202) Calculate Total Return From Annual Returns

202) How to Calculate Total Return From Annual Returns?

Most investors want to know how to calculate the total returns of their investments. There are many types of returns and the terms are confusing those who are not familiar.

Annual Returns for the fund based on calendar year. Basically, it means the return from 1 Jan to 31 Dec of the year.

The Total Return basically means the returns from the first day to the last day of investment.

Let's take a look at an example for a better understanding.

Assume below are the Annual Returns (AR) by calendar year for a fund.

2015: +10%
2016: -5%
2017: +8%

What is the total return from 2015 to 2017?

(1+Total Return) = (1+AR 2015) x (1+AR 2016) x (1+AR 2017)
(1+Total Return) = (1+10%) (1-5%) (1+8%)
(1+Total Return) =  (1.10) (0.95) (1.08)
(1+Total Return) =  1.1286
Total Return  = 1.1286 - 1
Total Return  = 0.1286 = 12.86%

Total Return for 2015 to 2017 = 12.86%


Let's use money amount to show the calculation.

Let's assume you invested $1000 on 1 Jan 2015. 
What is your investment value at 31 Dec 2017? Assume no charges and no payouts.

Use the FV=PV(1+i)^n formula.

On 31 Dec 2015, the value was:
FV = $1000 (1+10%)^1
FV = $1000 (1.10)
FV = $1100

On 31 Dec 2016, the value was:
FV = $1100 (1-5%)^1
FV = $1100 (0.95)
FV = $1045

On 31 Dec 2017, the value was:
FV = $1045 (1+8%)^1
FV = $1045 (1.08)
FV = $1128.60

Total Return = (End Value - Begin Value)/Begin Value
Total Return = ($1128.60 - $1000)/$1000
Total Return = 12.86%

Now, what is the Annualized Return?

Use the FV=PV(1+i)^n formula.
$1128.60 = $1000 (1+i)^3
1.1286 = (1+i)^3
(1+i)^3 = 1.1286
(1+i) = Root 3 of (1.1286)
(1+i) = 1.04115
i = 0.04115
i = 4.115%

The Annualized Return is 4.115%. 
Annualized Return is based on compounded year after year.


Annualized Return is DIFFERENT from Average Total Return. 

Average Total Return = Total Return / No. of Years

In this example, the Average Total Return = 12.86% / 3 = 4.287%.

Hope this example helps to explain the differences between:
a) Annual Return
b) Total Return
c) Annualized Return
d) Average Total Return