Answer: for multiple time periods is the sum of the one-period continuously compounded returns.

## Explanation Let's analyze each option: **Option A: "is higher than the holding period return for a given time period."** - This is **FALSE**. For positive returns, continuously compounded returns are actually **lower** than holding period returns. For example, if the holding period return is 10%, the continuously compounded return is ln(1.10) ≈ 9.53%, which is lower. **Option B: "for multiple time periods is the sum of the one-period continuously compounded returns."** - This is **TRUE**. This is a key property of continuously compounded returns. If you have continuously compounded returns r₁, r₂, ..., rₙ for periods 1 through n, the total continuously compounded return over all periods is simply r₁ + r₂ + ... + rₙ. This additive property makes them mathematically convenient for multi-period analysis. **Option C: "cannot be calculated for negative holding period returns because the natural logarithm of a negative number is not a real number."** - This is **FALSE**. While it's true that the natural logarithm of a negative number is not a real number, holding period returns are typically expressed as (ending value/beginning value) - 1. For negative holding period returns, the ratio (ending value/beginning value) is still positive (just less than 1). For example, if an investment loses 10%, the ratio is 0.90, and ln(0.90) ≈ -0.1054, which is a valid continuously compounded return. **Key Concepts:** - Continuously compounded return = ln(1 + holding period return) - For positive returns: continuously compounded < holding period return - For negative returns: continuously compounded > holding period return (in absolute value) - Multi-period continuously compounded returns are additive - Continuously compounded returns can be calculated for any holding period return > -100% (since ln(0) is undefined, but ln(positive number) is always defined)

Author: LeetQuiz .