Exercise - Conceptual FX Carry Trade

Exercise - Conceptual FX Carry Trade#

1. Currency and Carry#

The problem is based on data in data/fx_data.xlsx.

Use the GBP column of the tab, fx rates, which gives the direct exchange rate between the GBP and USD. (Being a direct quote means the exchange rates are listed as dollars per foreign currency.)

Combine this with the overnight interest rates given in the interest rates tab. As is typical with money-market rates, they are scaled by 360 to annualize. Thus, in the calculations below, be careful to divide them by 360.

1.1#

Using all these, calculate the time-series of returns to investing in the pound (from a US perspective.)

Denote this as \(\rGBP\).

  • Plot the cumulative return series for \(\rGBP\). That is, if the time-series of daily returns is retsGBP, then plot (1+retsGBP).cumprod().plot().

  • For comparison, plot the cumulative return of just investing in the US overnight rate, SOFR.

1.2#

Report the mean of the excess return,

\[\rxGBP \equiv \rGBP - \rUSD\]

which is the return of investing in pounds sterling minus the US SOFR rate. This is giving the excess return earned in the instance that the investor is borrowing with SOFR and investing it in pounds sterling.

  • Annualize the mean excess return, (by multiplying by 360.)

Would this carry trade have been profitable over this period?

1.3#

Was the interest rate differential positive or negative, (on average,) over this time?

If the carry trade was not profitable, describe step-by-step how one could take the opposite (short) side of this carry trade.

1.4#

Calculate the profit of shorting GBP on notional of £1mm GBP.

  • Assume that the notional is rebalanced every day to simplify the calculation. This allows you to simply calculate the excess return timeseries and multiply it by the notional.

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