Good evening everyone,

My weekly task is to go through the Economics part of the Level II curriculum. I was a bit afraid of it, because it was clearly my week point at the Level I and because I think that this topic covers a lot of material compared to its allocated number of questions.

In this level, the first challenge is to take into account the bid-ask spread for currency exchange rates. Just as we saw for security markets at Level I, exchange rate do not value a single “value”. That is, you cannot buy and sell a currency at the same price instantaneously. This is because you need to go through a dealer who has to make money for providing liquidity: this economical gain is provided by the bid-ask spread.

Let’s go back to the basics by looking at the exchange rate $\frac{CHF}{EUR}$. The currency in the denominator is the **base currency**; it is the asset being *traded*. The currency in the numerator is the **price currency**; it is the currency used to *price* the underlying asset which is in this case another currency. This is exactly like if you were trading a stock $S$. The price in CHF could be see as the $\frac{CHF}{S}$ “exchange rate”, i.e. the number of CHF being offered for one unit of $S$. Now as mentioned before, exchange are quoted with bid and ask prices:

$$\frac{CHF}{EUR} = 1.21 \quad – \quad 1.22$$

This means that $\frac{CHF}{EUR}_\text{bid}$ is 1.21 and $\frac{CHF}{EUR}_\text{ask}$ is 1.22. Again, you are trading the base currency: here Euros.

- The bid price is the highest price you can sell it for to the dealer.
- The ask price is the lowest price you can buy it for to the dealer.

If you want to make sure you got it right, just make sure you can’t instantaneously buy the base currency at a given price (which you believe to be the ask) and sell it at a higher price (which you believe to be the bid). In this example, you can buy a EUR for 1,22 CHF and sell it instantaneously for 1.21 CHF making a loss of 1.22-1.21=-0.01 CHF. In fact, the loss can be seen as the price of liquidity which is the service provided by the dealer for which he has to be compensated. So the lower value is the bid, the higher value is the ask (also called the offer).

Recall from Level I that you could convert exchange rates by doing:

$$\frac{CHF}{EUR} = \frac{1}{\frac{EUR}{CHF}}$$

This is simple algebra and it works fine as long as you don’t have the bid-ask spread to take into account. The problem is that at Level II, you do. To invert the exchange rate with this higher level of complexity, you have to learn the following formula:

$$\frac{EUR}{CHF}_\text{bid} = \frac{1}{\frac{CHF}{EUR}_\text{ask}}$$

This might look complicated at first, but I got something in my bag to help you learning it. Look do the following steps:

- Define what you want on the left-hand side of the equation (currency in the numerator, currency in the denominator, bid or ask).

$$\frac{A}{B}_\text{side}$$

- On the right-hand side of the equation, write the inverse function:

$$\frac{A}{B}_\text{side}=\frac{1}{\cdot}$$

- On the right-hand side, replace the $\cdot$ by the inverted exchange rate:

$$\frac{A}{B}_\text{side}=\frac{1}{\frac{B}{A}_\cdot}$$

- Finally, replace the remaining dot on the right-hand side by the opposite side:

$$\frac{A}{B}_\text{side}=\frac{1}{\frac{B}{A}_\text{opp. side}}$$

Let’s take show how this work using our base example:

$$\frac{EUR}{CHF}_\text{bid}=\frac{1}{\frac{CHF}{EUR}_\text{ask}}$$

Simple. You can simply apply this method interchangeably to suit your needs. Actually, you might wonder what you need that to compute cross rates, which will be the subject of another post. Until that, grasp the concepts presented here and stay tuned on this blog!

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