Q1. stock increased in value last year. Which will be greater, its continuously compounded or its holding period return?

A)   Neither, they will be equal.

B)   Its continuously compounded return.

C)   Its holding period return.

Q2. Over a period of one year, an investor’s portfolio has declined in value from 127,350 to 108,427. What is the continuously compounded rate of return?

A)   -16.09%.

B)   -13.84%.

C)   -14.86%.

Q3. If a stock decreases in one period and then increases by an equal dollar amount in the next period, will the respective arithmetic average of the continuously compounded and holding period rates of return be positive, negative, or zero?

A)   Zero; zero.

B)   Positive; zero.

C)   Zero; positive.

答案和详解如下：

Q1. stock increased in value last year. Which will be greater, its continuously compounded or its holding period return?

A)   Neither, they will be equal.

B)   Its continuously compounded return.

C)   Its holding period return.

Correct answer is C)

When a stock increases in value, the holding period return is always greater than the continuously compounded return.

Q2. Over a period of one year, an investor’s portfolio has declined in value from 127,350 to 108,427. What is the continuously compounded rate of return?

A)   -16.09%.

B)   -13.84%.

C)   -14.86%.

Correct answer is A)

The continuously compounded rate of return = ln( S₁ / S₀ ) = ln(108,427 / 127,350) = –16.09%.

Q3. If a stock decreases in one period and then increases by an equal dollar amount in the next period, will the respective arithmetic average of the continuously compounded and holding period rates of return be positive, negative, or zero?

A)   Zero; zero.

B)   Positive; zero.

C)   Zero; positive.

Correct answer is C)

The holding period return will have an upward bias that will give a positive average. For example, a fall from 100 to 90 is 10%, and the rise from 90 to 100 is an increase of 11.1%. The continuously compounded return will have an arithmetic average of zero. Since we can sum continuously compounded rates for multiple periods, the continuously compounded rate for the two periods (0%), means the rates for the two periods must sum to zero, and their average must therefore be zero.

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