Formula Sheets: FINA 5500
Exam 2
Currency Conversion
Quotes: DQ (direct quote): The dollar price of one unit of foreign currency (FC)
IQ (indirect quote): Number of units of FC per one dollar; DQ = 1 / IQ and IQ = 1 / DQ
Currency Conversion:
Converting USD into FC
Converting FC into USD
Using DQ
USD / DQ = FC
FC * DQ = USD
Using IQ
USD * IQ = FC
FC / IQ = USD
DQ0 (IQO) = Direct (indirect) quote, at the beginning of the period
DQ1 (IQ1) = Direct (indirect) quote, at the end of the period
% change in DQ = 100*(DQ1 – DQ0) / DQ0 ; or % change in DQ = 100*[100 / (100 + % change in IQ) - 1]
% change in IQ = 100*(IQ1 – IQ0) / IQ0 ; or % change in IQ = 100*[100 / (100 + % change in DQ) - 1]
Ask Price (A): The buying price for one unit of FC from the currency dealer; Bid Price (B): The selling price for one unit of FC to the
currency dealer; Bid-Ask Spread = 100* (A – B) / A
Cross-Quotes: DQ1= $ price of FC1; DQ2 = $ price of FC2;
The price of FC1 in terms of FC2 (how many unit of FC2 does it take to buy one FC1) = DQ1 / DQ2
The price of FC2 in terms of FC1 (how many unit of FC1 does it take to buy one FC2) = DQ2 / DQ1
Bid-Ask cross quotes (Let ASK1 and BID1 & ASK2 and BID2 be the Ask and Bid prices for FC1 and FC2 in DIRECT QUOTES) :
Ask price of FC1 in terms of FC2 = ASK1 / BID2 ; and Bid price of FC1 in terms of FC2 = BID1 / ASK2
Ask price of FC2 in terms of FC1= ASK2 / BID1 ; and Bid price of FC2 in terms of FC1 = BID2 / ASK1
Forward Premium or Discount: [(forward rate – spot rate) / spot rate] * [360/days to maturity] * 100
Dollar Return on foreign assets = (1 + Rf) (1 + Rx) - 1
Rf = return on foreign assets based on foreign currency
Rx = return on foreign currency = same as percentage change in DQ
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Variable Definitions
S= Current spot rate (price of foreign currency) in direct quote
S1 = Actual spot rate, 1 year from now
F = 11-year
year forward rate
FPH = the forward premium = [(F-S) / S] = [(F/S) - 1] from the home country’s
view point
FPF = the forward premium = [(S-F) / F] = [(S/F) - 1] from the foreign country’s
view point
H = Inflation rate in the home country
F = Inflation rate in the foreign country
ρ = Real rate of interest
E(S
( 1) = Expected
p
spot
p rate, 1 yyear from now, based on PPP
E(e) = [E(S1)/S] – 1 = The expected percentage change, or rate of change, in the
spot rate, based on PPP
e = (S1/S) – 1 = The actual percentage change, or rate of change, in the spot rate
Sr= real spot rate
iH = Nominal interest rate for the home country
iF = Nominal interest rate for the foreign country
Formula: Purchasing Power Parity (PPP)
Exact relationship:
E(e) =(1
(1 + πH) / (1 + πF) - 1
Approximate relationship:
E(e) = πH - πF
S1 = S0 * [ 1 + E(e) ]
SR = S1 *(1 + πF) / (1 + πH)
Fi h Equation:
Fisher
E
ti
(1 + i) = (1 + ρ) (1 + )
i = ρ +  + ρ
Approximately: i = ρ + 
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Formula: International Fisher Effect (IFE)
Fisher Equation: (1 + i) = (1 + ρ) (1 + )
i = ρ +  + ρ
A
Approximately:
i
l i=ρ+
iuh : Uncovered rate of return, home country’s viewpoint
iuf : Uncovered rate of return, foreign country’s viewpoint
iuh = (1 + if) (1 + % change in DQ ) – 1
iuf = (1 + ih) (1 + % change in IQ ) – 1
% change in DQ (direct quote)
quote)= (S1 - S0) / S0
% change in IQ (indirect quote) = [1 /(1+ % change in DQ] - 1
The IFE relationship holds when:
E(e)= (1 + iH) / (1 + iF) – 1
Approximately: E(e)= iH – iF
S1 = S0 * [1 + E(e)]
Formula: Interest Rate Parity (IRP)
Calculating the covered rate of returns (home & foreign country’s view point)
ich= Covered rate of return, home country’s view point
icf= Covered rate of return, foreign country’s view point
ich = (1 + if) (1 + FPh) – 1
icf = (1 + ih) (1 + FPf) – 1
The IRP relationship holds when the expected forward premium from the
home country’s point of view (FPh ):
FPh = (1 + ih)/(1 + if) – 1
S1= S0 * ( 1 + FPh)
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