# Question: Converting annualised rate to period rate

Hi all I have a simple, yet confusing to me, question regarding the conversion of an annualised rate into a period rate (e.g. into a 90-day rate). I am reviewing the example on pages 102 and 103 of Schweser book 5. The example gives the annualised 90-day LIBOR rate as 0.030. If we want to discount \$1 (paid in 90 days) back to the present value using the 90-day LIBOR we need to convert the 0.030 (annualised) into a period rate. Now I see two methods of doing that: 1. period rate = 0.030 x (90/360) = 0.0075 2. period rate = (1 + 0.030)^(90/360) – 1 = 0.0074 Of course to get the PV of \$1 paid in 90 days we simply calculate \$1/(1 + period rate) But my question is, in which scenarios do you use method 1 and which do you use method 2? Thanks in advance

It seems like Schweser pioneered that 2nd method. Personally, I stick to the first method since it is more intuitive for me. Either way you should be fine.

The two methods do result in a very small difference in the period rate (0.0075 and 0.0074 in the examples above). But when this is applied to a large notional amount then the difference could easily be in the hundreds of dollars. Enough to result in a wrond answer on the exam. I think, but am not 100% sure, that I’ve seen both methods used in the Schweser text.

^^^

By definition, Annualized yield is a compounded HPY yield. So, second method would be most appropriate. Infact, among mostly used yields (HPY, MMY and BEY), Annualized yield is the only yield which is compounded. So, to get back to period yield from its annualized yield, best would be to reverse compound it. Edit: if we are given MMY and from there we are asked to calculate Period yield (HPY), then using method 1 would be most appropriate.

i have a question that’s related to the period rate conversion, which is used in the covered interest rate parity relationship: E.G., SPY/EUR=59.50864, risk-free interest rate in France is 5.6%, and 6% in Syria. What must the 270-day forward rate of SPY/EUR be to make arbitrage impossible? Answer to the question: F(SPY/EUR) = S(SPY/EUR) * ((1+r SPY)^(270/360) / (1+r EUR)^(270/360)) = 59.67762 Why are we not using (1+r SPY * 270/360) / (1+r EUR* 270/360) in this case? I just want to know what kind of conversion we should use to convert annualized rate into period rate in the exam. Thank you!

Both Methods Have Very Specific Uses! The answer to all these questions comes from the question you should be asking yourself; Is the interest rate compounding, or simple interest? LIBOR is an add on, Simple interest rate so we multiply by time period Currency contracts are valued using Domestic and Foreign Risk Free Rates, which are compounding rates. i.e. we use the expession with the time period as a power Example: LIBOR/Simple Interest/Add on=1.05 x 180/360 Compounding/Risk Free/Equity Benchmark Index Returns=1.05^180/365 b/c these are compounding rates! PAY ATTENTION TO THE TYPE OF INTEREST RATE USED IN THE QUESTION

Thanks, it’s very helpful! So - if the question says “risk-free interest rate” we should prob think about compounding interest rates, if it’s “annualized 9-month interest rate” we should prob think about simple interest rates? Actually I’ve seen both in the currency contracts type of questions, but CFAI book tends to use the simple interest rate one more. Anyone can verify this? Investor83 Wrote: ------------------------------------------------------- > Both Methods Have Very Specific Uses! > > The answer to all these questions comes from the > question you should be asking yourself; > > Is the interest rate compounding, or simple > interest? > > LIBOR is an add on, Simple interest rate so we > multiply by time period > > Currency contracts are valued using Domestic and > Foreign Risk Free Rates, which are compounding > rates. i.e. we use the expession with the time > period as a power > > Example: > > LIBOR/Simple Interest/Add on=1.05 x 180/360 > Compounding/Risk Free/Equity Benchmark Index > Returns=1.05^180/365 b/c these are compounding > rates! > > PAY ATTENTION TO THE TYPE OF INTEREST RATE USED IN > THE QUESTION

No problem Skies. I like to think more in terms of the actual return benchmark being used in the problem instead of looking for question key words. For Example; If I see LIBOR is the ref. rate, then I know that the LIBOR is a simple, add on rate and therefore use the multiplication format of the expression. If I see that we are looking at Treasury Rates, then I know that it is a compounding, risk free rate. Simple, non-compounding rates are the expception rather than the rule. The only that I can think of off the top of my head would be the LIBOR and Bank Deposit CD rate (remember the LIBOR is pretty much a short-term CD rate in London applied to US Dollars anyway, so this is intuitive). Compounding rates are pretty much every other investment rate out there, there fore for those we use the ^T notation. Remember that Add on Rates=LIBOR, Bank CD Compund Rates=Risk Free Ref Rates If we discount by the LIBOR, then we multiply in the denominator. If we discount by a risk free rate, then we go to the ^T in the denominator.

Investor83 Wrote: ------------------------------------------------------- > Both Methods Have Very Specific Uses! > > The answer to all these questions comes from the > question you should be asking yourself; > > Is the interest rate compounding, or simple > interest? > > LIBOR is an add on, Simple interest rate so we > multiply by time period > > Currency contracts are valued using Domestic and > Foreign Risk Free Rates, which are compounding > rates. i.e. we use the expession with the time > period as a power > > Example: > > LIBOR/Simple Interest/Add on=1.05 x 180/360 > Compounding/Risk Free/Equity Benchmark Index > Returns=1.05^180/365 b/c these are compounding > rates! > > PAY ATTENTION TO THE TYPE OF INTEREST RATE USED IN > THE QUESTION This messed me up big time in L1 until I just memorized when you use simple add on vs compound. So far to me it looks like all of the FX uses the 1.05 X 180/350. In L1 derivatives I constantly screwed up the FRA payoff by using the compounded.

Calculating expected future FX rates from interest rate parity and calculating a forward premium or discount implied on a currency we multiply. But to value currency forward contracts, we use a compounding risk free rate.