In general, what does the bias-variance tradeoff look like when estimating covariance matrices with varying return frequencies (i.e. daily, weekly, monthly returns)?
From my observations I've noticed that, on average, lower frequency (e.g. monthly) returns result in higher estimates of asset variance and higher estimates of asset correlations while also having higher variance of those estimations. This leads me to hypothesize that lower frequency returns result in higher estimate variance compared to higher frequency returns. I've been looking for papers or proofs that show this more robustly but I'm falling short. Furthermore, what can I say about the bias of these estimates?