Guys just a little confused on the rate used to discount the spot rate. Maybe you could shine some light on this for me. There seems to be an inconsistency when you short or long. Sometimes when you a short you use either a domestic or foreign rate, and sometimes when you long you use a domestic or a foreign rate… more often then not, i’ve seen that you use a domestic rate. I’ve added the examples and questions I was referring to. EXAMPLE 5 pg.40 The spot rate for British pounds is $1.76. The US risk-free rate is 5.1 percent, and the UK risk-free rate is 6.2 percent; both are compounded annually. One-year forward contracts are currently quoted at a rate of $1.75. A. Identify a strategy with which a trader can earn a profit at no risk by engaging in a forward contract, regardless of her view of the pound’s likely movements. Carefully describe the transactions the trader would make. Show the rate of return that would be earned from this transaction.Assume the trader’s domestic currency is US dollars.
Solution:
The following information is given: S0 (spot) = $1.76 r-domestic = 0.051 r-foreign = 0.062 T = 1.0 The forward price should be F(O T) = [($1.76/1.062] (1.051) = $1.7418 With the forward contract selling at $1.75, it is slightly overpriced. Thus, the trader should be able to buy the currency and sell a forward contract to earn a return in excess of the risk-free rate at no risk. The spe_cific transactions are as follows: • Take $1.76/(1.062) = $1.6573. Use it to buy 1/ 1.062 = £0.9416. <<< why is this the r-foreign? • Sell a forward contract to deliver £1.00 in one year at the price of $1.75. • Hold the position for one year, collecting interest at the UK risk-free rate of 6.2 percent. The £0.9416 will grow to (0.9416)(1.062) = £1.00. • At expiration, deliver the pound and receive $1.75. This is a return of (1.75/1.6573)-1=0.0559 A risk-free return of 5.59 percent is better than the US risk-free rate of 5.1 percent, a result of the fact that the forward contract is overpriced.
EOCq 12 & 15
Q12. The euro currently trades at $1.0231. The dollar risk-free rate is 4 percent, and the euro risk-free rate is 5 percent. Six-month forward contracts are quoted at a rate of $1.0225. Indicate how you might earn a risk-free profit by engaging in a forward contract. Clearly outline the steps you undertake to earn this risk-free profit.
A. First calculate the fair value or arbitrage-free price of the forward contract: So (spot) = $1.0231 T = 180/365 r-domestic = 0.04 r-foreign = 0.05 F(O,T) = [l.0231/(1.05)^180/360 *(1.04)^180/365 = $1.0l83 The dealer quote for the forward contract is $1.0225; thus, the forward contract is overpriced. To earn a risk-free profit, you should enter into a forward contract to sell euros forward in six months at $1.0225. At the same time, buy euros now. i. Take $1.0231/( 1.05 )^180/365 = $0.9988. Use it to buy 1/( 1.05 )^180/365 = 0.9762 euros. <<< why is this the r-domestic? ii. Enter a forward contract to deliver €1.00 at $1.0225 in six months. iii. Invest €0.9762 for six months at 5 percent per year and receive €0.9762 x 1.05^180/365 = €1.00 at the end of six months. iv. At expiration, deliver the euro and receive $1.0225. Return over six months is $1.0225/$0.9988 - l = 0.0237 , or 4.74 percent a year. This risk-free annual return of 4.74 percent exceeds the US risk-free rate of 4 percent. Q15. The Japanese yen currently trades at $0.00812. The US risk-free rate is 4.5 percent, and the Japanese risk-free rate is 2.0 percent. Three-month forward contracts on the yen are quoted at $0.00813. Indicate how you might earn a risk-free profit by engaging in a forward contract. Outline your transactions. A15. First, calculate the fair value or arbitrage free price of the forward contract: S0 = $0.00812 per yen T = 90/365 r-domestic = 0.045 r-foreign = 0.02 F(O,T) = [$0.00812/(1.02)^90/365]*(1.045)^90/365 = $0.00817 The dealer quote for the forward contract is $0.00813. Therefore, the forward contract is underpriced. To earn a risk-free profit, you should enter into a forward contract to buy yen in three months at $0.00813. At the same time, sell yen now. i. The spot rate of $0.00812 per yen is equivalent to ¥123.15 per US dollar. Take ¥123.15/(1.045)^90/365 = ¥121.82. Use it to buy 1/(1.045)^90/365= 0.9892 US dollars. <<< why is this the r-foreign? ii. Enter a forward contract to buy yen at $0.00813 in three months. One US dollar will buy dollar will buy 1/$0.00813 = ¥123.00 iii. Invest $0.9892 for three months at 4.5% a year and receive $0.9892 x 1.045^90/365 = $1.00 at the end of 3 months. iv. At expiration, deliver the dollar and receive ¥123. The return over 3 months is (¥123/¥121.82) - 1 = 0.00969, or 3.88 percent a year. Because we began our transactions in yen, the relevant comparison for the return from our transactions is the Japanese risk-free rate. The 3.88 percent return above exceeds the Japanese risk-free rate Of 2 percent. Therefore, we could borrow yen at 2 percent and engage in the above transactions to earn a risk-free return of 3.88 percent that exceeds the rate of borrowing.
The issue you highlighted mainly revolves around the understanding of price currency and base currency. The methodology used by the curriculum usually considers the numenator as price currency and the denominator as base currency. For example, if you have a PKR/USD quote, this means that the USD is the base currency and PKR is the price currency. Generally speaking the base currency is the SAME as the domestic currency; while the price currency is considered as the foreign currency. Therefore, in my example, PKR will be foreign currency and USD will be domestic currency.
Now coming to your specific queries:
Query 1:
It has been explained in the question that the trader is based in US , so any currency other than dollars will be considered as foreign currency.
Query 2:
It is stated in the question that the dealer quote is $1.0225. As the Euro has been priced in terms of dollars so Dollar is the price currency and Euro is the base currency. Based on my explanation above, the price currency is the foriegn currency which is Dollars. The other currency, Euro, is the DOMESTIC currency.
Query 3:
The spot rate in the question suggest the price currency to be USD and the base currency to be JPY. However for the solution, the writer converted it as ¥123.15 per US dollar. The new denomination converted the USD to be the BASE (domestic) currency and the JPY as the PRICE (foreign) currency.
With respect, it doesn’t revolve around the understanding of price currency and base currency.
It’s nothing more nor less than CFA Institute’s convention to have the investment result in one unit of the investment currency.
Furthermore, as I mentioned above, it makes no difference. The percent return will be the same irrespective of the amount of the currency with which you start.
The individual raised queries as to how to decide between the use of domestic currency and foriegn currency. With respect, if you can read his question again, there are certain BOLD remarks that he has put (the areas where he is being confused).
I specifically addressed the bold remarks: the reason that CFA Institute divides by the growth factor for the investing currency is that they’re obsessed with having the result of the investment be one unit of the investing currency.
My point is that there’s no reason to want the result to be one unit of the investing currency. You get the same result – the same profit per unit of borrowed currency – no matter what. Divide by the growth factor of the investing currency, divide by the growth factor of the borrowed currency, divide by π, multiply by 123,456,789 . . . it doesn’t matter; the percent profit will be exactly the same.
I saw some modifications to be made in the original question, as I believe in the two following End of chapter questions the investor is USA based, so dometic rate would be the USD risk-free rate.
EOCq 12 & 15
Q12. The euro currently trades at $1.0231. The dollar risk-free rate is 4 percent, and the euro risk-free rate is 5 percent. Six-month forward contracts are quoted at a rate of $1.0225. Indicate how you might earn a risk-free profit by engaging in a forward contract. Clearly outline the steps you undertake to earn this risk-free profit.
A. First calculate the fair value or arbitrage-free price of the forward contract: So (spot) = $1.0231 T = 180/365 r-domestic = 0.04 r-foreign = 0.05 F(O,T) = [ l.0231/(1.05)^180/360 *(1.04)^180/365 = $1.0l83 The dealer quote for the forward contract is $1.0225; thus, the forward contract is overpriced. To earn a risk-free profit, you should enter into a forward contract to sell euros forward in six months at $1.0225. At the same time, buy euros now. i. Take $1.0231/( 1.05 )^180/365 = $0.9988. Use it to buy 1/( 1.05 )^180/365 = 0.9762 euros. <<< why is this the r-domestic? shouldn’t this be why is this r-foreign? ii. Enter a forward contract to deliver €1.00 at $1.0225 in six months. iii. Invest €0.9762 for six months at 5 percent per year and receive €0.9762 x 1.05^180/365 = €1.00 at the end of six months. iv. At expiration, deliver the euro and receive $1.0225. Return over six months is $1.0225/$0.9988 - l = 0.0237 , or 4.74 percent a year. This risk-free annual return of 4.74 percent exceeds the US risk-free rate of 4 percent. Q15. The Japanese yen currently trades at $0.00812. The US risk-free rate is 4.5 percent, and the Japanese risk-free rate is 2.0 percent. Three-month forward contracts on the yen are quoted at $0.00813. Indicate how you might earn a risk-free profit by engaging in a forward contract. Outline your transactions.
A15. First, calculate the fair value or arbitrage free price of the forward contract:
S0 = $0.00812 per yen T = 90/365 r-domestic = 0.045 r-foreign = 0.02 F(O,T) = [$0.00812/(1.02)^90/365]*(1.045)^90/365 = $0.00817 The dealer quote for the forward contract is $0.00813. Therefore, the forward contract is underpriced. To earn a risk-free profit, you should enter into a forward contract to buy yen in three months at $0.00813. At the same time, sell yen now. i. The spot rate of $0.00812 per yen is equivalent to ¥123.15 per US dollar. Take ¥123.15/(1.045)^90/365 = ¥121.82. Use it to buy 1/(1.045)^90/365= 0.9892 US dollars. <<< why is this the r-foreign? shouldn’t this be why is this r- domestic? ii. Enter a forward contract to buy yen at $0.00813 in three months. One US dollar will buy dollar will buy 1/$0.00813 = ¥123.00 iii. Invest $0.9892 for three months at 4.5% a year and receive $0.9892 x 1.045^90/365 = $1.00 at the end of 3 months. iv. At expiration, deliver the dollar and receive ¥123. The return over 3 months is (¥123/¥121.82) - 1 = 0.00969, or 3.88 percent a year.
