What are the advantages of a logarithmic return?

Benefit of using returns, versus prices, is normalization: measuring all variables in a comparable metric, thus enabling evaluation of analytic relationships amongst two or more variables despite originating from price series of unequal values.

Should I use returns or log returns?

In this context, log returns are far superior to arithmetic returns since the sum of repeated samples from a normal distribution is normally distributed. The arithmetic return for a portfolio is simply equal to the weighted average of each constituent’s arithmetic return.

What is the difference between simple return and log return?

The simple return of a portfolio is the weighted sum of the simple returns of the constituents of the portfolio. The log return for a time period is the sum of the log returns of partitions of the time period.

How does a logarithmic return compare to an actual return?

Comparing ordinary return with logarithmic return The difference between them is large only when percent changes are high. For example, an arithmetic return of +50\% is equivalent to a logarithmic return of 40.55\%, while an arithmetic return of −50\% is equivalent to a logarithmic return of −69.31\%.

What are simple returns?

The simple rate of return is the incremental amount of net income expected from a prospective investment opportunity, divided by the investment in it. A business would then accept a project if the measure yields a percentage that exceeds a certain hurdle rate used by the company as its minimum rate of return.

Are log returns stationary?

stock return is not always stationary. we make it stationary . hiL log returns are the first differences of log(stock prices) so the thinking is that first differencing the log stock prices can possibly help with making a series stationary. but it doesn’t mean that the resulting series is necessarily stationary.

When should I use log returns?

Log return is used for statistical evaluation such MSPE and out-of-sample R-square. Simple return is used for calculating economic value such as CER gain and Sharpe ratio. This is because Log return and simple return have the additivity property for, respectively, time-series and cross-section perspectives.

Why do we choose simple rate of return over log return for portfolio analysis?

Log returns cannot be added across securities of a portfolio in the same time period. Across different stocks within the same time period, there are no compounding element here. So for computing portfolio return across contribution from securities within the same time period, use simple returns instead.

Why do we use natural log?

We prefer natural logs (that is, logarithms base e) because, as described above, coefficients on the natural-log scale are directly interpretable as approximate proportional differences: with a coefficient of 0.06, a difference of 1 in x corresponds to an approximate 6\% difference in y, and so forth.

How do you use log returns?

Log returns can be added across time periods. For example, let’s say you have a stock worth $100 that rose to $120 in the first time period and then goes back to $100 in the second time period. Going by simple returns, you will get a 20\% increase in the first time period and -16.7\% decrease in the second time period.

What is a disadvantage of the simple rate of return?

The most important disadvantages are : Uses income data instead of cash flow data. Ignores the value of money.

What does log return mean?

Log Return is one of three methods for calculating return and it assumes returns are compounded continuously rather than across sub-periods. It is calculated by taking the natural log of the ending value divided by the beginning value. ( Using the LN on most calculators, or the =LN() function in Excel)

What are the advantages of simple return over log return?

So one of the advantages of simple return is that it can be used where portfolios are formed and portfolio returns have to be calculated because of its asset-additive property. Log returns are time-additive: The logarithmic return of an asset over a period of t to T is the sum of all logarithmic returns between the t and T.

Why are loglog returns time-additive?

Log returns are time-additive: The logarithmic return of an asset over a period of t to T is the sum of all logarithmic returns between the t and T. In other words, the log return over n periods is merely the difference in log between initial and final periods. This is an advantage because the sum…

What is the cumulative weekly log return for log returns?

So, our cumulative weekly log return is as follows: Since log returns are continuously compounded returns, it is normal to see that the log returns are lower than simple returns. To find n-period log returns from daily log returns, we need to just sum up the daily log returns. Therefore : We shall continue to use the same data as above.

Should I use log normal or daily returns?

Therefore when you approximate returns as log normal, you should probably stick to daily returns.