# Volatility and Non-Publicly Trade Assets

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?

You would have to have the unlikely situation where the extremes in variability in your time series are at their most severe exactly at the end-of-month points in time, filled in with very small deviations in the intramonth period.

It doesn’t have to hold mathematically, and it certainly doesn’t hold empirically - you can see the opposite of what you observed if you change your data set.

Mathematically, if the returns are independent and, correspondingly, not serially correlated, then annualized daily or monthly returns will be exactly equal.

If they are negatively autocorrelated such that positive daily returns tend to be followed by negative daily returns and vice versa, then you have a form of mean reversion. Monthly returns would tend to be more smoothed and less extreme and annualized monthly vol would be lower than annualized daily vol.

Conversely, if they are positively autocorrelated such that positive daily returns are followed by positive daily returns and vice versa, then you have momentum. The monthly returns would tend to be more extreme and annualized monthly vol would be higher than annualized daily vol.

For illiquid assets, the required illiquidity premium is theorized to be a concave function (increasing at a decreasing rate) of the trading horizon, which is referred to as the clientele effect. So when an illiquid asset gets ‘priced’ at less frequent intervals, the observed apparent smoothing of the returns may be a reflection of that.

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i think its a no. i foudn this on google. apparently ppl game sharpe by using monthly returns to lower std. daily returns have more noise so it adds to the volatility.

you can also read htis article that shows how annualized std is calculated.

overall private investments arent really sold when valued, so whether monthyl or daily, it feels like they make up the numbers so std should be lower.

You really can’t compare exchange traded assets (level 1 securities) with private market assets (level 3 securities) because the valuation procedures are so different. Many private markets assets are carried at cost or amortized cost for a period of time, so any volatility metrics based on valuation are meaningless. Investors in private markets are more likely to focus on IRR and MOIC for individual transactions and aggregate realized and unrealized transactions. Because of the valuation procedures mentioned above, unrealized returns are often lower than realized, because they haven’t realized the valuation bump from the exit.

From the perspective of a client at an RIA? I’d imagine the lack of available market data makes the ride appear smoother and this could benefit the client behaviorally.

Good responses, thanks. Sometimes I wish I had a more math heavy background than what my finance degree gave me so I could work through some of these things on my own.

It doesn’t change my belief that there’s a lot of misleading information surrounding private investments regarding the risk/return profile. I’m not opposed to private investments, but I think these products are often sold, not bought.

i was considering investing in some repes. but im concerned with rates moving up affecting their ability to exit profitbaility. theyll still exit cuz they like the t/o

Have you looked at any data for illiquid assets pertaining to autocorrelation?

I have not. I was just responding to your theoretical question about whether annualized monthly vol must be lower than annualized daily vol - the answer is that, mathematically, it doesn’t have to be. The positive/negative autocorrelation argument is just an illustrative example to show that two alternative mathematical models can result in higher or lower monthly vol respectively.

If, in your data, you find empirically that the annualized monthly vol is persistently lower than the annualized daily vol - the reason could be negative autocorrelation, or it could be something else entirely. I haven’t investigated but I’m sure someone has already - or you might yourself if so inclined!

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