# Logarithmic returns for realized variance?

I am wondering which method makes more sense when computing log returns. I am trying to compute log returns for realized variance, and I have the opening and closing prices for every minute.

Since the log return is defined as

$$r_{t+1} = \ln \left(\frac{p_{t+1}}{p_t} \right)$$

should I take the average of the open and closing prices at every point as use that as $p_t$?

Or should I find $r_{t+1}$ at every $t$ by assuming $p_{t+1}$ = closing price and $p_t$ = opening price?

• entirely depends on what you are trying to achieve. Similar question: "Should I buy a car today or in 20 years?" – Matt Feb 28 '13 at 2:45

It depends on your investment strategy. The most common approach is to use the close price of $p_t$ and $p_{t+1}$. The volatility you measure using this method implies the "assumption" that your are able to trade at close every day.