Forward/Spot Rates

CFA Level I
#1

This is on page 238 of the Econ Schweser book. How do you discern which country is considered “domestic” and which is “foreign”?

Example is below:

  1. The annual interest rates in the United States (USD) and Sweden (SEK) are 4% and 7% per year, respectively. If the current spot rate is SEK/USD 9.5238, then the 1-year forward rate in SEK/USD is:

A. 9.2568

B. 9.7985

C. 10.2884

I solved it as forward = 9.5238 * (1.04 / 1.07) = 9.2568, assuming that US was the domestic country. Is it safe to assume that the country used as the price currency (i.e., the first of the two that show up in the exchange rate) is considered the domestic country and the one used as the base currency is the foreign country?

Thanks

#2

Use a convention and keep it

keep numerator = DC denominator = FC

then use the rdc on the numerator, rfc on the denominator

since it is Spot = SEK/USD

Spot * (1+rSek)^T / (1+rUSD)^T = Forward

#3

I agree with cpk123 in regards to sticking with a convention for the purposes of calculating forward rates. As long as you remember that the Sd/f is multiplied by the ratio of domestic (+1) to foreign (+1) interest rates:

T-period-Forwardd/f=Spotd/f *[(1+id)T/(1+if)T]

It is also worth noting that forward rates do not necessarily specify domestic or foreign currencies. It is merely a rate for how much one currency (the price currency) will cost to buy 1 unit of another currency (the base currency). So you could just as easily recall that price currency is always the numerator and base currency is always the denominator.

As long as you remember to maintain the convention (ratio of price/base) as quoted in the required forward rate, you will apply the correct ratio of real currencies to the spot rate.

I think exchange rates appear to be trickier at first glance due to market quotations. This is LOS c) of reading 21. I think the key is to ensure that you understand that direct quotes are quoted as domestic/foreign and indirect quotes are foreign/domestic and you will be set.

Hope this helps

#4

SEK/USD means the number of SEK per USD. It is not ambiguous.

#5

You can also view those as a simple unit cancelation style problem. If you have SEK / USD then you would need to have the SEK in the denominator (as you did) and the USD in the numerator to get you a dimensionless answer. If you did it in reverse you would have the opposite (SEK^2 / USD^2) which does not exist.

Also always remember in these problems to use the 1.07 instead of just the .07. This is one of those things that test pressure can have you messing up easily (at least I feel)

Rob

#6

Robsvette - you are talking multiplying a SEK/USD * RATE/RATE

so there is NO CANCELLATION anywhere.

Cancellation would occur when you convert from one currency to another E.g. SEK/USD * USD/EUR to get SEK/EUR e.g.

And to the OP - you have done the problem wrongly.

The annual interest rates in the United States (USD) and Sweden (SEK) are 4% and 7% per year, respectively. If the current spot rate is SEK/USD 9.5238, then the 1-year forward rate in SEK/USD is:

9.5238 * (1.07)/(1.04) [SEK Rate on top, USD rate below]

to get 9.7985

Way to think about it: Rate in Sweden is higher than in the US. So the Currency is expected to DEPRECIATE. So you would get MORE SEK per USD - which is what is indicated by the 9.7985 > 9.5238.

#7

Thanks guys, makes sense now.

Checking via the expected currency depreciation or appreciation, as noted by cpk, will help avoid any mistakes.

#8

Suppose that the six-month spot rate is equal to 7% and the two-year spot rate is 6%. Which of the following is the best answer concerning the level of the one-and a half-year forward rate starting six months from now? The forward rate has to:

A) lie between 6% and 7%. B) be more than 6%. C) be less than 6%.

#9

1.07*(1+r)^3 = 1.06^4

r = 5.67%

so c) ???

also by elimination - since only 1 answer can be right - because essentially answer choices a) and b) both say the same thing - between 6% and 7% (choice a) is > 6% (which is choice b).

#10

c

#11

So if the question gave 30 day interest rates would you divide the rates by 12? and by 4 if the rates were quarterly?

#12

To the ops question. If given SEK/USD format, then think of 9.5238 SEK per 1 USD. Think of the / as “per”. Given that, SEK must be timed by 1.07 and USD timed by 1.04. Keep in mind that this is to eliminate arbitrage profit, therefore the higher interest rate must correspond to depreciation of the currency. As for vicky cool’s question. Assuming semiannual compounding, I got 5.86%. We earn 0.035 after 6 months using the first spot rate. We earn 0.1255 after 2 years. The difference (0.0905) is what we earn from month 6 to the end of the two years. Discount 1.0905 at 1.03 for 3 terms. Then subtract 1 and multiply by two.