Can someone please provide a comprehensive solution to Question 47-52, i.e. the Item set on Susan Winslow of CFA Level 3 Candidate Resources: Fixed Income Portfolio Management (2)? Having some real issues with solving the same. I’m providing the link of the page :
The solution to Question 47:
It is always unfortunate that even the best of practitioners or authors do not make the best teachers. The language written in the reading as well as the language written above is opaque. To ensure that, you understand it 100%, I will have to carry out numerical exposition.
Case 1: Intra-Market Carry Trade – There has to be a maturity mismatch
The yield Curve of INR is upward sloping.
1 year Spot rate = 6%
10 year Spot rate = 7%
Hence, 9 year forward rate after 1 year = (((1.07)^10/(1.06))^(1/9))-1 = 7.112% approx.
Imagine a 1 year and 10-year ZCB of FV 1000 each.
Price of 1-year ZCB = 1000/1.06=943.40 approx
Price of 10 year ZCB = 1000/(1.07)^10=508.35
We short 1-year ZCB and Invest in 10-year ZCB. Of course, to make figures compatible, we assume fractional securities are allowed and hence, invest in 943.4/508.35 =1.85581 number of 10-year ZCBs such that Net Cashflow is 0, to begin with. Hope you are understanding that we are borrowing at a 1-year interest rate of 6% and investing the same amount at the 10-year interest rate of 7%.
Scenario 1: Pure Expectation Theory (PET) holds good. This means Spot rates evolve as per the Forward Rate.
So, 9-year spot rate after 1 year = 7.112%
Outflow after 1 year on account of 1-year bond that was shorted = 1000
The Price of the 10-year bond after 1 year = 1000/(1.07112)^9 = 538.84
Hence, Sale Proceeds of 1.85581 number of 10-year bonds = 1.85581*538.84= 1000
Hence, this is a complete Breakeven situation.
Conclusion – In the case of Intra-Market Carry Trade ( Which is obviously Maturity Mismatched), there will be breakeven ( which means no profit no loss), if spot rates evolve as per the forward rates.
Note: This was done in CFA Level 2 Fixed Income: First Chapter.
Case 2: Inter-Market Carry Trade ( No maturity Mismatch)
1 year USD Interest Rate = 1%.
1 year INR Interset Rate = 6%.
Spot Rate right now (S0) = Rs.70/$
Hence, as per Covered IRP –
1-year Forward Rate = 70*(1.06/1.01) = 73.46535
Inter Market Carry Trade ( with no maturity mismatch ) is a bet against Covered IRP. In other words, we believe that the Spot Exchange Rate after 1 year ( S1) will not be equal to the Forward Rate.
However, if Spot Exchange rate after 1 year happens to be equal to forward rate, there will be no arbitrage as shown below.
Step 1 – Borrow $1000 at 1% per annum for 1 year. So, Outflow after 1 year = 1010.
Step 2 – Sell $1000 Spot at 70 to get Rs.70000.
Step 3 – Invest Rs. 70000 at 6% per annum for 1 year, getting 70000*(1.06) = 74,200.
Step 4 – Sell Rs. 74,200 after 1 year at the then Spot Rate assumed to be 73.46535 above. Hence, we get, 74,200/73.46535 = $1010. So, there is no arbitrage.
Conclusion for the purpose of the question – There would be breakeven in the case of Intermarket carry trade, without maturity mismatch if spot exchange rate emerges as per forward rate.
Case 3: Inter-Market Carry Trade ( No maturity Mismatch)
1 year USD Interest Rate = 1%.
1 year INR Interset Rate = 6%.
10 year INR Interest Rate = 7%.
Hence, 9-year forward rate after 1 year =7.112%
Spot Rate right now (S0) = Rs.70/$
Hence, as per Covered IRP –
1-year Forward Rate = 70*(1.06/1.01) =73.46535
Inter Market Carry Trade ( with maturity mismatch ) is a bet against Covered IRP and PET. In other words, we believe that the Spot Exchange Rate after 1 year ( S1) will not be equal to the Forward Rate of 73.46535 and we further believe that the 9-year interest rate after 1 year will not be equal to the 9-year forward rate of 7.112%
Since we want to show breakeven, we will assume that after 1 year –
S1(Exchange Rate) = Forward Rate = 73.46535
9-year spot interest rate, after 1 year = Current Forward Rate = 7.112%
Step 1 – Short sell 1 year USD ZCB at a price = 1000/1.01 = $990.099. Hence, Outflow after 1 year = $1000.
Step 2 – Sell $ 990.099 Spot at 70 to get Rs 69306.93
Step 3 – Invest Rs 69306.93 to buy a number of 10-year Rupee ZCB’s.
Price of 10 year Rupee ZCB today = 1000/(1.07)^10 = Rs 508.35
Therefore, the number of Rupee ZCB purchased today = 69306.93/508.35=136.33703 number of bonds.
Step 4 – Price of the 10-year Rupee ZCB after 1 year = 1000/(1.07112)^9 =
Rs 538.84
Hence, Sale Proceeds =136.33703*538.84=Rs 73463.34
Step 5 – Sell Rs 73463.34 after 1 year at the then Spot Rate i.e. S1 = 73.46535 to get $1000.
This is the same as the Dollar outflow of 1000 in Step 1.So break even.
Conclusion for the purpose of the question – There would be breakeven in the case of Intermarket carry trade, with maturity mismatch if –
Condition 1: Spot Interest Rates in the Future evolves as per the Forward Rate, i.e. PET holds good in the Money Market.
Condition 2: Uncovered IRP Holds Good, i.e. Spot Exchange Rate, later on, is equal to the forward Exchange Rate today, which means PET holds good in the currency market.
Now, let us revisit the 3 statements :
Statement 1 – Carry trades may or may not involve a maturity mismatch. : This is true as shown above in the 3 cases.
Statement 2 – Carry trades require two yield curves with substantially different slopes: This is False, as intra-market carry trade will have only one yield curve as in case 1. Even when 2 yield curves are there like Case 2 and Case 3, the slope of the yield curve is irrelevant for the purpose of evaluating the possibility of breakeven.
Statement 3 – Inter-market carry trades just break even if both yield curves move to the forward: This is not true, because, there are 2 conditions to ensure breakeven as detailed in Case 3 above rates
The solution to Question 48:
Statement IV: Inter-market trades should be assessed based on currency-hedged returns. This statement is correct
Let us take an example to understand the same better.
Say interest rate on USD (Home Currency) is 2%, on INR is 6% and on BRL is 8%. Now, for an Inter Market trade, we need to borrow in one currency and invest in the other. Therefore, USD is the funding currency and say INR is the investing currency. So, we borrow in USD at 2% and invest in Indian Markets at 6%, the investing currency INR needs to be Forward Sold (hedged), to bring it into USD terms, to determine the return earned through the trade. ( We need to check the return earned on a Covered basis) Same steps to be followed in case of BRL being the investing currency. Hence, statement IV is correct.
Statement V: Anticipated changes in yield spreads are the primary driver of inter-market trades. This statement is correct.
Taking the same example above, let’s suppose we are entering into an inter-market trade, by shorting a ZCB at 2% (USD), and investing the proceeds in Brazil (buying a ZCB) at 8%. Now currently we are standing at an interest rate differential (Yield spread) of 6%. Our return will consist of 3 parts – 1)Net Coupons from the bond ( if these are coupon bearing bonds and not ZCBs), 2) The Price change on both the bonds which is in turn a function of the change in Yield spread and 3) Change in currency exchange rate.(which is not the focus of this statement) Now, considering the short-trading horizon of active carry trade strategies, the Coupons components are near negligible ( if these are ZCBs, there is no coupon component). Hence, the only component that we are betting on is the Price change or the interest rate differential. Here in the example, we expect the spread to narrow ( say 4%; the USD interest rate increased to 3% and the BRL interest rate decreased to 6%). The same will result in a profitable position. Hence, to conclude, Anticipated changes in yield spreads are the primary driver of inter-market trades. Therefore, statement V is correct.
Statement VI: Whether a bond offers a relatively attractive return depends on both the portfolio’s base currency and the currency in which the bond is denominated. This statement is INCORRECT.
Due to Covered Interest Arbitrage, the relative attractiveness of bonds does not depend on the currency into which they are hedged for comparison. Hence, the ranking of bonds does not depend on the base currency of the portfolio
The solution to Question 49:
It’s already given that the Carry Trade will be via “Extending Duration”, which in turn means that we will borrow for 6 months and Invest for 5 Years.
Option 1 – We can go for Intra Market Carry Trade in the US, in which we are borrowing 6 months at 1.4%, and investing at 1.95%, earning 0.55%/2 ( Semi-annual Payments), i.e. 0.275% . There is no currency effect, because, it’s intra-market.
Option 2 – We can borrow USD 6 month at 1.4%, Invest at 5 year GBP at 1.1%, therefore, losing 0.3%/2, that is 0.15%. However, since, USD is going to depreciate by 1% against Euro and the Exchange rate between Pound and Euro will remain constant, the same implies that USD will also depreciate against Pound by 1%. Hence, there is a currency gain of 1%, which offsets the 0.15% loss. Hence, the Net Gain is 0.85% – Better than Option 1 ( 0.275%)
Option 3 – We can borrow 6 month Euro at 0.15% and invest in 5 year USD at 1.95%, earning 1.8%/2 = 0.9%. However, since, USD is going to depreciate by 1%, we lose 1% in Currency, such that our net return is only -0.1% as compared to 0.9% given in option C.
Therefore we choose Option 2 ( Option B) as it gives the highest return.
Thank you so much. The explanation was really comprehensive. Please share the solution of 50, 51, and 52 as well. It’ll be a big help