Earning Risk Free Rate

CFA Level III Derivatives
#1

Can someone please advise

If a fund was Shorting European stock market futures, selling euros, and buying US dollars how does it earn the US risk free rate?

Ta v much in advance

#2

I don’t think buying the US dollars comes into play here in order to earn the US risk free rate on this trade.

If you’re a US investor and you want to invest $100 in the EUR market you’ll have both euro stock market risk and currency risk.

You can hedge the currency risk by selling the Euros forward (if you knew how much your stock investments will be worth in the future), and you can hedge your market risk by selling stock market futures (now you do now how much you’ll get in the future, so you can use this future value to sell the Euros forward).

Because forward prices are just today’s price brought forward by the domestic rate, by selling the stock futures you’ll be earning the Euro risk free rate.

And since you’ve also hedged the currency, you know exactly how much USD you’ll receive for your EUR at the end of the futures contract.

When all the dust settles you’ll have just earned the US risk free rate. You can satisfy yourself with a simple example:

  • USD/EUR spot = 1.3
  • USD rf = 5%
  • EUR rf = 10%
  • USD/EUR 1 year-forward = 1.240909
  • Transaction:
    • Convert $100 to EUR = 76.92 EUR
    • Invest 76.92 EUR for 1 year @ 10% = 84.61 EUR
    • Convert 84.61 EUR back to USD at the forward price of 1.240909 = $104.99
    • = 5% return in USD terms. Voila.

Might be easier to just invest in the US and avoid all the hastle :slight_smile:

#3

Damn Voyager you nailed it

#4

Thanks, been brushing up on currencies since I ran into 2009 Q9 - calculating credit exposure of a currency forward. Check it out. Never know when this L2 stuff resurfaces.

#5

Pretty much crystal, Voyager. Cheers!

#6

Same question is in 2018 AM …but i think they have just asked for how much will be the end value …So either you can go long way or take a short cut calculation and get US $105

#7

I don’t disagree with your workings, but I thought a short position on EUR should necessarily mean a long position in USD i.e. buying USD 104.99 with EUR 84.61?When you enter the USD/EUR forward at 1.240909 means you are selling the EUR at a discount/buying USD at a premium. Hence, your forward is a losing position on expiry, which is why the forward contract has eaten into your foreign yield 10%.

I hope i am making sense… if not i’m gonna be in deep trouble this Sat

#8

Not sure what you’re asking here. But yes, in essence this is showing that due to interest rate parity the loss on the currency will eliminate the gain in yield. This was really just to show how hedging both the currency and the asset will result in earning the domestic risk free rate. You don’t have to do any of this calculation on the exam… you’d simply say that you earn 5% in domestic terms.

If you didn’t convert the EUR back to USD and instead purchased USD at the beginning of the hedge, you’d still earn the domestic risk free rate on USD initial investment.

#9

I was responding to your first statement “i don’t think buying USD comes into play here in order to earn US risk free”