Help Need- Appreciation and Depreciation of Currency

CFA Level III Fixed Income
#1

Hi guys,

I got some confusion on calculation of currency appreciation and depreciation of currency via the exchange rate and hope someone could help.

For example, given the spot rate of JPY/USD is 100 in 3 months earlier and now the spot is 95. If the question asks how much, in % term, the USD depreciates and How much the Japanese Yen appreciates. What would be your answer? Is there any ‘1/exchange rate’ needed for calculatin the appreciation of JPY?

Additionally, if the questions asks about the annualized rate of return, is it (1+rate of appreciation / depreciation)^4?

Thanks!

#2

JPY / USD = Spot * (1+interest of JPY ) / (1+interest of USD)

But what always gets me is the interest rates whether I should divide the annualized rate (whether 6 months or not).

then you compare to expected spot

Never base your fwd or premium on expected spot; same goes to roll yield. Calculate the forward / premium then base your deduction on it. Even if you are asked whether to hedge or not, always base it on the forward rate first then expected rate to compare to forward.

#3

Thanks Bilal. I understand the forward rate under covered interest rate parity. But I don’t understand if there is 1/exchange rate need when calculating the expected amount of appreciation iof USD or JPY, in percentage term. For instance, there seems 5% depreciate from USD, but the amount of JPY appreciation in percentage term would be slightly higher than value from depreciation of USD? Does the base currency and pricing currency matter and how to determine the base currency? The local investment curreny is base currency?

#4

Can you post a specific example or refer to one in the book so i can get what you’re referring to …

I always look at it from the point of : what’s my position. If i’m long USD, then I would focus on how much the USD appreciated.

Example, US based company has exposures in JPY and EUR. Thus it’s long in both. I would calculate forward rates based on spot and see if 1 appreciated vs the other.

#5

Given the spot exchange rate of USD/JPY being 0.01 and the interest rate of JPY is 5% and USD is 4%, what will your currency return from hedged currency position for 3 months? The forward rate for 3 months is 0.0095.

#6

return from hedged position = local bond return + premium or - (discount)

return from hedged position = domestric rf - (local bond - local rf )

(Forward - spot / spot) = - 0.9524%

Return from hedged position = 5% - 0.9524% = 4.0476 (assuming jpy is local) … ?

#7

sam not enough info, need to know which currency it’s earning or which one is domestic.

#8

Assuming that this is US investor who invests in Japan, the hedged currency return will be

(1.04^0.25)/(1.05^.025) -1 = - 0.24%

#9

The depreciation of the USD is (95 – 100) / 100 = -5.0%

USD/JPY has changed from 0.01000 to 0.01053; the appreciation of the JPY is (0.01053 – 0.01000) / (0.01000) = +5.3%.

To annualize it for a 360-day year, it’s (1 + rate)^4; for a 365-day year, it’s (1 + rate)^(365/90).

#10

Thanks guys and s2000!!

#11

You’re welcome.

(For what it’s worth, I think I’d fall under the rubric of “guys”.)