Daily log return, also known as natural log return, is a method of measuring the percentage change in the value of an investment over a period of one day. It is a widely used method in finance to measure the return of a financial asset such as a stock, bond or index.
The daily log return is calculated by taking the natural logarithm (ln) of the ratio of the current day's closing price to the previous day's closing price. The natural logarithm is used because it is a continuous function that ensures that small changes in price are accurately reflected in the return calculation.
For example, let's say the closing price of a stock on Day 1 is $100 and on Day 2 is $102. The daily log return would be calculated as:
ln(102/100) = ln(1.02) = 0.0198
This means that the stock has increased by approximately 1.98% over the two-day period.
It's important to note that daily log returns can be used to calculate the return on a single day or on multiple days by adding up the daily log returns. To calculate the return over multiple days, the daily log returns are added and then multiplied by the number of trading days in the period. This is known as the cumulative log return.
It's also worth to mention that Daily log returns are useful in finance because they are additive. This means that the total return for a period can be found by summing up the log returns for each day. This is useful for comparing returns over different periods, and for finding the average return over time.
In conclusion, Daily log return is a method of measuring the percentage change in the value of an investment over a period of one day. It is calculated by taking the natural logarithm of the ratio of the current day's closing price to the previous day's closing price. It's useful in finance because they are additive which means the total return for a period can be found by summing up the log returns for each day, it's useful for comparing returns over different periods, and for finding the average return over time. Log returns are widely used in finance to measure the return of a financial asset such as a stock, bond or index.