Does using higher-frequency data always improve CME estimates? What problems does data frequency introduce?

This is one of those CFA Level III topics that seems counterintuitive at first but becomes very logical once you understand the statistics behind it.

Frequency and Precision — The Split:

Why the asymmetry? Variance scales linearly with the number of independent observations. If you have 252 daily returns vs. 12 monthly returns in one year, you get roughly 21x more observations for estimating variance. But mean return precision depends on the total TIME SPAN of data, not the number of data points within that span. Subdividing one year into 252 daily slices doesn't give you 252 independent samples of the annual mean — it gives you 252 noisy glimpses of the same one-year outcome.

Example — Thornfield Asset Management:

Thornfield is estimating expected returns and volatility for Japanese equities using 5 years of data:

*After annualizing, the precision of the mean estimate is essentially the same because it depends on the 5-year span, not the observation count.

The Asynchronicity Problem:

As you move to higher-frequency data (daily or weekly), a new problem emerges: data from different markets may not reflect the same time period even though they carry the same date label.

Consider daily returns for:

• US equities (NYSE closes at 4:00 PM Eastern)
• Japanese equities (TSE closes at 3:00 PM Tokyo = 2:00 AM Eastern)
• European equities (LSE closes at 4:30 PM London = 11:30 AM Eastern)

When you compute a daily correlation between US and Japanese equities, the Japanese close happened roughly 14 hours before the US close. News released during US hours affects the US return today but the Japanese return tomorrow. This creates:

• Understated contemporaneous correlations — the true co-movement is split across two dates
• Spurious lead-lag relationships — US returns appear to "predict" next-day Japanese returns

Practical Guidelines:

• Use daily/weekly data for variance and covariance estimation but be aware of asynchronicity for international data
• Use long time spans (not just high frequency) for estimating mean returns
• For covariance matrices with many assets, ensure the number of observations exceeds the number of assets to avoid spurious zero-volatility portfolios
• If N assets > T observations, use factor-model covariance matrices instead of sample covariance

For more on CME estimation challenges, explore our CFA Level III community Q&A.