I hear a lot of advisors promoting private equity, private credit, private real estate, etc. with the promise of higher returns and lower volatility than their publicly traded counterparts. Logically I would expect these private investments to have less volatility than publicly traded assets, if we assume all else is equal or similar, because of the smoothing of returns that occurs when assets aren’t priced daily. I tested this myself by annualizing the volatility of daily, weekly, and monthly returns for the S&P 500 over a five year time frame and more frequently calculated returns led to higher annualized volatility.
My question is, does this have to hold true mathematically? For example, could the monthly returns of an asset ever have greater annualized volatility than the daily returns?