Reading 14 page 525 Example 8 question 5 and page 570 question 3.

Hi Guys maybe someone can shed light on the below. In question 5 page 525 the reciprocal of current spot rate is taken, while, in question 3 page 570 the reciprocal of the future spot is taken. Maybe I missing some details - would appreciate if anyone knows how to reason this.

Not sure if you’re observing the pattern correctly. Basically, the idea is to borrow in the lowest yielding currency and invest in the highest yielding currency. The general pattern is:

[(1 + interest rate of highest yielding currency) x (Future spot rate)] / (Current spot rate)

In example 8, there are only two currencies you have to worry about - JPY and AUD. Also, note that the question is asking for the return in JPY terms. So the math is straightforward (JPY has to be in the numerator):

(JPY/USD) x (USD/AUD) = (JPY/AUD)

Once you understand the above relationship, it’s simply a matter of plugging in the numbers in first formula.

In problem three, there are three currencies (imagine getting four currencies on the exam!) - USD, CAD, and EUR. USD is the lowest yielding (so you borrow this) while EUR is the highest yielding (so you invest in this). The question asks for the all-in return in USD terms. Means, our goal is to get to USD/EUR. There are multiple ways to solve this, and I think the way the solution presents the process is a bit confusing. Here is how I approached this:

Start with the second row in the table: EUR/CAD. Reciprocate this value.

Go to the first row in the table: CAD/USD. Reciprocate this value.

This gives you: (CAD/EUR) x (USD/CAD) = USD/EUR.

Plug in to our topmost formula to get the “gross” return: [(1 + interest rate of highest yielding currency) x (Future spot rate)] / (Current spot rate).

Overall, this is what you have for problem 3:

1 / 0.7218 = 1.3854; 1 / 0.7279 = 1.3738.

1 / 1.0055 = 0.9945; 1 / 1.0006 = 0.9994.

Multiply the values to get the exchange rates in terms of USD/EUR. Spot rate today = 1.3854 x 0.9945 = 1.3778. Spot rate one year from now = 1.3738 * 0.9994 = 1.3730.

Plug in to our first formula: (1.0220 x 1.3730) / 1.3778 = 1.0840. Remember that this is the “gross” return. You need to subtract the cost of the currency you borrowed in - in this case, the USD at 0.8%.

Not sure if this helps, but i have tried this process on a few other problems, and it has worked out well.