Forward premium

Hey guys, Taking the second schweser practice exam and had a question. If a currency is selling at a premium, that currency is expected to weaken, correct?

“Currency selling at a premium” is a confusing expression. Currency Forward selling at a premium makes more sense.

Given latter expression , I would say yes , it is expected by the market to depreciate . the forwward premium ( F/S0)/S0 would indicate a premium if the forward is larger , which means future exchange rates are higher . That means the currency is going to depreciate relative to domestic currency.

“Currency selling at forward premium” means that this (let us say foreign) currency is more expensive (in units of domestic currency) on forward than on spot. Such is the case when the domestic interest rate is greater than the foreign one. If you consider a forward price an indicator of market expectations (which is wrong in general) then this currency is expected to apprecciate.

Okay so here is the question. It’s a statement “Interest rate parity depends on covered interest arbitrage which works as follows. Suppose the 1 -year U.K. interest rate is 5.5%, the 1-year Japanese interest rate is 2.3%; the Japanese yen is at a one-year forward premium of 4.1%, and transactions costs are minimal. In this case, the international trader should borrow yen, invest in point denominated bonds, and use a yen-pound forward contact to pay back the yen loan.”

The guy is incorrect. Here is the answer "Although interest rate parity depends on covered interest arbitrage, Tyler is incorrect because if the U.K. rate is 5.5%, the Japanese rate 2.3%, and the Japanese yen is at a forward premium of 4.1%, then the investor should borrow pounds at 5.5%, invest in Japan, and convert back to pounds in one year earning the yen forward premium. The return in Japan would be 2.3% + 4.1% = 6.4%, inclusive of the forward premium. The risk free, covered interest arbitrage profit would be 6.4% - 5.5% = 0.9%, before transaction costs.

This doesn’t make sense to me. If the yen is selling at a premium, if you invest in Japanese bonds, you’re going to get the 2.3% rate but the yen should depreciate in value by the forward premium of 4.1%, correct?

Sounds like a LII question. Covered interest rate arbitrage:

At equilibrium, forward differential = r_DC - r_FC, or

forward differenrtial + r_FC = r_DC,

where FC is Japanese YEN, while DC is UK pound. But since

forward differential + r_FC = 4.1% + 2.3% = 6.4% is larger than r_DC = 5.5%.

(Not sure if 6.4% is called “covered interest rate”? Please correct me.)

Then the arbitrager will borrow at UK pound at more “favorite” rate, invest in assets denominated in Japanese, , enter a forward contract to deliver Japanese YEN,…lock in a profit 6.4% - 5.5% = 0.9%.

Thanks for the explanation but it didn’t help at all lol. Can you explain it tangibly instead of using a bunch of equations?

You’e an investor, you invest in Japenese bonds, earn 2.3%. The Yen is going to weaken at a rate of 4.1%. It’s saying the Yen strengthens at 4.1%. How is that possible? Forward premium = Foward Rate - Spot / Spot. If the yen’s spot was 100 yen/Euro and now it’s 110 yen/Euro, it’s selling a premium. it weakened. That’s not good.

Shouldn’t you be looking at DC/FC (for the currency convention) for F-S/S to be at a premium and hence not Yen/Euro but Euro/Yen.

Interest rate parity says for the forward to be priced correctly , the forward premium should equal the rate difference. If this is not true, then an aribtrage opportunity exists.( ex-ante )

IRP says the Forward premium should be 5.5-2.3 = 3.2%

The premium is actually 4.1% .

So the premium is more than the IRP says it should be.

When anything is over priced , short it . Then if things revert correctly , you 'll make money ( arb will be realized ).

So short the Fwd Yen/Pound rate i.e. borrow Pounds invest in Yen and go short the Fwd Yen/GBP . Then in 1 year , deliver the appreciated yen receiving GBP which you can pay off the loan and keep 0.9%

Janakisri, you say delieve r the appreciated yen, you mean appreciated yen contract, correct?

Your explanation makes sense. Thank you guys.

when a forward contract on Yen/GBP matures , The Short delivers Yen currency. The long gives the short GBP currency . The contract is then wound up.

So, we all end up the same answer? :slight_smile:

For a question like this, the [in]equation helps me to think, but it could confuse the graders…approximation is involved in the argument: forward differential = interest rate difference…

The arbitrager can make money if YEN appreciates, depreciates or does not change, because the profit does not depend on the spot exchange rate at the expiration of futures’ contract.

This was a helpful exercise. Thanks for all who participated.

why does this remind me of L2…not L3…argh.