The Volatility Conundrum: Why weekends might be hiding your portfolio's true swings

Hello there, smart money manager! Grab a coffee, let's chat about an intriguing puzzle that's been keeping finance nerds up at night. You've probably noticed that when you calculate your portfolio's volatility using daily returns, the number seems to be larger than when you use monthly or yearly figures. This discrepancy has been baffling investors for years. Today, we're diving into the mystery of time-adjusted returns and volatility estimation.

The Weekend Conundrum: When one day isn't really one day

Imagine you're tracking your portfolio's performance daily. On a Friday, your portfolio drops 2%. That seems like a big move, right? But what if that drop happened over three days, from Wednesday's close to Monday's open? Suddenly, that 2% doesn't seem so dramatic. This discrepancy is what we're here to unravel.

Why does this matter? Well, understanding how your portfolio moves helps you manage risk and make better investment decisions. If you're overestimating volatility due to non-trading days, you might be selling too soon or missing out on potential gains by staying put when you shouldn't.

The Time-Adjusted Returns Dance: Finding the perfect exponent

Pat from Portfolio Probe proposed adjusting returns for the number of trading days between them. But how much should we adjust? Joseph Wilson suggested dividing returns by the number of days to some power. So, we've got a range of adjustments here, from no adjustment (exponent = 0) to full compensation (exponent = 1).

But which exponent is right? To find out, we compared multi-day returns with their one-day controls. The mean absolute value or squares of the control returns should equal those of the multi-day returns. After some number-crunching, we found that an exponent around 0.23 seemed to do the trick for the S&P 500 index. But remember, this is just a starting point – other assets might require different adjustments.

The Volatility Dance-Off: Comparing time-adjusted returns

Now let's see how adjusting for time affects volatility estimates. We looked at six blocks of data from 1989 to present day, using 20-day time-adjusted returns. Even with the over-adjustment (exponent = 0.23), we found that "cycle" distributions were still smaller than "permute" distributions.

What does this mean? Even after accounting for non-trading days, there's still a pattern suggesting that daily volatility might be overestimated. This could imply that other factors – like news events or market dynamics – are at play here.

Portfolio Implications: What this means for C, BAC, MS, QUAL, and DIA

So, how should you adjust your portfolio management strategy based on these findings? Well, it depends on your risk tolerance and investment horizon.

- Conservative: If you're risk-averse, consider using time-adjusted returns to get a more accurate picture of volatility. This might lead you to trim exposure to highly volatile assets like C (Citigroup) or BAC (Bank of America), which have historically shown high daily volatility. - Moderate: For a balanced approach, monitor both adjusted and unadjusted volatilities. This could help you spot opportunities in assets like MS (Morgan Stanley), which might seem too risky based on daily figures but could be more manageable when adjusted for time. - Aggressive: If you're willing to take on higher risk, you might find that the overestimated volatility is actually a buying opportunity. Consider high-beta stocks like QUAL (ViacomCBS) or DIA (SPDR S&P 500 ETF Trust), which could benefit from your increased tolerance for daily swings.

Practical Implementation: Adjusting your strategy

Ready to incorporate time-adjusted returns into your portfolio management? Here's how you can get started:

1. Calculate adjusted returns: Use the formula `R_adj = R / (days ^ p)`, where `R` is the return, `days` is the number of days between observations, and `p` is the exponent you've chosen (around 0.23 for S&P 500). 2. Compare volatilities: Compute both adjusted and unadjusted volatilities to get a complete picture of your portfolio's risk. 3. Monitor regularly: Keep track of time-adjusted returns periodically – monthly or quarterly – to reassess your portfolio's risk profile.

Final Steps: Putting the puzzle pieces together

So, what have we learned today? Non-trading days might be skewing our volatility estimates, and adjusting for time can help us get a clearer picture. But remember, there's no one-size-fits-all solution here. Keep experimenting with different exponents and assets to find the strategy that works best for you.

Now, go forth and manage your portfolio like the seasoned investor you are – armed with the knowledge of time-adjusted returns!