Untitled

// This Pine Script™ code is subject to the terms of the Mozilla Public License 2.0 at https://mozilla.org/MPL/2.0/
// © TobbySimard

//@version=5
indicator("Alpha and Beta Calculation", overlay=false)

//alpha < 0: the investment has earned too little for its risk (or, was too risky for the return)
//alpha = 0: the investment has earned a return adequate for the risk taken
//alpha > 0: the investment has a return in excess of the reward for the assumed risk

// User Inputs
benchmark_symbol = input.symbol("INDEX:ETHUSD", title="Benchmark Symbol")
beta_length = input.int(40, title="Beta Period")
alphaPeriod = input.int(40, title="Alpha Period")

// Function to calculate return percentage
return_percent(src) =>
    ta.change(src) * 100 / src[1]

// Function to calculate Beta
calc_beta(asset_return, benchmark_return, length) =>
    avg_asset_return = ta.sma(asset_return, length)
    avg_benchmark_return = ta.sma(benchmark_return, length)
    sum_covariance = 0.0
    for idx = 0 to length - 1
        asset_variance = asset_return[idx] - avg_asset_return
        benchmark_variance = benchmark_return[idx] - avg_benchmark_return
        sum_covariance += asset_variance * benchmark_variance
    covariance = sum_covariance / (length - 1)
    beta = covariance / ta.variance(benchmark_return, length)
    beta

// Fetch Benchmark data
benchmark_close = request.security(benchmark_symbol, 'D', close)
benchmark_return = return_percent(benchmark_close)

// Fetch Asset data and calculate return
asset_close = close
asset_return = return_percent(asset_close)

// Calculate Beta for the asset
beta = calc_beta(asset_return, benchmark_return, beta_length)

// Calculate Alpha
alphaReturn = (close - close[alphaPeriod]) / close[alphaPeriod]
benchmarkAlphaReturn = (benchmark_close - benchmark_close[alphaPeriod]) / benchmark_close[alphaPeriod]
alpha = alphaReturn - (benchmarkAlphaReturn * beta)

// Plot Alpha
plot(beta, color=color.purple, style=plot.style_line, transp=40)
plot(alpha, color=color.green, style=plot.style_line, transp=40)