Racy Cases -26 The Law of One Price


V Pattabhi Ram and A V Vedpuriswar

“A commodity cannot command two different prices in two different markets,” said Professor Chatshow, kick starting a session in financial economics.  “That’s no great shakes,” screamed a backbencher, sporting a t-shirt carrying the legend, “me Tarzan, you Jane”.  That kind of irreverence, both in the learning mode and in the dress code, could be seen only at this b-school.  Yet that hadn’t stopped it from cracking into the elite league of India’s top ten.

“Explain,” snapped the professor.  Flowers responded.  “Let’s suppose a notebook costs Rs 20 at a stationery shop and Rs 25 at the nearby stationery shop.  What would I do?  Well, I would buy 1,000 notebooks from the first and sell 1,000 notebooks to the second and pocket Rs 5,000 in a single day”.  A lone voice asked, “but Flowers, would the second shop also buy at Rs 20?”  Flowers responded, “let us assume so.”  The girl in the middle row (GITMR) did some rapid arithmetic.  “Sir, at that rate, Flowers would earn Rs 150,000 a month or Rs 18 lakhs per annum. Then he would stop attending classes”.  Someone hissed, “Yup, this is the kind of money which even the professor doesn’t make”.  The class roared.

“Wisecracks apart, Flowers’ was a good example of what is called arbitrage”, said Chatshow.  And then asked, “Will Flowers really make Rs18 lakhs in one year flat?” Boka got into the act.  “Nope.  When Flowers drops into the shop on the third day to buy the third thousand, the shopkeeper might up the price by Rs 1 to touch Rs 21 to see whether Flowers would still buy.  Of course Flowers would, since the margin is still a healthy Rs 4 per note book.”  GITMR supplemented, “may be on day 4, the shop where Flowers sells would down the price by Rs 1 to Rs 23 to see what Flowers would do”.  Neta (becoming a politician was his dream) stood up. “Sir, before long the two shopkeepers, acting independently of each other and without even knowing the existence of each other, would have upped and downed their respective prices such that Flowers would have no more free killing. Once that happens Flowers would come back to the class”. The class roared.

Chatshow was happy at the way the discussion was progressing.  “Yes, money isn’t available for jam”, he said. “There is no such thing as a money machine.  This is what is known as the law of one price. It essentially means that arbitrage opportunities do not last long.”  And then added “for prices to equalize all investors don’t have to be investment savvy.  All that is needed is that enough number of investors have to recognize arbitrage opportunities!”  Goggles (because outside the classroom he was always seen in goggles) wondered whether it was such a profound statement.  Was it as profound as Newton’s law of gravity?  Or as momentous as the law of demand and supply that economics so famously preaches?  After all there were price mismatches. Two b-schools offered identical curriculum; yet one charged a fee thrice that of the other.   But he kept his thoughts to himself.

“Sir, we find arbitrage all over the place”.  It was GITMR.  “Modigliani and Miller made a fortune using it to develop the Net Operating Income theory,” she said.  “Two companies having the same EBIT and operating in the same business risk class cannot command two different prices in the market place.  If they do command, then the process of arbitrage will set in motion and before long the two values will become equal.”  The class clapped.  Chatshow waved them into silence. “Good. But is arbitrage used to explain anything else?” he asked.

Boka said, “I don’t know what it is called but I guess arbitrage could be a determinant of exchange rates.”  The class sat up.  They hadn’t been taught International Finance.  Boka narrated, “If a basket of apples costs Rs 220 in India and $ 5 in USA, the exchange rate has to be Rs 44 per dollar.  Suppose the rate is Rs 45, you could buy a basket in India at Rs 220, sell it in the US for $5, collect Rs 225/- (45 X $ 5) and make a pack of Rs 5 on the deal.”  There was silent admiration for Boka.

The professor said, “Yup.  This is called the purchasing power parity theory.”  Flowers, who fought for grades with Boka, remarked tongue firmly in cheek, “But sir, which American would eat Indian apples?”  Someone giggled. Ignoring the barb and the giggles, the professor proceeded, “The currency of the country where the price is lower, will be bought and the currency of the country at where the price is higher will be sold. This free flow will soon lead to equalization of the prices of the baskets in the two countries”.  And then asked, “Any other examples?”

Flowers decided to speak up.  “I guess forward rates need to reflect interest rate differentials”.  Chatshow didn’t like vague technical statements.  “Explain,” he snapped.  “Suppose the interest rate in India is 10% and that in USA is 5%.  Suppose you have $ 100,000 available for investment.  Suppose the dollar rate is Rs 40 spot.  Now if this money is invested in USA it would fetch $105,000 at the year-end.  If the amount is converted into Rs, the Rs 40 lakhs can be invested at 10% and grow to Rs 44 lakhs.  When this money is repatriated it wouldn’t be at Rs 40 per dollar.  For, that would give them $110,000.  In that case they would rush their dollars into India.  Instead, the price for the dollar would be Rs 41.90 viz Rs. 44 lakhs/$105,000.”

Chatshow was impressed.  “Good” he said. “This is called the interest rate parity theory.  If the forward rate doesn’t reflect this theory, investment in one currency will be more attractive than the other. Capital will flow into the attractive currency, making it appreciate. Soon, the effective returns for investors will be equalized across the two currencies”.  GITMR startled everybody by saying “High interest rates in one country will be offset by a depreciation in the currency of that country.”  Chatshow agreed that she could not be more right.  And then said, “If the notebook example was a case of arbitrage over space, this one is an example of arbitrage over time.”

Goggles wasn’t still impressed.  He wasn’t sure why he had this strange misgiving about the arbitrage theory.  He somehow felt it wouldn’t be true in every case.  And so he asked, “Prof, does it work every time? Does it work in India? Take close-ended mutual funds.  These when listed in the stock market quote at hefty discounts.  Why?”  As Chatshow got ready to answer, the gong went.  He promised he would explain it in the next class.  In the meantime, the professor suggested that the class should log on to the net to find some answers.

 

 

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About Pattabhi Ram

A chartered accountant by profession, a writer by passion and a teacher by accidental choice.
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2 Responses to Racy Cases -26 The Law of One Price

  1. Ranjan says:

    I become a hardcore fan of this blog. I hope to read one everyday. It is just wonderful like learning on the go.

  2. Ranjan says:

    Sincerely waiting for the next class, Dear Charshow!

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