A question from the circulum, mentions that they will differ if the Futures Price and Intrest Rate are negatively correlated. Please can someone explain why this is the case for me?
Thank you!
I think you are referring to this?
Future prices will be higher than foward prices when interest rates and future prices are positively correlated because futures gains/losses are settled each day, excess margin provides funds, earning more interests when rates are high.
Future prices are lower than forward prices when rates and future prices are negatively correlated because you require funds when rates are low.
Because gains/losses are settled each day, your margin account will increase with gains and decrease with losses. Because your margin account earns interest, you’ll earn more interest when rates increase, and less interest when rates decrease.
As the long position, if there is a positive correlation between the price of the underlying and interest rates, when the underlying increases in price your margin account increases and you’ll earn higher interest on that money, a favorable outcome; when the underlying decreases in price your margin account decreases, but you’ll lose less interest (rates go down), a (relatively) favorable outcome. As both outcomes are in your favor, you’d be willing to pay a higher price on the future than on a forward that doesn’t have a margin account and receives no benefit from changing interest rates.
If there is a negative correlation between the price of the underlying and interest rates, you earn less interest when your margin account increases, and lose more interest when it decreases, both unfavorable outcomes; you’ll pay a lower price for the futures.
What does it mean to short Forward (1,1)? And how it does work practically?
It means that you have entered into the short position in the forward contract: you agree to deliver the underlying at a specific time at the agreed price.
Practically, it means that you have effectively sold the underlying: you will gain if the price of the underlying decreases between the day you enter into the forward contract and the day it expires (and you have to deliver the underlying), and you will lose if the price of the underlying increases.
Thank you… S2000magician…for simple explanation… 
By (1,1) I think you are referring to an interest rate forward. Sine you are short, you agree to lend at a fixed rate deided today one month from now for a period of 1 month.
And yes, if rates derease, you actually get to earn a higher interest rate on the amount you lent. Which syncs with theory that shortis in the money when rates decrease.
My pleasure.
The gains/losses are based on the settlement price, correct (settlement price is the average of prices of trades of the futures contract in the closing period)?
What is the agreed price for a futures contract? Is it the settlement price? Or is it simply just some agreed upon contract price? I believe it’s the latter.
But then what is the value of a futures contract? I’m assuming the value (or price) of a futures contract is the settlement price?
Also, why does the price of futures converge to the spot price of the underlying? May you please provide an example?
That’s correct.
You’re correct: it’s the price to which the long and the short agreed when they entered into the contract. In general, it’s the spot price of the underlying asset increased at the risk-free rate for the term of the contract.
Each day at settlement the value to the short and to the long are both zero: the cumulative value of whatever gains and losses they have incurred has been settled by, respectively, increasing or decreasing the balance in their margin account. (Technically, the value could be somewhat different from zero because the cumulative settlement is based on changes from the original spot price, not changes from the futures price (which is the spot price plus interest). Each margin account will earn some interest, but unless the value in the margin account is the original spot price, there will be a difference between the interest earned on the margin balance and the interest on the original spot price. For our purposes, it’s probably not enough to concern us.)
Make sure that you understand what that statement means.
It doesn’t mean that the price of our futures contract will converge to the spot price at the expiration of the contract: our price is fixed; it doesn’t change.
It also doesn’t mean that the spot price converges to the price to which we agreed in our contract. First, the market doesn’t know the price to which we agreed. Second, even if the market did know, it would have the good sense not to care. The price of our contract has nothing to do with the spot price at expiration. In fact, contrary to what many people in finance say, the price of our contract is not even a predictor of what the spot price will be at expiration. It’s not intended to be; it’s intended to prevent arbitrage. That’s all.
What that statement does mean is that if you were to set (i.e., fix) an expiration date for a futures contract, and every day as you approach that fixed expiration date you were to look at the price of a futures contract expiring on that date and compared it to that day’s spot price, you would see that those prices will converge. Of course, that’s not surprising at all. Remember that the futures price is the spot price increased by the risk-free rate for the term of the contract. As we approach expiration, the term of the contract approaches zero. And if you increase the spot price by the risk-free rate for zero days you get the spot price.
So we are saying that the value of a futures contract is technically zero to the two parties (when we net the gains and loss).
How about the price of a futures to the market? As in, what if one party wants to sell a futures contract? What would be the price of it then? Is it just a market price that is not specified by the CFAI?
So the market price of a futures contract expiring at T = 3 will be equal to the spot price of the underlying at T=3?
What’s the difference between the contract price and the futures price? Is the contract price simply the price at which the underlying will be delivered that is specified by the 2 parties? If so, then how is that different from the futures price? I’m having a difficult time grasping the different terms you’re using despite rereading the material in the books and your paragraphs.
Example: Long forward with a contract price of $50 that expires at T=3. Are you saying that the underlying will be worth $50? That doesn’t make sense because spot prices do not converge to the contract price. Therefore, I’m assuming that the contract price is different than the futures price but I do not understand the difference.
No.
Today is March 22. If I have a futures contract on, say, Google stock that expires on June 22, the market price of that contract cannot be the June 22 spot price of Google. Nobody knows what the spot price of Google will be on June 22.
The market price of that contract is today’s spot price on Google increased by the risk-free rate for three months.
At the inception of the futures contract, there is no difference. It’s a futures contract : futures price and contract price mean the same thing: the agreed price at which the short will sell the underlying and the long will buy the underlying at expiration.
Later on, the price of the futures contract may change; the (original) contract price is fixed.
Yes.
At the inception of the contract, it isn’t different. However, over time the (current) futures price will change; the (agreed) contract price is fixed.
I’m sorry about that. I hope that we can fix that soon.
Not remotely. I have no idea what the underlying will be worth. Nor do you. That’s why I wrote that the futures price is not trying to predict the future spot price. That’s not its job. Its job is to prevent an arbitrage opportunity.
I agree: it makes no sense. And I agree: the spot price does not converge to a three-month-old contract price.
You will.
Suppose that on 12/23/16 you entered into a 3-month futures contract to purchase 10,000 shares of GOOG. The spot price at closing was $789.91. Let’s assume that the risk-free rate was 2%, and has remained the same since. In that case, the contract price would have been $789.91(1.02)3/12 = $793.83. Nobody honestly expected that GOOG would be selling at $793.83/share on 3/23/17, but that’s not the point of the futures price; it’s designed to prevent arbitrage. Note that the difference between the futures price and the spot price would have been $793.83 − $789.91 = $3.92.
Fast forward to 1/23/17. GOOG is selling at $819.31. The price of a futures contract expiring on 3/23/17 is $819.31(1.02)2/12 = $822.02. If you had entered into a 2-month futures contract to sell 10,000 shares of GOOG you would have effectively closed out your position. Your profit would have been $822.02 − $793.83 = $28.19/share, or $281,900. Note that the difference between the futures price and the spot price would have been $822.02 − $819.31 = $2.71.
Fast forward to 2/23/17. GOOG is selling at $831.33. The price of a futures contract expiring on 3/23/17 is $831.33(1.02)1/12 = $832.70. If you had entered into a 1-month futures contract to sell 10,000 shares of GOOG you would have effectively closed out your position. Your profit would have been $832.70 − $793.83 = $38.87/share, or $388,700. Note that the difference between the futures price and the spot price would have been $832.70 − $831.33 = $1.37.
Fast forward to 3/22/17. GOOG is selling at $830.07. The price of a futures contract expiring on 3/23/17 is $830.07(1.02)1/365 = $830.12. If you had entered into a 1-day futures contract to sell 10,000 shares of GOOG you would have effectively closed out your position. Your profit would have been $830.11 − $793.83 = $36.28/share, or $362,800. Note that the difference between the futures price and the spot price would have been $830.12 − $830.07 = $0.05.
The futures price is converging to the spot price.
That explanation makes perfect sense.
The futures price converges to the spot price for contracts that are closer to expiration. Intuitively, this is essentially due to less compounding happening from the spot price, S0, to the futures price, S0(1+RF)^T.
If there was more compounding, there will be a a larger gap between S0 and F0(T).
Does my intuition make sense?
Thanks so much, once again!
You got it.
You’re quite welcome.