The long term purchasing power of an individual depends upon two things: earning capability and inflation. The time value of money tells us that a dollar today is worth more than a dollar earned a year hence. There are at least 2 reasons for that: inflation rate and uncertainty. If you want to borrow a dollar from your friend, your lender friend will look for compensation in terms of inflation. If you go and ask money from the market, however, the lenders will look for compensation in terms of both inflation and uncertainty. They will perceive present as sacrosanct, and future as uncertain. And because their money is only going to come in future, they will seek compensation for that. Consequently, the interest rate implied on the debt will include 2 elements: Inflation rate and a premium for default which represents uncertainty risk.
Inflation is an implicit tax on every person's cash flows. If $100 is kept under a mattress for a year, and inflation rate during the year is 5%, the purchasing power of $100 is reduced to $95. That is why mattress is not a great idea, and it is important for the investor to at least make returns equal to the inflation rate. This will keep the real returns (the purchasing power) in tact.
The same rule applies to the exchange rates under the purchasing power parity. The exchange rates of currencies are determined by markets based upon their demand and supply. Both demand and supply depend upon a variety of factors. As of now the Indian rupee is trading at about Rs.71.50 per dollar. By end of 2017, it was Rs.63.84. These are of course determined by the free market.
However in the long run, fundamentals of the country will take precedence, and the exchange rates will settle based upon those factors. Under the purchasing power parity, the exchange rates are influenced, therefore determined, by the long term inflation rates in the two countries. For instance, let us begin with the 2017 exchange rate of Rs 63.84 per dollar. If the long term inflation rates of the US and India are going to be 2% and 6% respectively, in the next 5 years the exchange rate should settle at Rs.77.38. That represents the rupee depreciating about 4% each year against the dollar.
As of now, the US is the biggest economy with a GDP of $20 t, and China is behind with $12 t. India's GDP is $2.6 t. But when we apply purchasing power parity to the GDP, the numbers change drastically. China becomes number one with $26 t GDP, then the US ($20 t), and India comes third with $9.5 t. That is because instead of using market rates, we apply inflation-adjusted rates to the currencies.
The purchasing power parity theory compares the two currencies using a basket of goods and services, and concludes that the cost of an item in country A should be the same in country B in real terms. And the real values are calculated after removing inflation components attributed to them. The idea is to include a variety of goods and services, instead of one or two items, that are representative of the economy.
If the price of a pizza is $10 in the US and Rs.500 in India, the PPP exchange rate would be Rs.50 per dollar, considering both pizzas of equal quality. While market exchange rates are also influenced by factors not fundamental to the economy, such as perceptions and bias, PPP rates are considered more intrinsic.
As easy way to calculate the PPP rates between the two countries is to look at their PPP and nominal GDP. Here's how it is done: We know that India's GDP is about $2.6 t. At the prevailing exchange rate of about Rs.70, that is Rs.182 t. We also know that in terms of PPP it is $9.5 t. That means the implied PPP exchange rate is Rs.19.16. In 2017, it was about Rs.17.74; in 1990, it was Rs.5.76; that implies over 27 years the inflation differential has been about 4.25% which appears to be fair.
One thing comes out clear: The market exchange rates are not useful all the time.
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