Synthetic Index Fund

Hi all,

Can anyone explain synthetic index funds to me?

It seems to me you are taking a t-bill portfolio, seeing how much it will be worth at time t, and then doing some fancy calculations to see how many futures contracts you could buy and then pay off at time t.

But then they talk about div yield and effective units of stock purchased, and how investing the t-equitized amount in the stock market gets you to the same portfolio value (which I don’t think is true).

Schweser says: An investment in T equitized in t-bills + “number of contracts rounded” in futures = the number of contracts rounded discounted by the div yield. That makes no sense as t-bills earn the Rf rate and the futures would just earn the price movement. One side this equality is being discounted by the Rf rate and the other side is being discounted by the dividend rate.

Anyone has insight here?

Page 357 Vol 5 of CFA, Page 150 Book 4 Schweser

In continuous time measure , the expected future price is given by

Szero*e^(Rf-divyield)xt where Szero is the spot and both the Rf and the div yield are represented in continuous rate.

So for a div paying stock , you need less shares at time t0 to create the same return as a non-div paying stock.

It would be incorrect to say that the futures price ignores dividends and only depends on stochastic price movements which are represented by Rf as a risk measure.

Since you need less cash upfront in case of an index fund that has dividend yields than not , so you can discount the right side by the dividend yield to get the discount due to dividends.

Hope I am being clear although I suspect not . The mechanics of it are clear in my mind

Thanks for the thoughts.

I eventually understood that the equality I identified above only holds in Future Value terms, not Present Value terms. I thought there was a deeper concept I was missing, but now I am convinced there is not.