4,974.80
= $410.00
add the three calculated numbers together or click "ΣAutoSum" (Portfolio Market Value)
= $21,808.40
Last, divide the market value of AMZN ($16,423.60) by the Portfolio Market Value ($21,808.40) for each of the stocks.
= 0.7531
= 0.2281
= 0.0188
These values are the weight of the stock in your portfolio.
Go back to PulseWire
Enter into the "search box" the following...
AMZN*0.7531 + AAPL*0.2281 + TSLA*0.0188
and click Enter
Now you can use the "Alpha & Beta" Indicator to analyze your entire portfolio! Indicator
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