In part one and two of this series we covered the theory behind predicting dividends; this post is where the rubber hits the road.
The maths for our previous wordy description is
F = S * e ^ [(r-c) * t]
F : future or forward price of the stock
S : spot price
r : interest rate
t : time to the forward's maturity
c: convenience yield
We haven't mentioned the convenience yield yet. For equities the convenience yield is
c = q + l + E
q : dividend yield
l : stock lending yield (a big factor when a stock is being heavily shorted)
E : error term, or other miscellaneous factors
Solving the equation for q and assuming stock lending and the error term is minimal we find an equation we can use to predict dividends
q = r - ln(F/S) / t
In order to test this equation I took an S&P 500 future maturing in December 2013 and tracked it through the wild ups and downs through its three years of life. It was a pretty interesting time; the boom of 2013, not to mention Euro zone debt crises and Congress debt ceiling talks.
On the future's first day it predicted the dividend yield over the next 3 years would be 1.9%; the actual yield was 2.08%. Not bad.
The average deviation was about -0.2% over its life, i.e. it underestimated the dividend yield over its life time.
Still, in the volatile world of equities being about 10% off in longer range forecasts is unheard of.
The data I used to make these forecasts can be downloaded here (Open Office format).
The spread sheet can be improved upon - perhaps with more care the forecasts will be even more accurate.
Also, the realised dividend information used is actually from the SPY ETF - I couldn't find the dividend information for the S&P 500 index itself.
Lastly, the forecast is really for the future's convenience yield - there are quite a few factors which we assume to be small, that may have a large impact over certain periods of time.
Next time, we will investigate making predictions for individual stocks rather than indicies.