Very tough language given in the solution to a problem relating to carry trade in core. These were the 3 statements asking us to identify which statement is correct.

Carry trades may or may not involve a maturity mismatch.

Carry trades require two yield curves with substantially different slopes.

Inter-market carry trades just break even if both yield curves move to the forward

rates.

This answer was edited.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 mismatchThe 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.

– There would be breakeven in the case of Intermarket carry trade, without maturity mismatch if spot exchange rate emerges as per forward rate.Conclusion for the purpose of the questionCase 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