Calculating Asset Returns

The question pertains to a simple phenomenon. There is gold futures listed on Exchange A and Exchange B. Exchange A and Exchange B overlap times with A and B starting 8 hours later and A and B closing together.
On Exchange A, it trades for 8 hours. On Exchange B, it trades for 16 hours.

I calculate hourly returns for both exchanges. Since this is Gold Futures, they are highly correlated.

Thus Sum of hourly returns on B is greater than Sum of hourly returns on A. However Daily returns of Close-Close of both A and B are same.

If i extrapolate Daily returns to Annually, then sqrt(252)* Daily Returns shall give us the Annualized Returns.

How do i resolve the hourly and daily returns dilemma?

• What do you actually ask? How can daily returns be the same if the futures trade on A for 8 hours and on B for 16 ours? You can not annualized returns by the square-root - this holds for volatilities under some assumptions. What is the actual question? Can you make this more clear? – Ric Apr 15 '15 at 8:20
• The question is quite simple. I have to compare the volatilities at both these exchanges but I am unable to annualize them. How can I state their volatilities – shoonya Apr 16 '15 at 8:30
• You don't have to explain to me. What I mean is that you question up there is unclear. The chances that someone will take the time to answer it are higher if you formulate it clearly. At the moment it is not clear what you are asking. – Ric Apr 16 '15 at 8:37
• Hey, Can you tell me what part is unclear. Should i include a diagram? – shoonya Apr 16 '15 at 18:48