Question

Purchasing Power Parity

1 yr inflation is:

Euro         0.50%

US            1.25%

GBP          0.80%

The real risk free rate is the same around the globe.

The US 1 yr rate is 1.90%.

1.     What should the 1 year rates be in EUR and GBP?

2.     What are the expected changes in EUR and GBP?

3. If GBPUSD is 1.15 and one ounce of gold costs 1200 pounds, how much should it cost in USD?

4. If GBPUSD is 1.15, one ounce of gold costs 1200 pounds, and one ounce of gold costs $1600, describe the trades necessary to earn a riskless profit.

Answer 1

Answer.

1 year Inflation are as follow

Inflation in Euro (iE)= 0.50%

Inflation in US(iUSD)= 1.25%

Inflation in GBP (iGBP)= 0.80%

US 1 yr Nominal Rate (NUSD)= 1.90%

As we know that

1+ Nominal Rate = (1+ Real Rate)*(1+Inflation Rate)

For USD,

1+ NUSD= (1+RUSD)*(1+iUSD)

1+0.019= (1+RUSD)* (1+0.0125)

(1+RUSD)= 1.019/1.0125

(1+RUSD)= 1.00642

RUSD= 1.00642-1

RUSD= 0.0642 i.e. 0.642%

It is given that risk free rate of return is same around the globe

so R= 0.642%

Answer 1.

For Euro,

1+NE= (1+R)*(1+iE)

1+NE= (1+0.00642)*(1+0.005)

1+NE= 1.01145

NE= 1.01145-1

NE=0.01145 i.e. 1.145%

Nominal Rate in Euro(NE)= 1.145%

For GBP,

1+NGBP= (1+R)*(1+iGBP)

1+NGBP=(1+0.00642)*(1+0.0080)

1+NGBP= 1.01447

NGBP= 1.01447-1

NGBP=0.01447 i.e. 1.447%

Nominal Rate in GBP(NGBP)= 1.447%

Answer 2.

let 1 EURO = $1.2 (AT SPOT )

After 1 year

1(1+N_E)= 1.2(1+N_USD)

1*(1+0.01145)=1.20(1+0.019)

1 Euro= $1.20*1.019/1.01145

1 Euro= $1.21

so expected changes in Euro = (1.21-1.20)/1.20= 0.8333% (Euro will be costly as compared to $ after one year, increase in the value of EURO)

Similarly

Let 1 GBP= $1.14 (Spot)

After 1 year

1*(1+NGBP)=$ 1.14(1+NUSD)

1*(1+0.01447)= $1.14(1+0.019)

1GBP= 1.14*1.019/1.01447

1 GBP= 1.1451

Expected Changes in GBP= (1.1451-1.14)/1.14= 0.447 % (i.e. GBP would be costly as compared to $ after 1 year, i.e. Increase in value of GBP)

Answer 3

1 GBP= $ 1.15 (It is assume that , given exchange rate is after 1 year***)

Cost of 1 ounce gold = 1200 GBP

So Cost of 1 once Gold = 1200*1.15= $1380 (Ans)

Answer 4

As we have already seen in above case if Cost of 1 ounce gold in UK= 1200 GBP, then Price of same gold = $1380

If at the same time price of one ounce gold = $ 1600,

Then for risk less profit,

Take $ 1380 and convert it in GBP to get 1200 GBP,

Now, Buy One Ounce Gold @ 1200 GBP and same should be sell in $ to get $ 1600

So risk less profit= (1600-1380)= $220 ans

Note:-

If given rate in the part (3) is spot rate then we have to first convert it in exchange rate at 1 year i.e.

1 GBP = $1.15 (1+ N_USD)/(1+N_GBP), after that procedures will be same for remaining part of the answer .