I understand the difference in concepts for covered and noncovered interest parity. One is used for forward rate while another is for expected future spot rate. However, I’m not quite follow the difference in formulars
F=S0*(1+RA*T/360)/(1+RB*T/360)
E(St)=S0*[(1+RA)/(1+RB)]^t
To me, covered interest rate should be
F=S0*[(1+RA)/(1+RB)]^t
May I know why the formulars are formatted differently? And this applies to valuation of FRA as well.
Can you lock in the forward rate? Yes, therefore you can lock in all the components of covered interest rate parity and it is an arbitrage relation.
Can you lock in the future spot rate? no, thats why its EXPECTED. It is not bound by arbitrage.
If future spot = forward rate I.E if the forward rate is an unbiased estimator of the future spot rate then they are the same thing.
The formula you have for covered interest rate parity uses nominal interest rates, while the formula for uncovered interest rate parity uses effective interest rates.
If you use the same type of rate for each, the formulae will be the same.
(Remember, LIBOR is nominal, not effective.)
I understand the difference between future spot rate and forward. My question is on the formular side, why they’re discounted differently
Can you please double check on this? The example I found on Scheweser. Book 1. pg 274. actually uses nominal in uncovered parity.
I don’t have to double check anything; the formulae you wrote showed nominal interest rates for covered interest rate parity and effective interest rates for uncovered interest rate parity. I’m not saying whether either is right or wrong; I’m merely telling you the differences in what you wrote.
In practice (and on the exam), you’ll use whatever sort of interest rates they give you.
at the least, my take is that in CIRP since there is a market for forward rates it can be calculated based on what market gives you (thats why it is possible to use libor or some rate calculation)… Uncovered on the other hand is based on Relative Purchase Parity and Fisher, and with E(S) there is no market for it (cannot be arbitraged). They do not hold for the short term, and their calculations are theoretical hence LIBOR rates won’t be used. Notice how any calculations about Uncovered starts with if this or that holds… when rates are used it is always in conjunction with inflation or real rates…
Magician is right … the questions will only tell you so much, so use whatever they supply.
What’s the difference between nominal and effective? when I hear nominal, I think it includes inflation whereas effective is like a current yield on a bond…
Nominal means that it doesn’t take compounding into account; effective means that it does.
A 6% nominal rate, compounded monthly, means that you get 6% ÷ 12 = 0.5% per month, or [(1 + 0.5%)^12] – 1 = 6.1678% per year; teh 6.1678% rate is an effective rate.
A 6% effective rate, compounded monthly, means that you get [(1 + 6%)^(1/12)] – 1 = 0.4868% per month or 0.4868% × 12 = 5.8511% per year, nominal.
As for inflation, you’re thinking of nominal vs. real.