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

A)            positive                      positive

B)             zero                         zero

C)             zero                         positive

D)            positive                      zero

2、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)   -14.86%.

B)   -11.72%.

C)   -16.09%.

D)   -13.84%.

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

A)   Its continuously compounded return.

B)   Neither, they will be equal.

C)   Its holding period return.

D)   Not enough information to answer.

答案和详解如下：

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

Continuously Compounded

Holding Period

A)            positive                      positive

B)             zero                         zero

C)             zero                         positive

D)            positive                      zero

The correct answer was 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.

2、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)   -14.86%.

B)   -11.72%.

C)   -16.09%.

D)   -13.84%.

The correct answer was C)

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

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

A)   Its continuously compounded return.

B)   Neither, they will be equal.

C)   Its holding period return.

D)   Not enough information to answer.

The correct answer was C)

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