Annualizing Portfolio Statistics Across Different Trading Calendars

Summary

The document considers portfolio annualization when assets trade on different calendars, using traditional stocks and cryptocurrency as examples. Its central recommendation is to annualize each asset's expected return and covariance contributions using the appropriate factor for that asset before combining them with portfolio weights. Applying one annualization factor to a portfolio statistic formed from unadjusted mixed-calendar inputs can produce an inappropriate result.

The answer contrasts forming portfolio return and variance first and annualizing afterward with annualizing the return vector and covariance inputs first. It offers this ordering as the more sensible approach, but does not derive the scaling mathematically or give a worked numerical example. The discussion also does not fully specify how to handle cross-asset covariance when markets have different trading hours or how to define synchronized return intervals, both of which matter when constructing a multi-asset covariance matrix.

Key ideas

• Assets with different trading calendars may require different annualization factors.
• Annualize expected-return and covariance inputs at the asset level before applying portfolio weights.
• Combining unannualized inputs and applying one factor afterward can misstate portfolio statistics.
• The treatment of cross-asset covariance and synchronized return intervals is not specified.

Tags

# How to annualize with different trading days in single portfolio


# How to annualize with different trading days in single portfolio












Nowadays, traditional stocks have 252 trading days, and cryptocurrency have 365 trading days. If I want to find the annualized Sharpe ratio, how do I do that? Each element multiplied by 252 / 365? And the standard deviation Its variance w * c w't * 252 W1 * 252 , w2 *365

Something like that?

## Answer by KaiSqDist (score 0, accepted)

https://quant.stackexchange.com/a/78795

Since the assets have different number of trading days, it would make sense to annualize the individual components instead of "combining" them and annualizing the Sharpe ratio.

For example, if one creates a covariance matrix or vector of expected returns, then computes the portfolio variance and expected return by matrix multiplying with the vector of weights, then annualizes with $252$ or $365$ in the returns case, one would get an incorrect answer.

However, if you annualize the covariance matrix and vector of expected returns first by multiplying the individual components with their correct annualization factors, and then apply the vector of weights to get the portfolio variance and expected returns, one would get a more sensible answer.

Basically, instead of doing (1.), I would propose (2.):

- Compute CovMat/ER Vector > Obtain Port Var/ER > Annualize Port Var/ER (WRONG)

- Compute CovMat/ER Vector > Annualize CovMat/ER Vector > Obtain Annualized Port Var/ER (Better)

And I agree with Richard Hardy, you need to work on organizing your question.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.