Hi there,
I notice that in many formulas, when multiplying a series of numbers, we take 1 + the number
For example: question #2 on page 378 of Portfolio Management book . Question # 11-14 on page 380 of the of Portfolio Management book . We take 1 + r1 / 1 + r2
Do you know the reason behind this?
thanks
When you see this, you’re typically calculating a Future Value. Think of the “1+” number (actually, it’s a Future Value Interest Factor) as a translation factor that translates values at one point in time to values at a latter point.
If you have (as an example) a 10% interest rate per period, each period you’d end up with 110% (i.e. 1+ 0.10) of the amount you had at the beginning of the period. So,if you’re calculating a future value 2 periods out, it’d be the starting value (the Present value) x (1.1) x (1.1), or times 1.1^2
If you want a fuller explanation, here’s a video I put together for my classes.
Hi Busprof,
Thanks for the quick reply. I appreciated it. I also watched the video . I am not sure if the answer for my question is the same as the explanation in the video (it maybe the same, but I still do not understand) .
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.
you started with $1. Ended up with $1.42347
so you made $0.42347 on your initial $1 …
Show off!
Wait - let me get my calculator to check CPK’s math…
It’s not the math, you silly; it’s the dollar signs.