# Forwards question

If dividends growth rate on stock forward increases who gains, short or long?

long

Think of it like this. A long is always a buyer and a short is always a seller…for any asset. So if dividends growth rate on a stock increases that will increase the intrinsic value of the stock. Since its a forward the person who owns that stock in the future will benefit from the higher valuation. If the growth rate would have been higher when the forward was priced it would have cost more to enter into the transaction.

I think it is short. Because the short holds the asset now and sold it forward to long with a lower dividend, meaning higher price. Value of forward is less if dividends grow, PV of forward price - PV of Dividends. Higher dividends drains the stock’s value faster and long looses. Am I thinking wrong?

Yes if they declare a larger dividend than expected, but your question says the dividends growth rate increased, not the pending dividend.

Does it matter? Increase in dividend is free cash flow for short until expiration, because forward is priced to be arbitrage free at initiation. Any increase in the stock price will benefit long at expiration, but the additional dividends paid are loss for long since they were not factored in at contract initiation and the whole point that someone is long on the stock forward would be to capture all the growth. However, the expected stock price using discount models is irrelevant in forward evaluation.

It’s the dividend growth rate that increases, not just a few dividends. Dividend growth rate increases is just another name for “stock value increases” so obviously the long benefits.

if dividend growth rate increases then long benefits however if we look at the formula F = S x e power (rf - dy)n/N … if Dy increases then F will be lower… which is future price… it is confusing, that’s for sure…

Bilal Wrote: ------------------------------------------------------- > F = S x e power (rf - dy)n/N … if Dy increases > then F will be lower… which is future price… That’s before you went long, so it’s irrelevant.

I agree that the short benefits from an increase in dividends, since they are holding the stock in an arbitrage-free situation. If we have a forward price “X”, maturing at time “t”, the long could invest X / e^rt to have X dollars at time t. The short could purchase the stock at price “S”, and then hold it to time t to deliver the stock. These transactions must be equivalent to avoid arbitrage, so the forward price can be calculated as follows, where d is the continuous dividend yield: X / e ^ rt = Se^(-dt), ==> X = Se^(-dt+rt) Now say that the dividend yield “d” is higher than originally expected. This would cause the arbitrage-free forward price “X” to be lower. So the short gains and the long loses.

Same problem here…you are mixing the times of when the person goes long and when the dividend yield changes. Also, note that the dividend yield changes every minute of trading, so it will always be higher or lower than originally expected.

In order to answer this question, I do not think the dividend rate increasing is enough information. It does not provide dividend yield which is what the formula needs. If the growth rate of dividends increases doesn’t mean that the dividend yield increased. If the stock priced instantaneously increased at the same time, then your dividend yield could stay the same but the stock price went up and the long wins (however, compared to investing long in the stock, I believe the long stock investor wins by the dividends collected, it does matter because if you are managing vs a benchmark the benchmark will be based on the stock and you just did worse). If the short was performing arbitrage where the long the underlying stock and borrow at Rf, then the short would make money because the stock price would increase the value of underlying would offset the loss on his forward position. He would then receive the higher dividends and would like make money. However, note that he LOST on the forward. However, if the dividend rate increases and stock prices do not change. The short will win do to arbitrage pricing formula. Basically, the next day the same forward will have a lower price due to the formula and he can close out the position buy longing the new forward at a lower price. Since the long’s forward is worth less compared to new forward priced in the market the next day. His forward price must be the lower price and he lost money if he closes out the position. If he holds the forward to maturity, well I guess you can argue that he really didn’t lose but he did compared to just buying the stock and forgetting the forward. I am sure my thought didn’t come out clear but thats my 2 cents.

This thread is confusing. Let’s break it down. t=0: You go long a stock forward (you agree to buy a stock at time T, for \$K). There is no cost in entering a forward. 0 St increases in value t=T: Payoff for long contract is St - K, which is now greater. The long benefits. ______________________ We are not long and short the asset. We are long/short the forward contract. Agreed?

^ agreed. good explanation.

All the loss or gain on stock must only accumulate to Long because short is in arbitrage free position. However, dividend payout changes will effect short because FV of assumed continuous dividend cash inflows are removed when pricing forward. If suddenly firm decides to pay no dividends, its a cash loss to short or suddenly firm pays extra dividends its a cash gain to short. Yes if the stock price goes up and you value the forward Long may profit. But next day if the stock price goes down Long may loose. However higher dividends paid out to short mean while is a real additional cash flow.

janardhanc Wrote: ------------------------------------------------------- > All the loss or gain on stock must only accumulate > to Long because short is in arbitrage free > position. However, dividend payout changes will > effect short because FV of assumed continuous > dividend cash inflows are removed when pricing > forward. If suddenly firm decides to pay no > dividends, its a cash loss to short or suddenly > firm pays extra dividends its a cash gain to > short. > > Yes if the stock price goes up and you value the > forward Long may profit. But next day if the stock > price goes down Long may loose. However higher > dividends paid out to short mean while is a real > additional cash flow. Did anybody understand that?

this thread is a the WEEDS, and so is that post, GET OUT!

Nice explanation SeesFA, I think you are correct. I think the confusion relates to whether we are holding the stock’s price constant or not. For two identical stocks with the same price where the only difference is the dividend yield, the forward price “X” will be lower for the higher dividend yield stock. But if we are not holding the stocks price constant, your logic makes sense - and I think this is the correct interpretation. The stock price simply rises after the dividend yield increases. But similarly (and this is confusing) if the stock price stays the same, and the dividend yield increases, the SHORT is the one who gains.