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I am trying to calculate the volatility of five portfolios consisting of S&P 500 stocks.

The portfolios consist roughly each of 20% of the S&P 500 members between 2015-2022, rebalanced monthly to account for stocks entering and leaving the index. The portfolios are built based on the members ESG ratings (portfolios: 'low', 'mid-low', 'mid', 'mid-high' and 'high'), meaning they are also rebalanced yearly to account for changing ESG ratings. At any point each stock is weighted equally within a given portfolio. Note that I only use stocks that are actually rated by the agencies in question (Refinitiv and Bloomberg), meaning that roughly 20% of the index falls away.

I have the returns of each portfolio on a monthly basis (using the average monthly return of each portfolio-member). When I now calculate the volatility of these monthly returns (via standard deviation) over the whole period 2015-2022 I get results of around 5.00% which to my knowledge is way too low.

Am I doing something wrong when calculating the volatility? Thanks to anyone for the help!

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    $\begingroup$ Are you annualizing the returns? (multiplying by $\sqrt {12}$) $\endgroup$
    – Rylan
    Commented May 28 at 13:14
  • $\begingroup$ No, not the monthly ones. Do I need to annualize the monthly returns before calculating the volatility? And would I not do that via (1+r)^12 - 1 ? $\endgroup$
    – jjb97
    Commented May 28 at 13:32
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    $\begingroup$ I meant to say annualizing the volatility, excuse me, which you could do by multiplying by $\sqrt{12}$ $\endgroup$
    – Rylan
    Commented May 28 at 13:37
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    $\begingroup$ I did not realize I need to annualize volatility, but it makes sense when I think about it... 19% also fits better than 5% and makes the Sharpe-Ratios more realistic. Thank you very much! $\endgroup$
    – jjb97
    Commented May 28 at 13:47

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