Question

Suppose an investor purchases an asset for $1000, then

sells it four months later for $1040.

a) What is the holding period return?

b) What is the annual percentage return?

c) What is the effective annual return?

d) Calculate and compare the discrete and continuously compounded return. Explain the difference.

Answer 1

a. Holding period return = P1-P0/P0

P1 = $1040, P0 = $1000

HPR = (1040-1000)/1000

HPR = 4%

b. Annual Percentage return is simply computed using unitary method

If return for 4 months = 4%

Then return for 1 month = 1%

Hence, annual percentage return for 12 months or a year = 12% (4%/4 months * 12 months)

c. Effective annual return = (1+rperiod)^no of periods -1

r or HPR = 4%

No of periods = how many time we have to compound return in full year, so number will be No of months in a year/ holding period, 12/4 = 3

Effective annual return = (1+.04)3-1 = 12.486%

d. Discrete compunding return = (1+HPR)12/n, N=4

= (1+ .04)^12/4 -1 = 12.486%

Continuous compounding return e^rt - 1

=> e^(4*3)/100 - 1 = 0.12749 or 12.749%

The difference between discrete and compunded return is (12.749%-12.486%) = 0.26%

Discrete compunded return is calculated at specific intervals whereas, continous compounding uses a natural log based formula to compute the return over the smallest possible intervals.