FX Forward Discounts and Premiums

Not likely; it's probably at a forward discount.

Forward exchange rates and differences in interest rates represent expectations of future spot rates. Take any currency pair, where the two currencies have different interest rates. The currency with the higher interest rate will look weaker in the forward rate than it does in the spot rate.

The spot rate is what it is, since investors like to chase high interest rates. But when that's over, the money has to flow back out of that high interest rate currency, causing it to weaken. So high interest rate currencies usually have a forward discount, while low interest rate currencies will trade at a forward premium.

No, this might have been found by considering each forward point as 1/1,000 rather than 1/10,000.

Yes. With each point representing 1/10,000, the 6-month forward rate would be: $$\displaystyle 1.3010 + \frac{-73}{10,000} = 1.2937 $$

No, this would suggest a forward premium, since this rate is bigger than the spot rate.

It's important to note that forward points aren't the same as a percentage discount or premium. For that, you just use what looks like a holding period return calculation. In the case of the 6-month forward discount, it is found as: $$\displaystyle \frac{Spot + Forward~ points}{Spot} - 1 = \frac{1.3010 - 0.0073}{1.3010} - 1 = -0.561 \% $$ If you expect future spot rates to match forward rates, then this percentage change should equal the interest rate differential. So given a domestic interest rate for the GBP, the foreign interest rate for USD should differ by approximately 0.561%. Should the foreign rate be lower or higher by this amount?

No, just the opposite; it should be lower.

Good call!

Excellent!

To summarize: [[summary]]

Since the home (base) currency is trading at a forward discount, it must have the higher interest rate. The foreign currency is therefore trading at a forward premium in this pair, and it should then have a lower interest rate.

Take a spot rate of 1.3010, measuring the domestic currency in terms of a foreign price currency. If this f/d spot rate of 1.3010 has a 12-month forward rate of 1.3082, then the domestic currency has a __forward premium__ in this pair. If the forward rate was below spot, then it would be at a __forward discount__. If you are focused on a currency with a high interest rate, what type of forward rate would you expect?

For example, consider these bank quotes for a spot rate and forward points on the USD/GBP currency pair. | Spot | 1.3010 | |-------|--------| | 1-Mo | -12 | | 3-Mo | -36 | | 6-Mo | -73 | | 12-Mo | -145.7 | These forward points (which are also called "swap points" and "pips") are shown as negative values, meaning that the USD/GBP trades at a forward discount. The forward points are a fraction of 1/10,000 each. So for clarity, what is the 6-month forward rate for this pair?

For example, suppose the domestic rfr is 2.8%, and that lower foreign rfr is just 2.1%. A spot rate of 1.301 would suggest what lower forward rate (using 3 decimal places), just working on an annual basis?

Good job!

No, that's too far from the forward rate. Here's the calculation:

$$\displaystyle F_{f/d} = S_{f/d} \left( \frac{1 + r_f}{1 + r_d} \right) = 1.301 \left( \frac{1 + 0.021}{1 + 0.028} \right) \approx 1.292 $$ Now that's annual. If you want to see a shorter-term forward rate, which is quite common, then you'll need to add the time, meaning the fraction of days/360, to this calculation as $$t$$, like this: $$\displaystyle F_{f/d} = S_{f/d} \left( \frac{1 + r_f[t]}{1 + r_d[t]} \right) $$ Go ahead and try a similar calculation, but for a 75-day forward rate. Will your forward rate be higher or lower than this last one?

No, definitely higher. You just looked at the forward discount rate for a year. If you use less than a year, you'll have less of a discount. So this forward rate will have to be higher.

Of course.

And what is that 75-day forward rate, using 3 decimal places?

Perfect!

No, it's approximately 1.299 now. Here's the calculation:

$$\displaystyle F_{f/d} = S_{f/d} \left( \frac{1 + r_f \left[ \frac{days}{360} \right]}{1 + r_d \left[ \frac{days}{360} \right]} \right) $$ $$\displaystyle F_{f/d} = 1.301 \left( \frac{1 + 0.021 \left[ \frac{75}{360} \right]}{1 + 0.028 \left[ \frac{75}{360} \right]} \right) \approx 1.299$$ Practice well, and these forwards won't put you in a spot, so to speak!

Lower

Higher

Forward premium

Forward discount

1.2280

1.2937

1.3083

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1.292

Lower

Higher

Other responses

1.299

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