Discrete and Continuous Correlation

Abstract

It is well understood that the choice of a discrete and continuous compounding model affects investment returns, but leaves end-of-period wealth unaffected.

In a previous research note , we have shown that the compounding model also does not affect Sharpe Ratios when calculated properly, i.e. using arithmetic average and volatility when working with continuous returns, geometric averages and volatilities with geometric returns.

In this research note, we analyze whether the compounding model affects asset dependence, provide a formula to convert continuous and discrete correlations and assess whether the conversion is relevant in real-world applications.

Keywords: correlation, portfolio construction, normal distribution, lognormal distribution, copula, compounding