Can someone explain the following two senteces from example 1 reading 10 for me?
Suppose you are the manager of a mutual fund indexed to the Lehman Brothers Government Index. You are exploring several approaches to indexing, including a stratified sampling approach.
(Institute 570)
Institute, CFA. 2016 CFA Level I Volume 1 Ethical and Professional Standards and Quantitative Methods. CFA Institute, 07/2015. VitalBook file.
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What does it mean to have a mutual fund that is indexed to the LBGI? How do you index an index?
How can you be exploring several approaches to indexing if an index has in it whatever it has in it? So to follow an index you need to buy all its constituents or no?
It means that your fund is trying to track the results of that particular index.
The most direct way of doing that is to hold in your fund every security in the index, in the same proportions as they appear in the index. Generally, especially for bond indices, this is very costly and inefficient.
Another way, which you mention, is stratified sampling. You chop up the index holdings into a number of bins according to the characteristics you deem important, then choose a sample of the securities from each bin to hold in your fund. For a bond index, those characteristics might be maturity (you could have bins of 0 – 1 year, 1 – 2 years, 2 – 5 years, 5 – 10 years, 10 – 20 years, and greater than 20 years), optionality (straight bonds, callable bonds, putable bonds, convertible bonds), credit quality (investment grade, below investment grade), and so on.
Suppose that the index holds 20,000 bonds, and you plan to hold 500 bonds in your fund. If in the 5 – 10 year maturity, callable, investment grade bin the index has 200 bonds, or 1% of its holdings. Then you’ll have 1% of your holdings – 5 bonds – in that bin. You randomly select 5 of the 200 bonds and buy them.