I believe the custom factor below should do what you want.

class Downside_Volatility(CustomFactor):  
    # Use returns as the input  
    inputs = [Returns(window_length=2)]  
    # The trading days to calculate volatility over (can override)  
    window_length = 10  
    def compute(self, today, assets, out, returns):  
        # set any returns greater than 0 to NaN so they are excluded from our calculations  
        returns[returns > 0] = np.nan  
        out[:] = np.nanstd(returns, axis=0)

It's a little more correct to use log returns in the calculation (https://en.wikipedia.org/wiki/Volatility_(finance)) so this could be used too.

class Downside_Log_Volatility(CustomFactor):  
    # Use returns as the input  
    inputs = [Returns(window_length=2)]  
    # The trading days to calculate volatility over (can override)  
    window_length = 10  
    def compute(self, today, assets, out, returns):  
        # set any returns greater than 0 to NaN so they are excluded from our calculations  
        returns[returns > 0] = np.nan  
        log_returns = np.log(returns+1)  
        out[:] = np.nanstd(log_returns, axis=0)

Note the above code was edited from the original.

      returns[returns < 0] = np.nan

was changed to

        returns[returns > 0] = np.nan  

per the post below.

Fantastic, thanks for the help as always Dan!

Looking at the above code...

Shouldn't

# set any returns less than 0 to NaN so they are excluded from our calculations
returns[returns < 0] = np.nan

actually be:
returns[returns > 0] = np.nan

if you want downside volatility? Don't you want to set any returns ABOVE zero to NAN so you are only capturing the standard deviation of downside movements? I think your original code is actually calculating upside volatility.

Let me know if I'm missing something...

-Brian

Oops. Yes. The above would be upside volatility. My mistake. I edited the above so now it's correct. Thanks for pointing that out.

I'm wondering if I have the coding correct for the two custom factors below. Can someone lend a hand to let me know if the lines in BOLD are correctly written?

*# get index and calculate returns. SPY code is 8554
benchmark_index = np.where((assets == 8554) == True)[0][0]*

# Index Beta  
class Index_Beta(CustomFactor):  
    """  
    Index Beta:  
    Slope coefficient of 1-year regression of price returns against index returns  
    Notes:  
    High value suggests high market risk  
    Slope calculated using regression MLE  
    """  
    inputs = [USEquityPricing.close]  
    window_length = 252  
    def compute(self, today, assets, out, close):  
        **# get index and calculate returns. SPY code is 8554  
        benchmark_index = np.where((assets == 8554) == True)[0][0]**  
        benchmark_close = close[:, benchmark_index]  
        benchmark_returns = (  
            (benchmark_close - np.roll(benchmark_close, 1)) / np.roll(benchmark_close, 1))[1:]  
        betas = []  
        # get beta for individual securities using MLE  
        for col in close.T:  
            col_returns = ((col - np.roll(col, 1)) / np.roll(col, 1))[1:]  
            col_cov = np.cov(col_returns, benchmark_returns)  
            betas.append(col_cov[0, 1] / col_cov[1, 1])  
        out[:] = betas

# Downside Beta  
class Downside_Beta(CustomFactor):  
    """  
    Downside Beta:  
    Slope coefficient of 1-year regression of price returns against negative index returns  
    Notes:  
    High value suggests high exposure to the downmarket  
    Slope calculated using regression MLE  
    """  
    inputs = [USEquityPricing.close]  
    window_length = 252  
    def compute(self, today, assets, out, close):  
        **# get index and calculate returns. SPY code is 8554  
        benchmark_index = np.where((assets == 8554) == True)[0][0]**  
        benchmark_close = close[:, benchmark_index]  
        benchmark_returns = (  
            (benchmark_close - np.roll(benchmark_close, 1)) / np.roll(benchmark_close, 1))[1:]  
        # days where benchmark is negative  
        negative_days = np.argwhere(benchmark_returns < 0).flatten()  
        # negative days for benchmark  
        bmark_neg_day_returns = [benchmark_returns[i]  
                                 for i in negative_days]  
        betas = []  
        # get beta for individual securities using MLE  
        for col in close.T:  
            col_returns = ((col - np.roll(col, 1)) / np.roll(col, 1))[1:]  
            col_neg_day_returns = [col_returns[i] for i in negative_days]  
            col_cov = np.cov(col_neg_day_returns, bmark_neg_day_returns)  
            betas.append(col_cov[0, 1] / col_cov[1, 1])  
        out[:] = betas  

Hi Daniel,

Didn't test, but here is a working version using OLS if interested.

def REG(X,Y):  
    model = sm.OLS(Y, X).fit()

    return model.params

class Downside_Beta(CustomFactor):  
    inputs = [USEquityPricing.close]  
    window_length = 252  
    def compute(self, today, assets, out, close):  
        bench = close[:, assets.searchsorted(8554)]  
        benchmark_returns = np.diff(np.log(bench))  
        negative_bench_returns = np.where(benchmark_returns < 0, benchmark_returns, 0)  
        betas=[]  
        for col_ix, values in enumerate(close.T):  
            returns = np.diff(np.log(values))  
            betas.append(REG(negative_bench_returns, returns))

        out[:]=betas