Mini Chapter Six
Carry on an Investment
Probably one of the most overused terms in financial markets across asset classes is carry and roll, often used interchangeably. Letâ€™s tackle each of them separately but before that – in simple terms one can look at the carry + roll (expressed in basis points) as the change in Present Value of an investment/portfolio due to the ageing of that investment/portfolio of trades while assuming no change in the underlying market conditions (i.e. no change in yield curve). Carry here refers to the net accrual on an investment (adjusted for its funding cost), while roll is the capital appreciation/depreciation due to the change in yield as the investment ages.Â
Letâ€™s address them with different examples here:
 For cash instruments, one day carry would be the daily accrual adjusted for the funding cost, while a one day roll is the change in the yield / YTM of the investment with the passing of a day given no change in the shape of the yield curve.
 For a fixedfloat IRS, one day carry would be the daily net accrual implied by the difference between the fixed rate and the current floating rate, while one day roll would be the change in the PV of the swap with the passing of a day.
 For example a 5y KRW IRS at 4% vs a floating rate at 3.5% has 50bps of annualised positive carry for a receiver of the fixed rate. The roll for a day would be the PV of the yield differential between a 5y and a 4y 364 day IRS.Â Â
 Extending the above definition, carry plus roll can also be computed as the difference between the zero PV/zero arbitrage/breakeven forward rate and its underlying spot rate

 For eg. Assume that current 1y Korea IRS is at 3.65% and current 3m CD fixing is at 3.50% then 3m forward 9m IRS priced off the current yield curve is at 3.70% breakeven {calculated as $(\mathrm{3.65}\text{\hspace{0.17em}}\u2013\text{\hspace{0.17em}}\mathrm{3.50}\text{\hspace{0.17em}}\times \text{\hspace{0.17em}}\mathrm{0.25})\text{\hspace{0.17em}}\times \text{\hspace{0.17em}}\frac{4}{3}$ }. Further also assume the current 9m IRS is 3.58%.Â
 For a received position then, carry = 3.65%Â –Â 3.50% = 15 bps annualised (with quarterly payments or 3.75bps absolute for 3 months) and rolldown = 7bps absolute (3.65% – 3.58%) for 3 months on a 9 mnth tenor or 5.25bps absolute for 3 months on a 1yr tenor.
 Therefore, Total carry + rolldown over a 3m periodÂ = 3.70% – 3.58% = 12 bps for 9 months or 9bps in 12 months
 Notice from the example above, carry + rolldown of a spot 1y IRS for 3 months is equal to the 3 month rolldown for a 3 month forward 9 month IRS dealt today.
 Alternatively, the forward breakeven rate (3.70) minus the current spot rate (3.65) would be the absolute carry for a 9 month tenor which is the same as 3.75bp for a 1 year tenor. And the 3 month roll would be 1y spot level (3.65) minus the current level of the rolled down tenor (3.58), equal to 7bps for 9 months. That ties up with carry + roll of 12bps for 9 months or 9bps for 12 months.
 With most yield curves being inverted (negative slope) for most part of 2023, carry is negative on a received position as the forward breakevens are below the current spot. In the same vein steep yield curves (positive slope) would be positive carry on a received position.
 Sign of the roll would be the same as the sign of the carry for continuously positive and negative yield curve.
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Graph 1 & 2 – Carry & Roll Graph
Source: Pandemonium.
 What’s a positive carry position for a receiver is negative carry for a payer and the same would hold true for the roll also.
 Carry on FX trades – can be understood in exactly the same manner as for interest rates above, the only difference being the comparison of FX swap tenors on a common unit of time. Letâ€™s take the example of two different currencies – one that trades at a discount to spot (negative points for TWD or an appreciation bias) and the other that trades at a premium (positive points for INR or a depreciation bias).
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Tenors  TWD Forward points  TWD Forward Points Per Month (pips)  INR Forward points  INR Forward Points Per Month (pips) 

Spot  30.7  82.8  
1m  100  100  10.5  10.5 
3m  321  107  32.5  10.8 
6m  653  109  68.5  11.5 
12m  1260  105  162  15.5 
2y  2250  94  393  16.4 
Source: Pandemonium.
Carry like for interest rate swaps can be defined as the daily points accrual vs the funding. For FX deliverable markets the daily funding would normally be denoted by the Tom/Spot FX swaps but those do not exist in the for nondeliverable FX markets. So we typically end up using the 1m (or the most liquid front end tenor) points as proxy for the funding leg; as such we use the monthly carry as a proxy for daily carry.
From the above table note that receiving INR 2y points at 16.375 pips per month and funding it by paying the short end say 3m at 10.8 pips per month would imply a carry of INR 5.575 pips per month if the curve remains unchanged. As for the rolldown just like for interest rate swaps – the 6mfwd6m points in INR are at 93.5pips (162 – 68.5 = 93.5) vs 6m points only at 68.5 implies a 6m roll down of 25 pips or 4.167 pips per month (thatâ€™s again assuming no change to the curve).
For assessing the richness/cheapness of the points curve, one needs to be careful to not rely too much on just points per month as the interest rate curve steepness / flatness at the very front end and relative funding on local vs foreign currency plays a big part too upon adjustments for interest rate parity/other (changing) demand vs supply dynamics.