Scaling intra-day returns to daily returns is essential for long-term investors. In a 24-hour market, it is inefficient to scale intra-day returns at a minute-by-minute interval. Using one-minute intervals would not be appropriate. You should instead use a scaling factor that maps intra-day returns to daily returns. You should not use 5-minute intervals; however, there are many other ways to scale intra-day returns to daily returns.
For the purpose of calculating your portfolio’s daily return, you can divide the intra-day returns by the daily average market value to obtain the corresponding percentage return. The resulting percentage return can then be multiplied by 365 and scaled to daily returns. The following table lays out the various methods for converting intra-day returns to daily returns.
This article will explain some of the most common methods:
Exponent
To scale intra-day returns to daily returns, one must first identify the time lag t. A common mistake is to calculate returns at intervals of 5 minutes. The lag t should be at least one day. However, using a time lag of one day is also an effective way to scale intra-day returns to daily returns. Moreover, if we are interested in daily returns, we can use a scaled index and volume.
Stock Market
There is an obvious problem with comparing intra-day returns to daily ones. Using one-minute intervals is insensitive to the idiosyncrasies of the market. Ideally, we should map intra-day returns to daily returns using a scaling factor. In other words, we should not use one-minute intervals for intraday returns. However, this method has many advantages. First of all, it proves to be more practical than attempting to calculate the daily return from intra-day returns.
The evidence for scaling has been provided by a number of studies. Xu and Gencay (2003) provided strong evidence that returns of EUR/USD and USD-DEM are related. Others have reported the existence of scaling in currency exchange rates and the Norwegian stock market. The authors of the paper, Mantegna, and Stanley, also find evidence of scaling in the Standard & Poor’s 500. Furthermore, Guillaume et al. (2002) report that scaling laws are observed in time series that range from 10 min to two months.
Time Lag
Statistical analyses often require a time lag in order to properly interpret intra-day data. If there is a 5-minute gap between the daily and intra-day returns of the same stock, scaling factors are ineffective for this purpose. Fortunately, there are other methods for mapping intra-day returns to daily returns. Let’s look at some of these. This method is useful for many purposes, including identifying trends and evaluating performance.
In the following sections, we’ll explore the inverse cubic power law and how it relates to asymmetric returns. We’ll discuss the differences between positive and negative returns, as well as Tsallis statistics, and apply it to real stock data and diversified time lags. We’ll also briefly discuss how to use this method with various stock and currency pairs.
Stock Market Volatility
One way to scale intra-day returns to daily returns is to use a time-series or cross-section-based predictor. Both of these are highly unbiased. However, there exist some differences between these two approaches. First, cross-section-based predictors are less efficient than time-series-based ones. Second, they do not include reversion to the mean, which is common in intraday market fluctuations.
Here, we examine the scaling properties of USD-DEM returns, examining both positive and negative tails. We also examine parallel shifts, which indicate that the distribution of USD-DEM returns is self-similar. Furthermore, we study the distributions of USD-JPY and USD-GBP returns in different time intervals. This work provides empirical evidence that intra-day returns scale to daily returns.
Standard & Poor’s 500
The S&P 500 index represents the largest cap U.S. equities market and includes 500 of the most prominent companies across the largest industries. These companies are all publicly traded on the NASDAQ or NYSE. In total, the S&P 500 index represents approximately 75% of the market. As a price-only index, the S&P 500 does not contain dividends.
Previous research has shown that currency returns exhibit a power-law scaling pattern, which has been observed for a variety of time intervals. In particular, Gopikrishnan et al. (1998) found evidence of this scaling law for returns of the depository’s 30-main German stocks. The scaling laws were found to be evident for currency returns from 10 minutes to 16 days.