All right.
Let's continue with short selling and short positions.
And we have the currency pair euro US dollar.
And in this notation, a euro is the base currency and the US dollar is the, quote, currency.
And now let's assume that today's price is 1.1.
So we have to pay $1.1 to get €1 and then tomorrow's price is 1.25.
So the price for the euro increases and we can benefit from that with a long position in the euro.
So the long position in the euro is equivalent to a short position in the US dollar.
And then we have the following transactions here.
So today an investor buys €1 and he pays $1.1 and one day later he sells the euro for $1.25 and the
profit is $0.15.
So we benefit from rising euro prices with a long position in the euro or a short position in the US
dollar.
And like for any other instrument, we can calculate the simple return of this transaction.
So with today's price divided by yesterday's price minus one.
But first of all, let's create here the variables and let's calculate the simple return for this long
transaction and the simple return is plus 13.63%.
And we could also say that the euro appreciates by 13.64% relative to the US dollar.
So that's the simple return.
Now, coming to a question that seems to be a no brainer.
So what return would you expect for the corresponding euro short position?
So I do think that more than 90% of you would say that it's -13.64%.
And that's definitely the intuitive answer here.
So if the euro appreciates by 13.64% relative to US dollar, then at the same time it seems to be equivalent
that we say that the dollar depreciates by -13.64% relative to the euro.
So that's the most intuitive answer.
But surprisingly, this is incorrect.
And to calculate the return of the short position, first of all, we have to convert the price or the
interest rate to the inverse rate.
So to the US dollar, euro rate where the euro is short and the dollar is long and we can simply do
this with one divided by.
So we have here actually the same prices, but now we have today 0.9 €1 to buy $1 and tomorrow it's
only 0.8 euro to buy $1.
And this leads to the following transactions.
So today an investor buys a $1 and he pays 0.9 €1, and one day later he sells the dollar for 0.8 euro.
And the total losses here round about €11 cents.
And also for this short transaction, we can calculate the simple return.
So t one divided by T zero minus one.
And surprisingly, this is not -13.64%, but -12%.
So we could also say that the US dollar depreciates by 12% relative to the euro.
And this is equivalent to the other statement that the euro appreciates by plus 13.64%.
So this is or this could be kind of a surprise for you.
And the take home message is that when using simple returns, the long position return is unequal to
the short position, return times minus one.
So these are not the same.
And there's also a solution.
And also here, no surprise, the lock returns some more appropriate than working with short positions.
And we will see this in more detail in the next lecture.
Thanks for watching and see you there.
Bye.