LOS 61c - futures vs. forwards prices? IR correlation

[catfancier]

I can understand why a positive correlation between interest rates and the price of the underlying will cause futures price to be > than the forward price - as the price of the underlying rises the long receives mtm cashflows from the futures contract which can be reinvested at rising interest rates, hence the futures contract is preferred. But, why does a negative correlation mean the opposite? i.e. that the forward price > than the futures price? If the underlying rises in price, the long in the futures still receives mtm cashflows - granted that now they must be reinvested at lower interest rates in the negative correlation scenario. But surely this is still preferable to having nothing to reinvest until settlement date as with the forward contract? why is it not the case in this scenario that the futures price is still greater than the forward price, only less so than when the correlation was positive?
I see the same problem from the short perspective. When the correlation between Interest Rates and the price of the Underlying is positive the shorts prefer forwards as when the underlying rises in price they don’t have to finance the mtm cashflows of a future at rising interest rates. Hence the forward is the preferred contract for the shorts, and the price falls below that of the comparable future. But why when this correlation turns negative do the shorts suddenly prefer the futures? even if their financing costs of the mtm cashflows starts to fall it is still a cost that they would not incur at all were they in a forward contract.
It would seem more logical to me, that when the price of the underlying is rising, the futures price would be greater than the forward price, regardless of the direction of interest rates. As the long can earn some return on their mtm cashflows and hence drive up the futures price, while the short doesn’t want to have to finance these cashflows whatever the interest rate, and so prefers the forward contract, which drives it’s price down. And similarly when the price of the underlying is falling the reverse relation would hold regardless of the direction of interest rates as the long prefers the forward for which it incurs no finance costs, and the short prefers the futures for which it can earn reinvestment returns on it’s mtm cashflows (irrespective of whether these returns are at rising or falling rates).
What am I missing?

 

[swaptiongamma]

>>>But, why does a negative correlation mean the opposite? i.e. that the forward price > than the futures price
Let me try to explain this to you.
So now you know that the interest rates in 2010 are going to go up and at present you have got 2 choices to invest in either a Forward on a Fixed Income Security or a Future on a Fixed Income Security.
Consider Future on a FIS - When interest rates rise, the underlier value falls. Since you have a future, the clearing house will do the MTM after trading hours and deduct money from your margin account, so means you are in need to money (‘deficit’) at the very-exact time when interest rates have gone up (i.e the price to borrow money has gone up.)
now consider the other position
Consider Forward on a FIS - When interest rates rise, the underlier value falls. Since you have a forward, no MTM activity occurs and you are in no need to borrw any money, so you are hardly affected by the interest rates going up.
What would you prefer? - Forward position on a FIS, right? - Thus this demand of Forward dertivatives drives the price of forward contract up.
In 1 line -> IR UP –> FIS DOWN –> MTM CASH DEFECIT –> Need to Borrow at bad times –> noone preferes a future when IR and underlier have negative correlation –> demand of Forward increases and drives the price up –> hence ForwardP > FutureP

 

[catfancier]

Thanks for going through that example swaptiongamma, however i’m afraid i’m still not convinced.
I agree with the idea that in this situation one would prefer to hold the forward. However I would argue that the reason for this is becuase the underlying has fallen in value, and not becuase of the negative correlation. I think this becuase of the following counterexample:
Lets suppose that instead of knowing that interest rates were going to rise, you knew there were going to decline, so that you expected the price of the underlying FIS to rise. In this case you could either (1) go in a long futures contract, where you receive MTM cashflows becuase the price of the underlying had risen. You could reinvest these to earn a return. This return may not be large, since interest rates are falling. But it is still a return which is greater than zero. Or (2) you be be long in the forward contract. You would be sitting on an unrealised gain, but you would have no MTM cashflows. You could not therefore reinvest these, and therefore you have no opportunity to earn reinvestment income until the contract settles. Therefore the total return on the forwards contract would be less, as it does not generate reinvestment income. This must surely make it less attractive, and therefore the price must be lower than the comparable future. This is despite the correlation between the underlying and interest rates being negative.
I have only read this LOS in one of the texts from an external materials supplier, and not direct from CFAI text. I’m going to go away and read the CFAI text in case there are some other factors at play which were not mentioned in other text.

 

[swaptiongamma]

Your view point total makes sense and looks appealing. Now I wonder why Schweser or the CFAI did not consider both perspectives when saying negative correlation drives the forward price up and positive correlation drives the futures price up.

 

[barthezz]

good point catfancier, just wish joey would be here to clarify…

 

[sandmannoir]

The way I rectified it in my head when I read the section was to compare Forwards & futures to zero coupon & coupon bonds. When interest rates drop, a zero coupon bond value will be higher than a coupon bond value due to the lower reinvestment rate of the actual coupon. I’m not saying that’s the exact way to view it, but that’s how I’m trying to keep it straight in my head for exam time.