Can someone please explain why trading a positive roll yield is trading the forward rate bias? I understand the forward rate bias to be that a higher yielding currency appreciates rather than depreciates. So far so good. A positive roll yield is when (f1- f0)- (s1-s0) >0. I.e. the forward premiums are higher. What is the connection to this with interest rates? I am unable to reconcile these 2 concepts together.
The point is to keep the prospective of base currency.
Roll yield is kind of hedge cost and is typically negative. A negative roll yield indicates that the hedger was trading against the forward rate bias by buying a currency at forward premium or selling a currency at a forward discount. Otherwise, is the positive roll yield. The magnitude of the roll yield is given by |(F-S)/S| and the sign depends on whether the investor needs to buy or to sell the base currency forward.
When the hedge involves selling the low-yield currency and buying the high-yield currency in the P/B pair, then it connects to interest rate. For example, the currency P you want to hedge is the low-yielding currency. Then you should buy the currency B which is high-yielding currency. When you roll down this position the spot rate (S p/b) you received is higher than the forward rate (F p/b)you pay due to the forward rate bias. And there is a positive roll yield.
@Okachiang “When you roll down this position the spot rate (S p/b) you received is higher than the forward rate (F p/b)you pay due to the forward rate bias. And there is a positive roll yield.” Isn’t it the opposite? The forward rate should be higher than the spot rate?
You’re right, the forward rate should be higher than the spot rate. I made a mistake. And the what you should pay is spot rate (S p/b) and what you should receive is the forward rate (F p/b) when you hedge this forward position.
The process should be like this.
We have 2 currencies HYC and LYC
HYC = 10% rrates
LYC = 2% rates
Spot HYC/LYC = 100
Fwd HYC/LYC = 108 (I know not exactly right but kept the maths simple for my beneifit)
ABC is at a discount, XYZ at premium
We sssume UCIP does not hold. Spot will stay at 100.
Carry Trade
Borrow LYC Deposit HYC pick up 8% gain
LONG HYC Short LYC
Forwards
Negative roll yiield happens
Long LYC short HYC When it comes at expiry (spot not moved)
At expiry
Fwd Deliver 108 HYC Receive 1 LYC
Spot Sell 1 LYC Receive 100 HYC (or think need 1.08 LYC to cover 108 HYC)
= Loss of 8%
Positive roll yiield happens
Long HYC short LYC When it comes at expiry (spot not moved)
At expiry
Fwd Deliver 1 LYC Receive 108 HYC
Spot Sell 108 HYC Receive 108/100 = 1.08 LYC (or think need 100 HYC to cover 1 LYC)
= Gain of 8%
Carry trade = Long HYC
Fwd rate bias = Long HYC
+ve carry - LONG HYC
@Okachiang - thank you for your explanation. When ft> st there is a positive roll yield and when currency B appreciates rather than depreciates there is a forward trading bias.
I guess this is my confusion. You are describing this as 2 independent events. I read the text as simply saying that selling a forward premium and buying a forward discount is in itself violating uncovered interest rate parity. I was confused why this was.
