Schweser has the following paragraph that to me just doesn’t make sense at all:

“Note that a derivatives based enhanced indexing strategy will have less breadth than a stock based enhanced indexing stategy because the investor uses a derivatives contract to gain exposure to equity AND earns an excess return with non equity strategies (using cash for duration mgmt of fi). Due to its lower breadth, it will requite a higher IC to earn as high an IR as a stock based strategy”.

Why does using a derivatives = less breadth? It is still the same number of independent decisions being made, just a different strategy to obtain exposure? I feel like I am fundamentally missing something here.

I feel like it might be because the excess return from a derivatives based enhanced indexing strategy is simply from managing duration, which according to them does not require making many independent decisions. You just figure out what the duration should be, and that’s it.

With an equity based enhanced indexing strategy, you underweight/overweight stocks in the index to generate the additional alpha. In an index, you have several stocks which you can overweight or underweight which means higher breadth.

So, changing the weighting of several stocks involves more decision making then just changing the duration.

Think of it this way, with a stock based semi active strategy, you have hundreds of possible stocks to under/overweight in order to gain excess return,lets use 100 as an example - Sq root of 100 = breadth. With derivatives based, you gain exposure to equities buying futures with cash, so your breadth on the derivatives sides is limited to the quantity of futures positions available on the particular equity index. Lets say there are 10, so your breadth would be the square root of 10. Your breadth on the Fixed Income side of the Derivatives based is limited to your duration titling options on the yield curve, whatever that might be, lets say that there are 12 as an example. So your total BREADTH for the Derivatives Based Semi Active strategy is the sq root of (10+12) which is less than that of the stock based semiactive which is the sq root of 100.

So you mean to say that desired future contracts may not be available and thereby leading us to choose a alternate future contract that doesn’t reflects our complete independent choice?

No, I’m saying that your choice isn’t independent: if you want to limit the exposure to a position you already hold, you need to take the opposite position: your choice is restricted, so the decision isn’t completely independent.