Khonglo wrote: Here is an example 1 on page 325 (Portfolio Management book):
Year 1 . Return 15%
Year 2 . Return -5%
Year 3. Return 10%
Year 4. Return 15
Year 5. Return 3%
Calculate the holding period return?
The solution is: (1+R1)(1+R2)(1+R3)(1+R4)(1+R5)-1 = 42.35%
What is the reason for adding 1 to the return then subtract the product by 1? Thanks
To piggyback on busprof’s answer, the way you calculate the holding period return (in general) is to compare the amount of money you have at the end to the amount of money you had at the beginning; the difference is your return in dollars (or euro or pounds or some other currency), and the difference divided by the beginning amount is your return in percent.
Imagine you start with $1,000. Your return the first year is 15% of $1,000, or $150. You end the year with $1,000 + $150 = $1,150, which is 1.15 (= 1 + 15%) times your original amount.
Your return the second year is −5% of $1,150, or −$57.50. You end the year with $1,150 − $57.50 = $1,092.50, which is 1.0925 (= (1 + 15%)(1 − 5%) = 1.15 × 0.95) times your original amount.
You continue this way for 5 years; you end year 5 with $1,423.47 which is 1.42347 (= (1 + 15%)(1 − 5%)(1 + 10%)(1 + 15%)(1 + 3%)) times your original amount. Therefore, your return (your profit) is $423.47 which is 0.42347 = (1.42347 − 1) times your original amount, or (1 + 15%)(1 − 5%)(1 + 10%)(1 + 15%)(1 + 3%) − 1 times your original amount.