# Implied dividend estimation

I am looking at two different ways of estimating the expected / implied dividends from market data.

### 1. Dividend futures

I know that this asset class is not very liquid and might not be representative enough. However, assuming that I have prices which are good enough, how could I estimate the implied divided from the contract price?

For instance, if I have an exchange traded contract whose settlement is the sum of actual dividends paid during 2013, could I just take the current contract price and capitalize it up to the settlement date in order to obtain the implied dividend for 2013?

EDIT: Example added for illustration purposes:

On 05 july 2013, the quoted prices for Santander Dividend Futures are:

• 2013 contract; Maturity 20 Dec 2013; Price: 0.58
• 2014 contract; Maturity 19 Dec 2014; Price: 0.41
• 2015 contract; Maturity 18 Dec 2015; Price: 0.32

For simplicity assume that:

• Each contract is linked to the sum of all dividends paid during the corresponding calendar year.
• Appropriate risk free rates for each contract are: 0,1%; 0,3%; 0,5%.

If I want to estimate the total amount of implied dividends for each year, could these figures be obtained as:

$$D_{2013}=0.58e^{(0,001*0.46)}=0.5802$$ $$D_{2014}=0.41e^{(0,003*1.46)}=0.4118$$ $$D_{2015}=0.32e^{(0,005*2.45)}=0.3240$$ Or am I missing something?

### 2. Index / single-stock futures

Alternatively, if I wanted to estimate the dividend yield for a stock, what are the limitations of calculating the implied yield directly from the market prices as:

$$F=S_0e^{(r-q)T} \; \; \; \; \; \Rightarrow \; \; \; \; \; q = \frac{rT-\ln{\frac{F}{S_0}}}{T}$$

I guess there must be certain shortcomings with this aprroach, since usually the synthetic forward is obtained through the put-call parity instead of using the futures prices.

-
I am fairly familiar with Dividend futures, especially long dated index dividend futures traded on Eurex. Since the maturities are quite long for some of these names (2021's dividend for example) the discounting problem becomes essential. Typically, due to the structure of margin posting when trading futures, little margin is required upfront today for a contract that settles in 2021 Dec, thus using traditional discounting models, like the one used in classical DCF's are really equivalent. This would motivate a lower discount rate, since roughly 8% of the contract's value is posted. –  Algos Dec 11 '13 at 17:26
Hi Algos, thanks for your comment. So, if I already have an appropriate discount rate, could I just use the proposed approach to recover the implied dividends from dividend futures? Or are there any other factors / adjustments that I might be missing? –  sets Dec 12 '13 at 10:27
The dividend future is probably the best estimate for what the market expects the dividend is going to be for a certain year. However, be aware of illiquidity and the bid-ask spread. A second note would be that extraordinary dividends and stock spin-offs may not included when the dividend futures are settled. –  Algos Dec 12 '13 at 17:11

You could compute index dividend yield from ATM options using linearized put-call parity (assuming index options are European.)

The present value of the dividend payment is: $PV(div) = P - C + (S - K) + K(e^{rT} - 1)$

where $r$ is interest rate to the option expiration and $T$ is time to maturity in years. Then the implied dividend is:

$d = \frac{PV(div)}{T*S}$

I realize it's not a complete answer, but it's a starting point. Note: whether using futures or options, the implied dividend value would represent the portion paid until the contract expiry.

-
Thanks Eli. I know you can estimate implied dividends through the put-call parity. However, I am interested in understanding the implications of other alternative ways to estimate implied dividends. In particular, I am trying to understand the use of dividend futures (provided you have a representative price), and the use of traditional stock/index futures. Any help in this regard will be highly appreciated –  sets Apr 26 '13 at 13:53
I see... It is an interesting research point. I may need to experiment with the data though. –  Eli Apr 26 '13 at 17:19
What modifications would you need to make in order to get the PV(div) of an option whose stock will pay multiple dividends at different times before expiry? Or is this the PV of the whole div stream? –  frickskit Oct 15 '13 at 21:53
It's the PV of the entire stream. P.S. I'm working on revised model, this one uses one day of data and introduces a lot of noise. It would be better to regress from approx 90 days set of ATM options. –  Eli Oct 21 '13 at 18:30