Apologies if this has been asked before, I couldn't find it, or if this is so basic, but I feel it needs asking.

I'm sure we've all seen tables like this outlining fund performance.

What I'm unclear on is how to interpret those return values.

Say for example I put \$100 in FundA, and it performs like this (extreme values to make my point clearer)

``````Year    Value of my account   Performance %
2010    \$100
2011    \$10                   -90%
2012    \$20                   +100%
2013    \$40                   +100%
2014    \$80                   +100%
2015    \$100                  +25%
``````

Would the "5 Year Return" advertised by a bank, in a table like the one above be:

a) 0% - because I started with \$100 and ended with \$100

or

b) 47% - the average of -90, 100, 100, 100, 25

I would expect and hope the answer is 'a', but... is it?

https://www.td.com/ca/markets-research/mutual/mutual.jsp

and here's a Google Doc Sheet with the numbers, none of them match the advertised performance

• That td link is generic. Which specific fund are you referring to? May 11, 2017 at 18:22
• @RonJohn Sorry, it's TD Canadian Bond Index - eTDB909, choose "Mutual Funds" tab, then "Index Funds" in the now visible tab. Then "Performance" in the new tab. May 11, 2017 at 18:25

Those are annualized returns not average annual returns. One formula for annualized return over a period (assuming continuous compounding) is

``````V1 - V0
-------  * e^(-T)
V0
``````

To convert to annual compounding you'd use:

`````` V1 - V0
--------- ^ (1/T)
V0
``````

Where `V1` is the ending value, `V0` is the starting value, and `T` is the time frame in years. Since `V1 - V0 = 0`, the annualized return over 5 years using either method is 0%.

You know the answer, but wish it wasn't so.

EDIT: To get from \$100 to \$114.46 in 5 years is 3.434% compound growth. 100*1.34344. Since most stocks pay dividends, your account balance will not exactly reflect the growth in the price of the mutual fund.

• I woke up in a cold sweat thinking maybe it was 'b' - that's true. May 11, 2017 at 18:14