econ 8: exchange rate calculations

what is a cross rate?

exchange rate between two currencies derived thorugh a third currency

how to calculate CAD/EUR given USD?

CAD/USD * USD/EUR (invert if necessary)

what are market conventions?

• use defined currency pair, not direct/indirect quotes

• most currencies quoted to 4 decimal places

• japanese yen 2 dp

what is triangular arbitrage

• cross rate quotes must be consistent

• else traders can exploit discrepancy for riskless profit

how to work out how much EUR apprecaites agaisnt USD in a year?

(expected spot rate in one year (USD/EUR) / spot rate ) -1

what is the forward rate

exchange rate agreed today that will occur on a future date

what affects forward rate

• spot exchnage rate

• interest rate between the two currencies

what are forward points(pips)?

forward rate - spot rate

• >0 → premuium

• <0 → discount

how to calculate forward rate using forward points?

spot exchange rate + forward exchange rate /10,000

what is the arbitrage relationship formula?

rearrange the forward rate formula

1+r_{d}=S_{f/d}\cdot\frac{\left(1+r_{f}\right)}{F_{f/d}}

or

1+r_{d}=\frac{1}{S_{d/f}}\cdot\left(1+r_{f}\right)F_{d/f} (reciprical)

how to calculate forward rate?

F_{f/d}=S_{f/d}\cdot\left(\frac{1+r_{f}}{1+r_{d}}\right)

S = spot exchange rate

r_f = foreign interest rate

r_d = domestic interest rate

foward rate as a percentage

rearrange arbitrage equation

\frac{F_{f/d}}{S_{f/d}}=\frac{1+r_{f}}{1+r_{d}}

percentage change using interest differential

\frac{S_{t+1}}{S_{t}}-1=\frac{r_{f}-r_{d}}{1+r_{d}}

note here: F_{t}=S_{t+1}

forward rate calculation for fraction of year \tau

F_{f/d}-S_{f/d}=S_{f/d}\cdot\left(\frac{r_{f}-r_{d}}{1+r_{d}\tau}\right)\cdot\tau

note this is out of 360 days not 365