I am reviewing the Temasek 2013 Annual Report when I come across this interesting picture on page 7 of the report (page 9 in the PDF viewer).

It says that investments made by Temasek prior to March 31, 2003 have earned an annualized rate of return of 16% over the last decade. It also says investments made after March 31, 2003 earned an annualized return of 20% over the last decade. I don’t have their portfolio so I can’t prove or disprove that, but here is what I don’t understand.

If you go one page up to page 6 of the report (page 8 in the PDF viewer), you get this interesting picture.

In this picture, Temasek says that its 10 year return ending March 31, 2013 was 13%.

So here is my question: how do investments made prior to March 31, 2003 earn 16% over the last decade and investments made after March 31, 2003 earn 20% over the last decade magically average out at 13%?

**Update: I had a loyal reader point out that I had glossed over a very important distinction: the top figure uses “annualized” while the bottom figure uses “compound” so they are not using the same numbers. Let me explain. Let’s assume I invest $1,000 and in year 1 I earn a 50% return. Then in the second year, I take the money I started with and the interest reinvest it and also earn a another 50% return. I now have $2,250. 1,000 +(.5. x 1,000) = 1,500 + (1,500 x .50) = $2,250. My compound return is 50%. My annualized number however is 62.5%. I made $1,250 over 2 years from a $1,000 investment so my annualized rate of return is 62.5%. Thanks to a loyal reader for pointing out the wording issue. It should be noted that using the “annualized” rate of return is a sneaky way of inflating returns.**