Roll Yield Calculation

CFA Level III Fixed Income
#1

Hi,

Can someone please explain me the last step in Example 8: Roll yield and interest rate, p. 190 Schweser Notes? They calculate the % roll yield with the following formula: % forward premium / discount = % roll yield = (1.00)(1.028 / 1.036)0.5 - 1 = -0.387%.

I(price) = 2.8%, I(base) = 3.6%.

No idea why they suddenly use ()0.5 and get to this result.

Thanks,

Marion

#2

Can you elaborate a bit. PL. state the problem in whole.

#3

“A USD-based investor has exposure to the ZAR. The USD interest rate is 2.8% and the ZAR interest rate is 3.6%. Determine the roll yield for the investor if he hedges his ZAR exposure with a six month forward”.

Aahh now I understand why they use the ()0.5… But I still don’t understand their calculation. I thought that the roll yield was: (F - S) / S.

Thanks.

#4

Covered interest rate

#5

I haven’t looked through the entire 2019 CFA curriculum, but I can tell you that in the 2017 curriculum there were at least four definitions of roll yield, in various readings at various levels:

  • There was a commodities reading at Level I that defined roll yield as the difference between the spot price and a futures price, or the difference between two futures prices with different expirations.
  • There was a commodities reading at Level II that defined roll return by comparing the prices of two futures contracts: the near-term futures price minus the farther-term futures price. It further divided this difference by the near-term futures price to get the roll return as a percentage.
  • There was a currency management reading at Level III that defined roll yield as the (absolute value of) the difference between the spot price and a futures price, that difference being divided by the spot price to get the roll return as a percentage.
  • There was a commodities reading at Level III that defined roll yield as the difference between the forward premium on the new contract and the forward premium on the old contract when the old contract expires and is rolled over to the new contract.

Only the last one is a correct definition of roll yield.

#6

Price/Base= $/€. This means for every base currency.

Fwd. Quote = S ( 1+int. Rate in Price Currency/ 1+ int. Rate in Base Currency)0.5-1

RY=(F-S)/S

Substitute F with S as in the above eqn. The S in numerator and in denominator will cancel out, leaving you with what has been given in the text

#7

Why are you subtracting 1?

#8

Sorry Bill. My bad.

F = s(1+I’d)/(1+if) 0.5

BTW, most humbly your take on the RY is a little more confusing. I know situation is no better at the CFAI but I firmly believe it is /F-St//S0.

I don’t want any other defn. PL. Correct my understanding .

#9

Hense why I said “covered interest rate” .

Gotta make the poster think a little :slight_smile: