 # Relative PPP for finding Spot Rates -- Q

In the below Q, they provide beginning spot rate (\$1.50) and ending spot rate (1.60) but if I try to obtain the ending spot rate using Relative Purchasing Power Parity, I don't get it (the spot rate goes down, not up). Am I missing something or was this a careless mistake on their part? P.S. In another similar Q in this topic they use IRP to find the end of year spot rate so I thought using Relative PPP would make sense since you shoudl theoretically get same results. A U.S. investor purchased a U.K. bond one year ago. The exchange rate at the time was 1.5 to 1 (dollars to pounds) and the beginning-of-period ratio of the price levels of the consumption baskets was 2 ( to £). During the year, inflation in the U.S. was 5% and in the U.K. was 10%. Today the exchange rate is 1.6. What is the end-of-period real exchange rate? A) 1.64. B) 0.84. C) 1.45. Your answer: B was correct! The end-of-period real exchange rate is calculated as: X = S (PF/PD). Here, the new price levels are 1.1 for the U.K. (1 × 1.1 = 1.1) and 2.1 for the U.S. (2 × 1.05 = 2.1). Hence, the end-of-period real rate is 0.838 [= X = S (PF / PD) = 1.6 (1.1 / 2.1)].

the trick with end of yr real exch. rate is to remember to first adjust the inflation rates by the consumption ratios of each country

This was my approach: New US consumption = 2*1.05 = 2.1 New UK consumption = 1*1.10 = 1.1 Real FX rate = 1.6*(1.1/2.1) = .8384

bpuldog: thats exactly what i did too. my only point was why i cannot get the 1.6 on my own using PPP and the inflation rates given (if for example they did not provide the spot rate after one year) audrey: not sure what you mean? can you show the math of that using the question above?

the show NY Wrote: ------------------------------------------------------- > bpuldog: thats exactly what i did too. my only > point was why i cannot get the 1.6 on my own using > PPP and the inflation rates given (if for example > they did not provide the spot rate after one > year) > > audrey: not sure what you mean? can you show the > math of that using the question above? There’s not enough information in this question to get 1.6 on your own, based on the formulas listed on the back of my Stalla guide (PM section).

bpdulog: why isnt there enough information? you have beginning spot rate in USD, the UK inflation rate, the US inflaation rate, and the time. S1 = (\$1.50) (1.05)/1.10) = \$1.43. This does not equal the 1.60 they provide. Take a look at another problem in which they ask for FCRP and to derive the exchange rate in one year, they use Relative PPP. I'm still simply trying to make the point that Relative PPP should get you to the same S1. Lee Okazaki is a Japanese investor who is considering investing in the United States equity and bond market. The world risk premium is 5%. The risk-free rate is 2% in Japan and 3.5% in the U.S. The current exchange rate is 120 yen/ and the ratio of the price levels of Japan to U.S. consumption baskets is expected to be 120 to 1 in one year. The 1-year interest rate in Japan is 2.5% and the one-year rate is 4% in the U.S. The expected inflation rate in the U.S. is 2% and in Japan the expected inflation rate is 1%. Okazaki is considering buying common stock in a U.S. firm that has a world beta of 1.1 and an estimated sensitivity of yen-denominated returns to changes in the U.S. dollar of 0.7. What is the required return for this investment? A) 7.85%. B) 7.55%. C) 9.55%. The correct answer was A. The International Capital Asset Pricing Model (ICAPM) for a two world currency is: E® = Rf + BgMRPg + y\$(FCRP\$). Rf is the domestic risk free rate, in this example Japan. Bg is the World beta. MRPg is the world market risk premium. Y\$ is the domestic currency sensitivity. Foreign currency risk premium (FCRP) is the foreign currency risk premium calculated by taking the expected appreciation minus the interest rate differential. Note the first part of this is the expected appreciation of the exchange rate. Using relative purchasing power parity (PPP) the expected spot rate is 120 × (1.01 / 1.02) = 118.8. The exchange rate is currently 120yen/, and a year from now it will be 118.8 yen/. FCRP = [E(S1) - S0] / S0 – (rDC - rFC) = [(118.8 – 120) / 120] – (0.02 - 0.035) = 0.005 E® = 0.02 + 1.1(0.05) + 0.7(0.005) = 0.02 + 0.055 + 0.0035 = 0.0785

If they didn’t provide the \$1.60, I would use the \$1.43.

yes i agree. i think it may have something to do with the real exchange rates. in the econ chapter i think we assume real exchange rates are constant. so you can do PPP becuae you assume the change in nominal rate is compeltely explained by inflation. i say this because i think i noticed that in the PM material there was a Q that said real exchange rates hold, and in that QW, PPP could be successfully used to get the same nominal spot rate in the future as was provided. in the Q above,. there is no mention of that.