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)