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) positive zero
D) zero positive
The correct answer was D) zero positive
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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Can anyone please use an example to show me the calculation for above two rates? Thx a lot!
(Continuously Compounded) (Holding Period)
A) positive positive
B) zero zero
C) positive zero
D) zero positive
The correct answer was D) zero positive
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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Can anyone please use an example to show me the calculation for above two rates? Thx a lot!