# Can you derive fx correlations given the historic correlations of base pairs

Say for USDJPY and GBPUSD, I have the historic data and calc the volatility and correlation between these pairs.

Because GBPJPY = GBPUSD x USDJPY. Can I calculate the correlation for GBPJPY directly from these statistics, without having to calculate from the historic time series data?

I am not sure if its valid to use cosine rule, eg: Vol C ^ 2 = Vol A ^ 2 + Vol B ^ 2 - 2 * rho (A, B) * Vol A * Vol B Or if this is just for implied correlations.

As I tried it for some historic data and it didn't work.

• What kind of returns are you calculating, logarithmic returns ($\ln p_t - \ln p_{t-1}$) or simple returns ($\frac{p_t-p_{t-1}}{p_{t-1}}$) ? – Alex C May 2 '19 at 19:22
• the correlation between the actual fx fwd rates – locke84 May 7 '19 at 8:59