First lesson on money machines

There are two very elegant and obvious axioms in finance. The first one is that a rupee today is worth more than a rupee tomorrow. Simply put, if I give to you the rupee I have today, you should return to me more than a rupee tomorrow. The second one is that a secure rupee is worth more than a risky rupee.

Let us make this matter frivolous by bringing in my obsession with food. There is this friendly neighbourhood restaurant where the special dish today is Chicken Biriyani, cooked in my favourite Avadhi style rather than the not so good Hyderabadi style. A plate of it costs Rs. 100 (no, in reality Chicken Biriyanis are cheaper but 100 seems such a nice round number!) My plan was to devour a plate of it for lunch.

This is when you come along and ask to borrow that Rs. 100. You promise that you will return the money tomorrow. This of course means that I cannot eat the Biriyani today but will have to eat it tomorrow. Skipping the meal for you today will mean that I will be hungrier tomorrow than I am today. To satisfy this enhanced hunger, I will need to order a mutton champ worth Rs. 50 along with the Biriyani worth Rs. 100. Therefore, I will lend Rs. 100 to you today only if you return Rs. 150 to me tomorrow. This result stems from the time value of money, which is the first axiom mentioned above.

But that is not all. There is a distinct possibility that the special dish will not be Chicken Biriyani tomorrow. To eat the chicken biriyani, I will have to go to another restaurant slightly farther off and that will cost me a taxi fare of another Rs. 50. Therefore, I will risk lending you the Rs. 100 today only if you return to me Rs. 200 tomorrow to cover both the mutton champ and the taxi fare. This result stems from the second axiom, which basically talks bout risk.

I do not like risk. You may think that is because I hail from a middle class Indian family and for middle class Indian families, financial security is the one and only goal. That may be true to some extent but the major reason is that studying risk involves a lot of math and I hate it. Luckily, most beginners of financial theory seems to share this attitude of mine and most basic theories of finance are based only on the time value of money with risk factored in much later.

Today I want to write about a money machine. To introduce it, I will go back to the frivolous example I quoted above. Suppose that you say that you will not return the money to me tomorrow but day after tomorrow. Of course, by day after tomorrow, I will be hungry enough to eat a Kulfi as dessert after the biriyani and the champ. The Kulfi costs Rs. 25. Keeping the risk factor out for the time being, I will lend you the Rs. 100 today only if you return to me Rs. 175 day after tomorrow.

This brings us to what appears to be an obvious conclusion. The longer I lend the money for, the higher I will expect the return to be. Conversely, the longer I borrow the money for, the greater the interest I will have to pay. This is why banks give higher interest rates on three year fixed deposits compared to one year fixed deposits. This is why the Estimated Monthly Instalments (EMI) we pay against loans add up to a higher value when paid over a longer period of time.

It is at this juncture that you will start thinking that a theory built on something as dubious as chicken biriyani cannot be serious. What if you start a bank and do the opposite? What if you charge lesser interest for longer lending and your friend charges you lesser interest for longer loans? Will you become the next financial magician and investors from the world over flock to you and your friend? Yes, they will flock to you all right but you will be bankrupt sooner than you can say bankrupt, along with that good friend of yours. This is because you would have created a money machine. Let me explain how.

Let us assume that you charge an interest of 20% when you lend money for one year and 7% when you lend money for two years. Your friend borrows money for one year and pays an interest of 20% but pays only 7% interest when he borrows for two years. You and your friend work as a team. Therefore, your firm lends and borrows at 20% for one year and 7% for two years.

I go to your firm, which is called Morons Ltd., and deposit Rs. 1000 for one year. Since we are keeping risk out of the picture, I am sure that I will get Rs. 1200 at the end of the first year. Even if I just keep the money with me for another year, I will have Rs. 1200 at the end of two years. I go to your firm again and show to you that I will have a guaranteed Rs. 1200 with me at the end of two years. As per your rules, you will then lend me 120/ (1.07^2) = Rs. 1048.1. Thus, I have gained Rs. 48.1 without doing anything.

You may always smirk and say that a paltry gain of Rs. 48.1 will hardly make me a millionaire. But remember that I need to do it only 147 times to become a millionaire!

I think two clarifications are necessary here. The first one is that money machines do not exist. This is because money attracts more brains than anything else (definitely science!) and so the moment any such arbitrage opportunity opens up, people flock to it either to neutralize it or to render the fools responsible for it bankrupt. The second clarification is that risk free investments do exist. Government bonds are supposed to be risk free.