Glad that question 47, 48 and 49 was solved comprehensively. Can somebody please provide the solution of the rest?
Hi, because I was limited to 3 replies per topic, I’m providing the solutions for the rest here :
The solution to Question :
In Option A, we are of course enjoying the interest rate differential, however, that differential is getting offset by the Forward Differential, as per Covered IRP, because we are supposed to be Currency Neutral. Hence, there is no scope of any return from both Option A.
The explanation given in the Candidate Resource for Option C is Optimum and I cannot improve upon the same. I would just like to add that –
Synthetic Long Futures ( F+) = Long Spot (S+) and Rf Borrowing.
Synthetic Short Futures( F-) = Short Spot(S-) and Rf Investing.
In light of this, you may interpret the explanation given in the Candidate Resource reproduced below :
This combination of futures positions does create a duration-neutral, currency neutral carry trade, but it is not the highest available carry. Since the T-note futures price reflects the pricing of the 5-year note as cheapest to deliver, the long position in this contract is equivalent to buying the 5-year Treasury and financing it for 6 months. This generates net carry of 0.275% = (1.95% – 1.40%)/2. Similarly, the short position in the German note futures is equivalent to being short the 5-year German note and lending the proceeds for 6 months, generating net carry of –0.225% = (0.15% – 0.60%)/2. The combined carry is 0.05%, half of what is available on the position in B
Let us understand Option B via a diagram. ( Refer to the diagram attached)
The Swap arrangement is Duration Neutral, because, according to the arrangement, we are supposed to receive 3 years GBP interest rate( Swap 1), which is our asset and at the same time, we are supposed to pay 3 Year Interest on Euro ( Swap 2), which is our liability. Hence, there is duration neutrality. Similarly, considering the other legs, we have a liability of 6 month from Swap 1 ( we are supposed to pay 6m Libor on GBP) and at the same time, we have an asset of 6 months from Swap 2 ( we are supposed to receive 6-month Libor on Euro).
The Swap arrangement is Currency Neutral,because, in the arrangement, if we are Long on GBP, via 3-year bond, we are also short on GBP via the 6 month Bond. Same for Euro legs.
The solution to Question 51:
Let’s analyze all the options.
Option B : Buying the Greek 5-year in each of the portfolios, hedging the currency in the GBP-based portfolio, and leaving the currency unhedged in the dollar-based portfolio.
Breaking it down, gives us 3 parts :
Investment in Greece ( with USD as base ; using USD as the funding currency and investing in Greek Bond) :
Yield differential earned on investing in the 5 Year Greek bond, funding with USD 6m Libor : (5.7-1.4)/2 = 2.15%. Since the position is unhedged, gain via appreciation of Euro = 1%. Hence, total gain = (2.15 + 1)% = 3.15%.
Investment in Greece ( with GBP as base ; using GBP as the funding currency and investing in Greek Bond) :
Yield differential earned on investing in the 5 Year Greek bond, funding with GBP 6m Libor : (5.7-0.5)/2 = 2.6%. Since the position is hedged, gain via premium on Euro Forward =(0.5-0.15)% = 0.35% Hence, total gain = (2.6 + 0.35)% = 2.95%.
Investment in Greece ( with Euro as base ; using Euro as the funding currency and investing in Greek Bond) :
Yield differential earned on investing in the 5 Year Greek bond, funding with Euro 6m Libor : (5.7-0.15)/2 = 2.775%. That’s it, since the currency of Greece is Euro only.
Hence, Total Gain = (3.15+2.95+2.775)% = 8.875%.
Option A :Buying the Mexican 5-year in each of the portfolios and hedging it into the base currency of the portfolio.
Since, Mexican yields are expected to decline to 7.0% at all maturities, the price of the Mexican Bonds at the end of the period will be : PMT – 7.25/2 = 3.625, FV – 100, n – 9 ( since we are standing at 0.5th year), i/y – 7/2 = 3.5, CPT PV – 100.95. Hence, Capital Gain = (100.95/100-1) : 0.95%. So, there will be a Capital Gain component while investing in the Mexican bonds whose yields are expected to decline to 7%, as against other Bonds, whose yields are expected to remain unchanged.
Following the same steps as Option B,
Investment in Mexico ( with USD as base ; using USD as the funding currency and investing in 5 Year Mexican Bond) :
Yield differential earned on investing in the 5 Year Mexican bond, funding with USD 6m Libor : (7.25-1.4)/2 = 2.925%. The capital Gain component on the Mexican bond = 0.95%. Since the position is hedged, loss via premium on USD Forward =(7.1-1.4)/2% = 2.85% Hence, total gain = (2.925+0.95 – 2.85)% = 1.025%.
Investment in Mexico ( with GBP as base ; using GBP as the funding currency and investing in 5 Year Mexican Bond) :
Yield differential earned on investing in the 5 Year Mexican bond, funding with GBP 6m Libor : (7.25-0.5)/2 = 3.375%. The capital Gain component on the Mexican bond = 0.95%. Since the position is hedged, loss via premium on GBP Forward =(7.1-0.5)/2% = 3.3% Hence, total gain = (3.375+0.95 – 3.3)% = 1.025%.
Investment in Mexico ( with Euro as base ; using Euro as the funding currency and investing in 5 Year Mexican Bond) :
Yield differential earned on investing in the 5 Year Mexican bond, funding with Euro 6m Libor : (7.25-0.15)/2 = 3.55%. The capital Gain component on the Mexican bond = 0.95%. Since the position is hedged, loss via premium on Euro Forward =(7.1-0.15)/2% = 3.475% Hence, total gain = (3.55+0.95 – 3.475)% = 1.025%.
Hence, Total Gain = (1.025-1.025-1.025)% = 3.075%.
Option C : Buying the Greek 5-year in the Euro-denominated portfolio, buying the Mexican 5-year in the GBP and USD-denominated portfolios, and leaving the currency unhedged in each case.
Similarly, analyzing Option C :
Investment in Greece ( with Euro as base ; using Euro as the funding currency and investing in 5 Year Mexican Bond) : 2.775% ( as calculated above)
Investment in Mexico ( with GBP as base ; using GBP as the funding currency and investing in 5 Year Mexican Bond, keeping the position unhedged.
Yield differential earned on investing in the 5 Year Mexican bond, funding with GBP 6m Libor : (7.25-0.5)/2 = 3.375%. The capital Gain component on the Mexican bond = 0.95%. Since the position is unhedged, loss due Peso depreciating 2% against Euro ( Euro vs GBP remaining constant, hence, a depreciation of 2% against GBP as well), would result in a total gain of (3.375+0.95 – 2)% = 2.325%.
Investment in Mexico ( with USD as base ; using USD as the funding currency and investing in 5 Year Mexican Bond, keeping the position unhedged.
Yield differential earned on investing in the 5 Year Mexican bond, funding with USD 6m Libor : (7.25-1.4)/2 = 2.925%. The capital Gain component on the Mexican bond = 0.95%. Since the position is unhedged, loss due Peso depreciating 1% against USD (Peso will depreciate 2% against Euro and USD will depreciate 1% against Euro), would result in a total gain of (2.925+0.95 – 1)% = 2.875%.
Hence, Total Gain = (2.775+2.325+2.875)% = 7.975%.
Hence, out of all the Options, Option B gives the highest expected return
The solution to Question 52
Let’s analyze all the options.
Option A. Buying the Greek 5-year in each portfolio and hedging it into Pesos.
Breaking it down, we get
Investment in Greece ( with USD as a base; using USD as the funding currency and investing in 5 Year Greek Bond, and hedging via Peso) :
Yield differential earned on investing in the 5 Year Greek bond, funding with USD 6m Libor : (5.7-1.4)/2 = 2.15%. Since the position is hedged, gain via premium on Peso Forward =(7.1-0.15)/2% = 3.475%. Again, we are exposed to Peso, therefore, loss due to Peso depreciation against USD =1% Hence, total gain = (2.15+3.475-1)% = 4.625%.
Investment in Greece ( with the UK as a base; using GBP as the funding currency and investing in 5 Year Greek Bond and hedging via Peso)
Yield differential earned on investing in the 5 Year Greek bond, funding with GBP 6m Libor : (5.7-0.5)/2 = 2.6%. Since the position is hedged, gain via premium on Peso Forward =(7.1-0.15)/2% = 3.475%. Again, we are exposed to Peso, therefore, loss due to Peso depreciation against GBP =2% Hence, total gain = (2.6+3.475-2)% = 4.075%.
Investment in Greece ( with Euro as a base; using GBP as the funding currency and investing in 5 Year Greek Bond and hedging via Peso)
Yield differential earned on investing in the 5 Year Greek bond, funding with Euro 6m Libor : (5.7-0.15)/2 = 2.775%. Since the position is hedged, gain via premium on Peso Forward =(7.1-0.15)/2% = 3.475%. Again, we are exposed to Peso, therefore, loss due to Peso depreciation against Euro =2% Hence, total gain = (2.775+3.475-2)% = 4.25%.
Hence, Total Gain = (4.625+4.075+4.25)% = 12.95%.
Option B: Buying the Greek 5-year in each portfolio and hedging it into USD.
Breaking it down gives us 3 parts :
Investment in Greece ( with USD as a base; using USD as the funding currency and investing in Greek Bond, and hedging via USD) :
Yield differential earned on investing in the 5 Year Greek bond, funding with Euro 6m Libor : (5.7-1.4)/2 = 2.15%.
Investment in Greece ( with GBP as a base; using GBP as the funding currency and investing in Greek Bond and hedging via USD) :
Yield differential earned on investing in the 5 Year Greek bond, funding with GBP 6m Libor : (5.7-0.5)/2 = 2.6%. Since the position is hedged, gain via premium on GBP Forward =(1.4-0.15)/2% = 0.625%. Again, we are exposed to USD, therefore, loss due to USD depreciation against GBP =1% Hence, total gain = (2.6 +0625-1)% = 2.225%.
Investment in Greece ( with Euro as a base; using Euro as the funding currency and investing in Greek Bond) :
Yield differential earned on investing in the 5 Year Greek bond, funding with Euro 6m Libor : (5.7-0.15)/2 = 2.775%. Since the position is hedged, gain via premium on Euro Forward =(1.4-0.15)/2% = 0.625%. Again, we are exposed to USD, therefore, loss due to USD depreciation against Euro =1% Hence, total gain = (2.775 +0625-1)% = 2.4%.
Hence, Total Gain = (2.15+2.225+2.4)% = 6.775 %.
Option C : Buying the Mexican 5-year in each portfolio and not hedging the currency.
.Similarly, analyzing Option C :
Investing in the Mexican bond will generate a Capital Gain Yield of 0.95%
Investment in Mexico ( with USD as a base; using Euro as the funding currency and investing in 5 Year Mexican Bond and leaving positions unhedged): 2.875% ( as calculated above)
Investment in Mexico ( with GBP as a base; using GBP as the funding currency and investing in 5 Year Mexican Bond, keeping the position unhedged.) = 2.325%
Investment in Mexico ( with Euro as a base; using USD as the funding currency and investing in 5 Year Mexican Bond, keeping the position unhedged.
Yield differential earned on investing in the 5 Year Mexican bond, funding with USD 6m Libor : (7.25-0.15)/2 = 3.55 %. The capital Gain component on the Mexican bond = 0.95%. Since the position is unhedged, loss due to Peso depreciating 2% against the Euro would result in a total gain of (3.55+0.95 – 2)% = 2.5%.
Hence, Total Gain = (2.325+2.875+2.5)% = 7.7%.
Hence, out of all the options, Option A gives the highest expected return.
Hi, coming back to the above, maybe I got it wrong but @S2000magician please check as well! —> under question 51 (which is btw question 27 under reading 20 in my book) —> I can see in the above explanation, when HEDGING the transaction to the base currency of the portfolio for GBP, that you mention: yield differential earned = (5.7 - 0.5) / 2 = 2.6% (correct) but then when hedging, you take the 6mo rate (but this is annualized (!) if correct, hence you should take (0.5 - 0.15) / 2 = 0.175 = 0.175% and not 0.35% ! Meaning when hedging the currency, you basically cancel out the ‘possible profit’ of funding in a lower yielding currency.
And if my thought behind ‘hedging into the base currency’ of the portfolio is correct (and again Magician let me know if Im wrong) but then an easier way of calculating this for example with the MXN bond and funding in GBP currency, but hedging in EUR, you can actually take the coupon payment for 6 months from the 5yr Greek Bond (5.7% / 2 = 2.85%) minus the EU as funding currency - 0.15% /2 = 0.075% = total profit —> 2.85 - 0.075 = 2.775 %
Hope this makes sense and is correct ? As Im quite lost otherwise in understanding the hedging of the return into the base currency of the portfolio… been looking at these questions for 1.5hr now… :S