Five Parity Conditions

1
Five Parity Conditions

• 1. Interest Rate Parity aka Covered Interest
  Parity.
• 2. Unbiased Forward Rates.
• 3. Uncovered Interest Parity.
• 4. Real Interest Parity.
• 5. Purchasing Power Parity.

2
Unbiased Forward Rates

• On the average, forward rate spot rate that
  will prevail at maturity.
• If does not hold, the prospect of profits
  exists. Arbitrage? Not!
• Make money with no investment but with risk Buy
  low, sell high!
• FX that exhibits a forward premium (discount)
  will appreciate (depreciate).

3
Uncovered Interest Parity

• Combine interest rate parity with unbiased
  forward rates.
• Transactions are identical to those of interest
  rate parity but with no forward hedging. There
  is FX risk.
• Seek profit by borrowing low and investing high
  but this is not arbitrage.

4
UIP Intuition

• RFgtRD implies S1ltS0. A high interest rate
  currency will depreciate (IRP exhibit forward
  discount).
• Similarly, a low interest rate currency will
  appreciate (IRP exhibit a forward premium).

5
UIP Formulas
6
Ex-post application of uncovered interest parity.

• True ex-post by definition.
• Split up domestic currency rate of return on a
  foreign security into two components rate of
  return of the foreign security and the
  appreciation of the foreign currency.
• Investment in a foreign security means investment
  in two different factors.

7
Application of ex-post uncovered interest parity

• CAC 40 rose by 53.64 , euro depreciated by
  14.94 (vis-à-vis C)during a certain year.
• What rate of return did Canadian investor
  achieve?
• 30.69 (153.64)x(1- 14.94) 1
• 30.69 measured in Cs, 53.64 measured in
  euros.

8
Who ripped off Charlie Canuck?

• Focus SP500 for 2003.
• RU, rate of return in Us, 19.
• RC, rate of return in Cs, 1.7.
• Jan03U0.63/C vs. Dec03U0.737/C.
• Appreciation of C (.737/.63)-117.
• (119)(11.7)(117)

9
Charlie Canuck continued

• Whats depreciation of U? 17? Not!!
• Jan03C1.587 vs. Dec03C1.357.
• Uappreciation(1.357/1.587)-1 -14.5
• Exact Relation (117) (1-14.5)-1
  (1Cappreciation)(1Uappreciation)-1
• One plus appreciation of one currency equals the
  reciprocal of one plus appreciation of the other
  currency.

10
Two Useful Transformations

• Appreciation in one currency vs. appreciation in
  the other currency.
• Rate of return on a security measured in one
  currency vs. rate of return on the same security
  measured in another currency.
• Must know how to transform data provided!
• When applying the transformations, bear in mind
  that the data are in the form of percentages.

11
Real Interest Parity

• Real interest rates tend to be equalized across
  currencies.
• High inflation currency exhibits high interest
  rates.
• (1foreign interest rate) / (1foreign inflation
  rate)(1domestic interest rate) / (1domestic
  inflation rate).

12
RIP Formulas
13
Purchasing Power Parity

• Law of one price a commodity must trade at same
  exchange rate adjusted price.
• Domestic price S x Foreign price.
• If gt holds buy foreign, sell domestic.
• If lt holds buy domestic, sell foreign.
• Commodity arbitrage tends to make inequality
  disappear.

14
Big MacCurrencies Down Unda

• BM price in U.S. U2.32
• BM price in Aus. A2.45
• PPP implies S(A/U) A2.45/U2.32
  A1.06/U.
• Compare to actual S A1.35/U.
• U overvalued, A undervalued.
• Overvaluation of U 27.36 implies
  undervaluation of A 22.

15
More on Aussie Big Macs

• Price of BM in Aus. In UA2.45/A1.35 U1.82.
• Compare with US price U2.32.
• Overvaluation of BM in Aus. -22.
• The overvaluation of a commodity in a country
  reflects the overvaluation of that countrys
  currency.

16
PPP across time

• PPP holds at start of year
• PPP holds at end of year
• (Send/Sstart) (1Id)/(1If)
• (1af) (1Id)/(1If)
• Intuition A high inflation currency will
  depreciate.

17
PPP across time Formulas
18
Canadian Exporter

• Transactions Exposure - FX cash flows it will
  receive over the next 6 months are contractually
  set.
• Operating Exposure FX cash flows it may receive
  beyond the 6-month time horizon from contracts as
  yet unsigned.
• More subtle forms of operating exposure in
  vignettes.

19
Four operating exposure vignettes

• 1. Aspen Skiing Revenues exhibited positive
  operating exposure.
• 2. Laker Airways Ditto, but negative operating
  exposure.
• 3. Petróleos Mexicanos Revenues
  denominated/determined by U.
• 4. YCF Revenues denominated in APeso but
  determined by U.

20
Aspen Skiing

• Colorado resort all balance sheet items and cash
  flows in greenbacks.
• Yet exposed to C, FFr, etc.
• In 1983, U appreciated, I.e. C, FFr
  depreciated.
• Domestic and foreign clientele shifted holidays
  to Banff, Chamonix, Chicopee.

21
Aspen Skiing

• Y-axis Cash flows in U X-axis S(U/C)

22
Aspen Skiing Lesson Gleaned

• Although you operate exclusively domestically,
  if your clientele has the option of purchasing in
  a foreign market, you exhibit positive exposure
  to that foreign markets currency. A U.S. firm
  with Aspen Skiing as client likewise possesses
  the same type of exposure.

23
Aspen Skiing Two Hedges

• Hedge positive operating exposure of cash flows
  to C, FFr, etc.
• Denominate some debt in C, FFr, etc. Result
  negative transactions exposure of debt offsets
  positive operating exposure of revenues.
• Buy resorts in Canada, France, etc. Result some
  revenue streams rise, other fall with rise in C,
  FFr, etc.

24
Laker Airways

• Early exploiter of air transport deregulation in
  late 70s. Target market Price conscious Brit
  tourists vacationing in Florida.
• Cost structure jet fuel U-denominated.
• Financed jets with cheap U-debt provided by US
  Ex-Im Bank.
• Steep U appreciated in early 80s spelled doom
  for Laker Airways.

25
Laker Airways Exposures

• Jet fuel both transactions and operating
  exposure to U.
• Debt transactions exposure to U.
• Revenues negative operating exposure to U.
  When U appreciated target clientele shifted
  holidays from Florida to Palma de Mallorca, Islas
  Canarias, Marbella, etc.

26
Laker Airways Lessons Gleaned

• If your business involves assisting a domestic
  clientele purchase goods/services in a foreign
  country, you have negative operating exposure to
  that foreign countrys currency.
• Dollar denomination of debt aggravated the firms
  negative exposure to the greenback.

27
Sir Freddies Egregious Error

• Error Denominated debt in Us.
• Appreciation of U resulted in Sterling value of
  costs and debt service increasing Sterling value
  of revenues decreasing.
• Sir Freddie got squeezed!
• Hedges debt denominated in Sterling cater to
  Yank clientele vacationing in UK.

28
Petróleos Mexicanos

• Most of output sold in world oil markets, ergo
  U-denominated.
• Revenues exhibit both transactions and operating
  exposure to U.
• Hedge debt denominated in Us.
• Negative transactions exposure of debt service
  offsets positive exposure of revenues.

29
Yacimientos Pertrolíferos Fiscales (YPF)

• Most of output sold domestically, i.e., Argentine
  peso denominated.
• Debt denomination in Us also makes sense!
  Huh??
• No price controls on domestic oil.
• PPP applies to oil. If U rises, peso price of
  oil rises.

30
YPF

• Revenues currency of denomination is peso but
  currency of determination is U.
• PPP Ppeso Pworld(U) X S(AP/U).
• For PPP to hold, Ppeso must rise if S rises.
• Hedge debt denominated in Us.
• Transactions exposure of debt offsets operating
  exposure of revenues.

31
Pemex YPF Lessons Gleaned

• Pemex Transaction exposure of debt service
  (denomination of debt in a foreign currency) can
  offset the positive transactions/operating
  exposure of a revenue stream.
• YPF As in Pemex, but revenue stream possess only
  positive operating (no transactions) exposure to
  a foreign currency.

32
Canuck Ltd.

• Canadian firm operating exclusively in Canada.
• Competitor in Canada sources product in the UK.
• Canuck Ltd. has positive exposure to the Pound
  Sterling, PS.

33
Canuck Ltd.s Operating Exposure

• Measured as slope of Canucks risk profile.
• Vertical axis cash flow measured in reference
  currency (C).
• Horizontal axis FX rate measured in direct
  quotation (C/PS).
• Somehow calculate slope PS1.923M, say.
  Interpretation?
• Regression model improves this approach slope
  calculation and statistical test.

34
Hedging operating exposure

• Use denomination of long-term debt.
• How to determine extent of exposure? Simple
  regression (use direct quotation).
• Regress domestic currency CF on FX exchange rate.
• Or regress domestic currency rate-of-return on
  -age appreciation of FX.

35
Measuring Operating Exposure

• Slope term of simple regression.
• X-variable S in direct quotation also
  appreciation in S.
• Y-variable cash flow in reference currency also
  growth rate in cash flow.
• Critical statistics slope term, t-statistic for
  slope term.

36
3 possible regression specifications

• Y CF in reference currency and X S (direct
  quotation) e.g. Tin Man.
• Y growth rate in CF measured in reference
  currency and X appreciation of S (direct
  quotation) e.g. Marubeni-Iida.
• Y rate of return on stock measured in reference
  currency and X appreciation of S (direct
  quotation) e.g. Selamat Malam.

37
Simple Regression Slope

• Denominated in units of foreign currency.
• As if that amount of FX received per period.
• Null hypothesis slope 0, I.e., no operating
  exposure.
• Alternative hypothesis slope not 0, I.e.,
  operating exposure exists.
• Reject null absolute value of t statistic gt 2.

38
Ballad of the Tin Man

• Application of regression approach.
• Simple regression slope coefficient is not
  significant. Ergo, no operating exposure to PS,
  PS denominated debt not appropriate.
• Although the acquired company generates PS CFs,
  debt employed in acquisition should be U
  denominated.
• Ballads currency of denomination is PS,
  currency of determination is U.

39
Tin Man Possible Conclusions
40
Tin Man effects of different debt denominations

• Message of regression CF(gross of debt service)
  in Us not affected by FX rate.
• With PS debt Rise in PS causes a reduction in U
  net of debt service CF.
• With U debt Rise in PS causes no change in U
  net of debt service CF.
• PS debt causes negative exposure to PS.

41
Real Exchange Rate

• Inflation adjusted exchange rate
• Must account for two inflation rates domestic
  and foreign
• Real FX Rate at t (Nominal FX Rate at t) X
  (1Foreign Inflation Rate/1Domestic Inflation
  Rate) t
• Important over long time horizons when inflation
  exerts its effect

42
PPP and Real FX Rates

• PPP implies that real FX rates dont change
• All inflation rates cancel out
• Result real FX rate at end of period nominal
  (and real) FX rate at start of period
• Interpretation If inflation is the sole cause
  of a change in FX rates, then the FX rates
  although changing in nominal terms are constant
  in real terms.

43
PPP and Real FX Rates
44
Thai T-Shirt Tale application of real FX rate

• Gauge profitability at start vs. end of year
• Profitability Baht profit margin per T-shirt
• Two different year end scenarios examined
• First scenario Violation of PPP, nominal FX rate
  constant, real FX rate changes
• Second scenario Consistent with PPP, nominal FX
  rate changes, real FX rate constant

45
Thai T-Shirt First Scenario

• Real value of baht (currency of cost) rises
• Real value of C (currency of revenue) drops
• No nominal change in FX rate
• Profit margin is squeezed
• Conclusion Profitability impaired if currency of
  cost appreciates or currency of revenue
  depreciates in real terms

46
Thai T-Shirt Second Scenario

• Real FX rate does not change
• Nominal FX rate changes
• Profitability is unaffected, real value of profit
  margin remains intact
• Conclusion Nominal exchange rate may change but
  if real exchange rate does not, profitability is
  not affected.

47
Thai T-Shirt Addendum

• If currency of cost depreciates or the currency
  of revenue appreciates in real terms,
  profitability is enhanced
• No numerical example given for this case

48
To assess competitive advantage, get real!! (not
nominal)
49
Mean-Reversion of Real FX Rates

• Empirical evidence real FX rates are
  mean-reverting, i.e., real appreciation
  (depreciation) is followed sooner or later by
  real depreciation (appreciation)
• Consistent with PPP holding in the long run i.e.,
  real FX rates dont change in the long run
• Implication Episode of competitive advantage
  gain (loss) will sooner or later be followed by
  competitive advantage loss (gain)

50
Translation Exposure

• Accounting rules for the determination of FX
  exposure found in Section 1650 of CICA Handbook
• Applies to both GAAP and IFRS
• Emphasizes transactions exposure, tending to
  ignore operating exposure
• Translation Transactions Exposure
• May yield an inaccurate view of a firms true FX
  exposure

51
Translation vs. Transactions/Operating Exposure

• Canadian firm with operating exposure to sterling
  creates translation exposure to establish a
  perfect hedge.
• Operating exposure C revenue stream positively
  exposed to sterling (Canadian competitors import
  from UK).
• Translation exposure debt denominated in
  sterling.

52
Translation vs. Transactions/Operating Exposure

• Canadian firm based on accounting rules or
  translation exposure is damaged by the rise in
  sterling.
• In fact, market value of stockholder wealth is
  not affected.
• Translation exposure does not yield a true
  picture of Canadian firms FX exposure.