extrinsec value itm options Spx Spy

[JackRab]

Let's say there are no market forces directly involved in a company share price.
spot price on ex-dividend date__100
next ex-dividend date__90 days
estimated dividends__3

The spot price is going to move progressively from 100 until 103 the day before it goes ex-dividend.
what is the today's price of the 90 dte future ?. Without considering interests. And, will remain the same value during the 90 days or is going to move following the spot price. I think it's going to stay.

Until in this thread was said that the spot moves direction the future I thought it was the other way. So, I thouhgt the correct srategy was buy futures and sell spot, because the price of the future is going to increase more compared to the spot price.

Thank you.

Taking zero interest into account...

Spot = 100
Div (at t=90) = 3
Future (with dte=60, June future) = 100
Future (with dte=90, July future) = 97
Future (with dte=120, Aug future) = 97

If tomorrow the spot moves up to 105;

Spot = 105
Div (at t=90) = 3
Future (with dte=60, June future) = 105
Future (with dte=90, July future) = 102
Future (with dte=120, Aug future) = 102

You have to let go of the assumption that the spot will move towards the Futures price, the Future is merely a financing tool... It doesn't really say anything about what the market expects the price of a stock to be in N days.

So, like @sle points out, the Future price is basically the spot, but since you don't pay the full spot price to hold it, it's usually valued higher than the spot, since no cash outlay... and arbitrage makes sure the Futures price = spot + interest for N days.
If you buy a Future, and sell the spot at 100, than you have a positive cashflow at time of trade (or more correct at settlement) because you receive cash for selling short the stock. That 100 will bear interest, if that interest component is 2 over duration of the hold (which is until expiry of Future contract)... than the Future should be trading at 102. So in short, if you could trade that Future below or above 102, there's an arbitrage opportunity....

With dividend involved, a Future doesn't give you the right to get the dividends, since that right is only for shareholders... therefore, the Future price is also trading at Spot - Dividend.

In total, Future = Spot + interest component - dividend.

So... it's not that spot moves towards future or vice versa because of market reactions... it happens that way because of the financing. They will merge towards each other and at expiry.... then F=S.

 

[raf_bcn]

Hi

After re reading the thread.Maybe it is very basic stuff.
For me the influence of the interest rate in the fair future price is clear, but the dividends influence it isn't, mainly when there is an ex-dividend date in the middle of the contract.
_If the future (dte=90) is 97 you will buy for 97 a share that will be valued in 100. That is a 3,09% benefit in 90 days. More than the stock holder who is going to recieve 3% dividends.
Is that a fair price?

Some basic questions. Omiting interests rates and market forces pushing stock prices.

1_ The actual price of the future is the spot price less the amount of dividends the share is going to receive during the duration of the future contract.
The price of the future doesn't discount the amount of dividends that are not going to be distributed during the live of the future contract.

2_The spot price of the stock is accumulating the value of the dividends that the company is accumulating. So, If the ex-dividend date of a company it is in a few months, and it will be a 3 dllar dividend, the stock price will progressively incorporate that amount.

3_If the above conclusions are right then we could find some occasions when the ex dividend date and the expiration of the future doesn't match, and will occur that the ex-dividend date it is one day and the expiration of the future is one month later. In these occasions will occur the following.



time,days _____ 1 - 30 - 60 - 89 - 90(ex-dividend) - 120 - 160 - 179 -180

share value ___100 - 101 - 102 - 103 - 100 - 101 - 102 - 103 - 100

1)future dte= 90 - 97 - 98 - 9 - 100 - 100 - 100 - 100 (exp.)

As you can observe if in day 90 we buy a stock and sell future we win a non risk 2%
And imagine what happen if instead of buying stock we do it with options. Stock options are american style so thefollow the spot price.

Tank you.

 

[JackRab]

I think you need to reset your mind, and start with the basics of how accounting works.

Let's assume Company has only cash and doesn't do anything at the moment. The total cash value is 100 mln. And there are 1 mln shares on the market, so the stock value is 100,- if valued at fair value... (which it should, since the company isn't doing anything more than accumulating interest on cash, let's assume interest = 0%). So... Spot = 100

Now, Company has decided it doesn't need much cash on hand, since it has no clue what to do with it... and wants to pay a yearly dividend of 10 dollars for the next 10+ years. The next dividend payment is at the end of the year in December, a nice Christmas cash bonus.

So at the end of the year, 15th December, Company pays out 10 mln in dividend. The total cash on books is then 90 mln. Which means the stock price at fair value is Spot = 90

There is no progressively incorporating of any dividends... since the company isn't really making any profits... it's just paying out the cash that it has. So each year when dividend is paid, the Spot drops with 10 dollars. If we leave any interest accumulation out of the way, after 10 years, the Spot is 0,00

Now, let's say futures are traded... and they expire on 20th of December every year... Futures do not have the right of a dividend with them, since only stock has that right. Then these would be the values (excluding any interest rate, since we assume 0%);

F(expiry t=1) = 90
F(expiry t=2) = 80
F(expiry t=3) = 70
F(expiry t=4) = 60
F(expiry t=10) = 0

Which equals the Spot after each dividend, since the future owner receives the stock only at 20th Dec, right AFTER the dividend. Since the stock doesn't move... and the only reason for owning the stock is getting the dividend, which the Futures don't get... the Futures don't move either.

Now in real life... usually Company does make a profit. Say the yearly profit is 10 mln dollars in interest accumulation since the interest rate = 10%. So basically, Company is paying out the full profit in dividends every year, EPS = 10 and dividend = 10.

Gradually, the cash goes up from 100 mln to 110 mln. Then at the end of the year, they pay 10 mln in dividend... so cash drops back to 100 mln afterwards. Same happens with the stock, if we assume fair value/book value valuation.

Beginning of the year Spot = 100... end of the year, before dividend Spot = 110, ex-dividend Spot = 100

(--- Now, this only is the case, if everyone has the same idea about valuation and future cashflows/earnings... and everyone agrees that we want to make 10% yearly, which has to do with risk free rates etcetcetc ---)

In this case... with the futures should also have the same yearly % rise as the stock will have. Because otherwise there's an arbitrage opp.

So: F(expiry t=1) = S x (1+r)^1 - Div....
(or more to the point F(expiry t=1) = PV Cashflows x (1+r)^1... but since the future has no right to the dividend, the PV Cashflows is excluding the dividend, resulting in the same)

F(expiry t=1) = 100 x 1.10 - 10 = 100... which is the same as the Spot at the beginning of the year.

But!!!!!!.....

Just before dividend (14th Dec), Spot = about 110... since it has accumulated most of the interest on cash for the year.
F(expiry t=1) at this moment... = 110 x (1.1)^0.0027 - 10 (Div) = 100

You see what happens....the spot/company accumulates profit, which is the same as the (risk-free) interest and the Future doesn't... since arbitrage makes it stay put, because a future doesn't cost any money (let's assume no margin reqs)... it doesn't bear interest and doesn't make any income on that.

The only reason a future would move... is when the stock moves because of a change in income perception. Let's say they suddenly make 15 dollars per share, 5 more than risk-free rate... that would mean the moment that news is released.. the Spot jumps up to 105... and the Future as well since the connection should hold.

(I'm cutting a small corner here, since you should in this case discount earnings with the risk-free rate as well... but I hope you're getting the point).

So... I think I answered your questions here... it basically all depends on earnings above risk-free rates which will move the Spot. If the earnings = risk-free rates... then the future should stay exactly where it is because of F(expiry t=1) = S x (1+r)^1 - Div


(PS... I assume we'll continue this in a few days, when you have run through this thoroughly... )

 

[raf_bcn]

Hi
Thank you very much for the response. I will read carefully.
The numbers in my previous post are almost inintelligible. I am uploading a file to easily see what I mean.
In my example the future with 150 dte is the key, because remains at 100 while the stock goes up due to the incorporation of dividends.
So in my opinion it could be a good way to hedge.

 

[ironchef]

I think you need to reset your mind, and start with the basics of how accounting works.

Let's assume Company has only cash and doesn't do anything at the moment. The total cash value is 100 mln. And there are 1 mln shares on the market, so the stock value is 100,- if valued at fair value... (which it should, since the company isn't doing anything more than accumulating interest on cash, let's assume interest = 0%). So... Spot = 100

Now, Company has decided it doesn't need much cash on hand, since it has no clue what to do with it... and wants to pay a yearly dividend of 10 dollars for the next 10+ years. The next dividend payment is at the end of the year in December, a nice Christmas cash bonus.

So at the end of the year, 15th December, Company pays out 10 mln in dividend. The total cash on books is then 90 mln. Which means the stock price at fair value is Spot = 90

There is no progressively incorporating of any dividends... since the company isn't really making any profits... it's just paying out the cash that it has. So each year when dividend is paid, the Spot drops with 10 dollars. If we leave any interest accumulation out of the way, after 10 years, the Spot is 0,00

Now, let's say futures are traded... and they expire on 20th of December every year... Futures do not have the right of a dividend with them, since only stock has that right. Then these would be the values (excluding any interest rate, since we assume 0%);

F(expiry t=1) = 90
F(expiry t=2) = 80
F(expiry t=3) = 70
F(expiry t=4) = 60
F(expiry t=10) = 0

Which equals the Spot after each dividend, since the future owner receives the stock only at 20th Dec, right AFTER the dividend. Since the stock doesn't move... and the only reason for owning the stock is getting the dividend, which the Futures don't get... the Futures don't move either.

Now in real life... usually Company does make a profit. Say the yearly profit is 10 mln dollars in interest accumulation since the interest rate = 10%. So basically, Company is paying out the full profit in dividends every year, EPS = 10 and dividend = 10.

Gradually, the cash goes up from 100 mln to 110 mln. Then at the end of the year, they pay 10 mln in dividend... so cash drops back to 100 mln afterwards. Same happens with the stock, if we assume fair value/book value valuation.

Beginning of the year Spot = 100... end of the year, before dividend Spot = 110, ex-dividend Spot = 100

(--- Now, this only is the case, if everyone has the same idea about valuation and future cashflows/earnings... and everyone agrees that we want to make 10% yearly, which has to do with risk free rates etcetcetc ---)

In this case... with the futures should also have the same yearly % rise as the stock will have. Because otherwise there's an arbitrage opp.

So: F(expiry t=1) = S x (1+r)^1 - Div....
(or more to the point F(expiry t=1) = PV Cashflows x (1+r)^1... but since the future has no right to the dividend, the PV Cashflows is excluding the dividend, resulting in the same)

F(expiry t=1) = 100 x 1.10 - 10 = 100... which is the same as the Spot at the beginning of the year.

But!!!!!!.....

Just before dividend (14th Dec), Spot = about 110... since it has accumulated most of the interest on cash for the year.
F(expiry t=1) at this moment... = 110 x (1.1)^0.0027 - 10 (Div) = 100

You see what happens....the spot/company accumulates profit, which is the same as the (risk-free) interest and the Future doesn't... since arbitrage makes it stay put, because a future doesn't cost any money (let's assume no margin reqs)... it doesn't bear interest and doesn't make any income on that.

The only reason a future would move... is when the stock moves because of a change in income perception. Let's say they suddenly make 15 dollars per share, 5 more than risk-free rate... that would mean the moment that news is released.. the Spot jumps up to 105... and the Future as well since the connection should hold.

(I'm cutting a small corner here, since you should in this case discount earnings with the risk-free rate as well... but I hope you're getting the point).

So... I think I answered your questions here... it basically all depends on earnings above risk-free rates which will move the Spot. If the earnings = risk-free rates... then the future should stay exactly where it is because of F(expiry t=1) = S x (1+r)^1 - Div


(PS... I assume we'll continue this in a few days, when you have run through this thoroughly... )

Mr. JackRab,

May I ask you a question:

So, if I am long (short) a call with a delta of 0.xx, I can either delta hedge my position with an equivalent short (long) spot future at expiration with xx shares, or short (long) xx shares directly?

If so, which is a better hedge?

Thank you.

 

[JackRab]

Hi
Thank you very much for the response. I will read carefully.
The numbers in my previous post are almost inintelligible. I am uploading a file to easily see what I mean.
In my example the future with 150 dte is the key, because remains at 100 while the stock goes up due to the incorporation of dividends.
So in my opinion it could be a good way to hedge.

Which stock are you looking at? I would always go with the shorter term future, since that is the most liquid and easier traded.... you can always do a futures rollover when it's about to expire.

 

[JackRab]

Mr. JackRab,

May I ask you a question:

So, if I am long (short) a call with a delta of 0.xx, I can either delta hedge my position with an equivalent short (long) spot future at expiration with xx shares, or short (long) xx shares directly?

If so, which is a better hedge?

Thank you.

For me that would depend on liquidity and costs... if the liquidity of the futures contract is decent enough, so spread is the same as the underlying stock, and the costs are the same or lower... then go with the future... If not, just stick with the stock... the only risk then is some dividend exposure, but usually that shouldn't be that much of an issue

 

[ironchef]

For me that would depend on liquidity and costs... if the liquidity of the futures contract is decent enough, so spread is the same as the underlying stock, and the costs are the same or lower... then go with the future... If not, just stick with the stock... the only risk then is some dividend exposure, but usually that shouldn't be that much of an issue

Thank you for your answer. Clear up one of my "wondering" thoughts.

 

[raf_bcn]

Hi
It is not a specific position with a specific underlying. It is a theoretical position to understand if this is correct,

If you buy the stock on the ex-date this means that you do not get to get the dividend, it's been allocated away and is sitting in a custodian bank account. So your strategy would not work, the only thing you are doing is essentially lending money to the buyer of the futures contract

or this is correct

Then maybe if on the ex-dividend date we buy shares and sells futures we are hedging and will obtain the dividend without risk, on the expiration day.

If the numbers I showed are correct, specifically the Future dte=150, then it seems it is a good way to capture some dividend without risk, buy stock and sell future on the ex dividend date.
The basis, difference between spot underlying and the future, is 0 on the ex dividend date. And the basis will increase, and tat's the amount we are going to get.
But, again, it is theory.

 

[JackRab]

Everything @sle says is correct...

You're (again) misunderstanding the concept of dividends.

The fact that a stock goes up during a year is not due to dividends... but merely because perceptions about revenue and profits.
Assume stock A and stock B both make 10 dollars profit every year... the only difference is that stock B pays a dividend of 10 at the end of the year.

So, keeping everything else equal and forgetting about any other stock influences... you could argue both stock A and stock B go up gradually from 100 to 110 during the year. And at the end, B drops back down to 100, because it pays the dividend.

Both investors in A and B have the same amount of capital... 100 at start and 110 at the end. Stock A investors have the 110 in stock invested.
Stock B investors have 100 in the stock and 10 in cash...
Future A will be 100 at the start... and 110 at the end of the year.
Future B will be 90 at the start... and 100 at the end of the year.

That's about it...

There's no real 'capture' of dividends... you are either entitled to it (as an investor in the stock) or not (as a futures holder).

PS. the projections in your little overview are incorrect. The future(dte150) should be at 102 at expiry.

If the numbers I showed are correct, specifically the Future dte=150, then it seems it is a good way to capture some dividend without risk, buy stock and sell future on the ex dividend date.
The basis, difference between spot underlying and the future, is 0 on the ex dividend date. And the basis will increase, and tat's the amount we are going to get.

On the ex-dividend date the stock already traded ex-dividend. Ex-div mean exclusive of dividend... so there's nothing to capture... remember, the future(dte150) should be at 102 at expiry.