@Karl, the algorithm score is not quite the same as Information Ratio because algorithm score only computes the standard deviation (volatility) of the algo returns as opposed to IR's which is standard deviation of [Rp - Rb] aka "Active Returns". Below is contest scoring code:

def volatility_adjusted_daily_return(trailing_returns):  
    """  
    Normalize the last daily return in `trailing_returns` by the annualized  
    volatility of `trailing_returns`.  
    """  
    todays_return = trailing_returns[-1]  
    # Volatility is floored at 2%.  
    volatility = max(ep.annual_volatility(trailing_returns), 0.02)  
    score = (todays_return / volatility)  
    return score  
def compute_score(returns):  
    """  
    Compute the score of a backtest from its returns.  
    """  
    result = []  
    cumulative_score = 0  
    count = 0  
    daily_scores = returns.rolling(63).apply(volatility_adjusted_daily_return)  
    cumulative_score = np.cumsum(daily_scores[504:])  
    latest_score = cumulative_score[-1]  
    print ''  
    print 'Score computed between %s and %s.' % (cumulative_score.index[0].date(), daily_scores.index[-1].date())  
    plt.plot(cumulative_score)  
    plt.title('Out-of-Sample Score Over Time')  
    print 'Cumulative Score: %f' % latest_score  

@Karl, love to humor you, again. In your equation above:

excess_returns = algo_returns - spy_returns :: algo returns above the benchmark ie. attributable to algorithm's alpha
Score = (todays_return / volatility) :: excess_returns / std(excess_returns)

Where do you see this implementation the subtraction of SPY returns to algo returns and the subtraction of SPY volatility to algo volatility in actual code of score below?

def volatility_adjusted_daily_return(trailing_returns):
"""
Normalize the last daily return in trailing_returns by the annualized
volatility of trailing_returns.
"""
todays_return = trailing_returns[-1]
# Volatility is floored at 2%.
volatility = max(ep.annual_volatility(trailing_returns), 0.02)
score = (todays_return / volatility)
return score

It does not compute excess returns, only algo returns and (are you laughing now?)
it does compute excess volatility, only algo volatility to conform to IR. Do you get it now?

Quite simply Karl, and just quote Investopedia:

What is a 'Zero-Beta Portfolio'
A zero-beta portfolio is a portfolio constructed to have zero systematic risk or, in other words, a beta of zero. A zero-beta portfolio would have the same expected return as the risk-free rate. Such a portfolio would have zero correlation with market movements, given that its expected return equals the risk-free rate or a relatively low rate of return compared to higher-beta portfolios.

Read more: Zero-Beta Portfolio https://www.investopedia.com/terms/z/zero-betaportfolio.asp#ixzz54jvu6pte
Follow us: Investopedia on Facebook

And by the way Karl, I tried to give you hints in my other thread and just in case you haven't read it, here is it below and quote myself:

@Karl, "Relativity", a word made famous by Prof. Albert Einstein is the key to understanding Information Ratio in the context of market neutral strategies. What does the hedge fund industry use as benchmark for market neutral strategies? Three month US Treasury Bills (aka risk free rates) not SPY. Below I quote a Morningstar whitepaper ( http://advisor.morningstar.com/uploaded/pdf/alt_marketneutralmfcs.pdf) :

Because market-neutral funds hedge out broad
market risk, a cashlike benchmark (such as Treasury
bills) is more appropriate than a stock or bond
market index.

@Karl,

Not really.. let's ask more precisely:
How do we characterise the Returns in excess of SPY even as Beta-to-SPY gets to zero?

The Holy Grail! Have you found it, please share?