FRF

The difference between compound and simple returns may not be very significant for

small returns

The log of a sum does not equal

the sum of logs (it's a function like any other))

Continuously compounded multiperiod returns are the sum of continuously compounded single-period returns. In contrast to simple returns, it is much easier to derive the time series properties of sums than of products.

Continuously compounded multiperiod returns are the sum of continuously compounded single-period returns. In contrast to simple returns, it is much easier to derive the time series properties of sums than of products.

A key advantage to compound returns

is that they are symmetric, while simple returns are not. This means an investment of $100 that yields a simple return of 50% followed by a simple return of 50% will result in $75

The lowest daily return of 23% corresponds to the stock market crash of 1987, while the best day in the index, 15%, was at the end of the Great Depression. The returns have a what skewness and, more importantly, what kurtosis.

small negative skewness and quite high kurtosis.

the returns have a daily autocorrelation of about 3% Squared returns are a proxy for volatility. The 22% autocorrelation of squared returns provides very strong evidence of the predictability of volatility and volatility what

volatility clusters.

actions that change the prices of equities such as stock splits and stock buybacks, without affecting the value of the firm. We need to use the what prices which automatically take this into account. For the S&P 500 this makes no difference

adjusted closing prices