Forecasting Dividends - Part 3

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]

where

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

where

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.