Hello all,

Can someone please help me with conceptually understanding why a “positive (negative) roll yield will reduce (increase) hedging cost compared to the initial spot price.”

Thank you.

Hello all,

Can someone please help me with conceptually understanding why a “positive (negative) roll yield will reduce (increase) hedging cost compared to the initial spot price.”

Thank you.

Isn’t it an extra income received and thus decreasing money duration gap (reducing amount of hedging need) ?!

I suspect this is not so for every type of yield curve. In inverted YC roll down return should be negative as short end rates are higher than lond end rates and bonds thus yields increase (prices decrease) approaching maturity => negative contribution to Rolling Yield.

Where can I find the presented statement ?

Hi Romero,

Not sure I fully follow your rationale. It seems like you are referring to rolling yield in terms of roll down return (fixed income concept); although I might have misread that. The rolling yield I am referring is at the end of the CME book; i’ll try to get the exact source after work.

Yes, I am referring to Fixed Income part of CFAI curriculum.

Rolling Yield = Yield Income + Rolldown yield

Yield Income = Coupon/Current bond price

Roll down yield = Price1/Price0 - 1

Rolling Yield is a part of total return. But I have never met direct mentioning that positive roll yield reduces hedging cost. It is only my suggestion.

Sorry, my missing, the concept of Roll Yield is very well described in Currency management part. I will check it tomorrow if nobody answers your question until then.

Whether roll yield is positive or negative will depend on:

- whether the foreign currency is trading at forward discount/premium and
- whether hedging is through buying or selling the base currency.

I will give two cases for comparison:

You are a **US-based fund manager**, and your funds hold **UK gilts** (government bonds), which you means you have a **long position in GBP**. Now you want to hedge the GBP against USD (with the spot rate at USD/GBP 1.28 or GBP 1 = USD 1.28). To HEDGE your FX risk, you will need to **short GBP** (base currency) **forward**.

If the base currency (GBP in my example) is trading at a forward discount, then F < S. To hedge, you will short GBP futures (at a lower price) and then long GBP futures nearer to contract expiration (at a higher price), i.e. loss on the futures contract => resulting in a negative roll yield.

So lets assume the 3-month Futures Price is USD/GBP 1.20. You short (sell) GBP futures at 1.20 for 3 months. As the contract is close to maturity, the futures price will approach the spot price 1.28 and you proceed to close the contract by buying GBP at 1.28 => there will be a **loss** on the futures contract (since you sell GBP low and buy GBP high in your hedge), which implies negative roll yield, so this will **increase your hedging cost**.

If GBP was trading at a forward premium (e.g. 3-mth USD/GBP 1.35), then the fund manager would sell GBP futures at 1.35 and then later buy GBP back at 1.28 spot to gain (positive roll yield) => this would reduce your hedging cost.

Now let’s turn the story to another fund manager.

You are a **UK-based fund manager**, and your funds hold **US Treasuries** (government bonds), which you means you have a **long position in USD**. Now you want to hedge the USD against GBP (with the spot rate at USD/GBP 1.28). To HEDGE your FX risk, you will need to **short USD** (term currency) **forward**.

If the base currency (GBP in my example) is trading at a forward discount, then F < S. Or you can say USD is trading at a forward premium.

So lets assume the 3-month Futures Price is USD/GBP 1.20. You short/sell USD futures at 1.20 for 3 months. In base currency terms, you are now buying GBP. As the contract is close to maturity, the futures price will approach the spot price 1.28 and you proceed to close the contract by buying USD (selling GBP) at 1.28 => there will be a **gain** on the futures contract (since you buy GBP low and sold GBP high in your hedge), which implies a positive roll yield, so this will **reduce your hedging cost**.

If GBP was trading at a forward premium (e.g. 3-mth USD/GBP 1.35), then the fund manager would buy GBP futures at 1.35 and then later sell GBP back at 1.28 spot => loss on futures contract (negative roll yield) => this would increase your hedging cost.

It’s a bit long, but hope you get the story.

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Thank you fino_abama,

It is pleasure to read you !

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Thanks for the detailed answer. The way I had tried to learn it was:

Long position:

if F>S -> Negative roll yield -> increased hedging cost

if F<S -> Positive roll yield -> reduced hedging cost

If you are trying to hedge your currency and take a short position, like in the examples above; reverse all the signs:

if F>S -> Positive roll yield -> reduced hedging cost

if F<S -> Negative roll yield -> increased hedging cost

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