An individual may hold her wealth in the form of landed property, bullion, bonds, money etc. For simplicity, let us club all forms of assets other than money together into a single category called ‘bonds’.
Typically, bonds are papers bearing the promise of a future stream of monetary returns over a certain period of time. These papers are issued by governments or firms for borrowing money from the public and they can be traded in the market.
Consider the following two-period bond. A firm wishes to raise a loan of ₹ 100 from the public. It issues a bond that assures ₹ 10 at the end of the first year and ₹ 10 plus the principal of ₹ 100 at the end of the second year. Such a bond is said to have a face value of ₹ 100, a maturity period of two years and a coupon rate of 10 per cent. Assume that the rate of interest prevailing in your savings bank account is equal to 5 per cent. Naturally you would like to compare the earning from this bond with the interest earning of your savings bank account. The exact question that you would ask is as follows: How much money, if kept in my savings bank account, will generate ₹ 10 at the end of one year? Let this amount be X.
Therefore, X ( 1 + (5 / 100) ) = 10
In other words, X = 10 / ( 1 + (5/100) )
This amount, ₹ X, is called the present value of ₹ 10 discounted at the market rate of interest. Similarly, let Y be the amount of money which if kept in the savings bank account will generate ₹ 110 at the end of two years. Thus, the present value of the stream of returns from the bond should be equal to
PV = X + Y = [ 10 / ( 1 + (5/100) ) ] + [ (10 + 100) / ( ( 1 + (5/100) )2 ) ] = 109.29 (approx.)
It means that if you put ₹ 109.29 in your savings bank account it will fetch the same return as the bond. But the seller of the bond is offering the same at a face value of only ₹ 100. Clearly the bond is more attractive than the savings bank account and people will rush to get hold of the bond.
- Competitive bidding will raise the price of the bond above its face value, till price of the bond is equal to its PV.
- If price rises above the PV the bond becomes less attractive compared to the savings bank account and people would like to get rid of it. The bond will be in excess supply and there will be downward pressure on the bond-price which will bring it back to the PV.
- Thus, under competitive assets market condition the price of a bond must always be equal to its present value in equilibrium.
Now consider an increase in the market rate of interest from 5 per cent to 6 per cent. The present value, and hence the price of the same bond, will become
[ 10 / ( 1 + (6/100) ) ] + [ (10 + 100) / ( ( 1 + (6/100) )2 ) ] = 107.33 (approx.)
It follows that the price of a bond is inversely related to the market rate of interest.
Different people have different expectations regarding the future movements in the market rate of interest based on their private information regarding the economy. If you think that the market rate of interest should eventually settle down to 8 per cent per annum, then you may consider the current rate of 5 per cent too low to be sustainable over time. You expect interest rate to rise and consequently bond prices to fall. If you are a bond holder a decrease in bond price means a loss to you – similar to a loss you would suffer if the value of a property held by you suddenly depreciate in the market. Such a loss occurring from a falling bond price is called a capital loss to the bond holder. Under such circumstances, you will try to sell your bond and hold money instead. Thus speculations regarding future movements in interest rate and bond prices give rise to the speculative demand for money.
When the interest rate is very high everyone expects it to fall in future and hence anticipates capital gains from bond-holding. Hence people convert their money into bonds. Thus, speculative demand for money is low. When interest rate comes down, more and more people expect it to rise in the future and anticipate capital loss. Thus they convert their bonds into money giving rise to a high speculative demand for money. Hence speculative demand for money is inversely related to the rate of interest. Assuming a simple form, the speculative demand for money can be written as –
As mentioned earlier, interest rate can be thought of as an opportunity cost or ‘price’ of holding money balance.
- If supply of money in the economy increases and people purchase bonds with this extra money, demand for bonds will go up, bond prices will rise and rate of interest will decline.
- In other words, with an increased supply of money in the economy the price you have to pay for holding money balance, viz. the rate of interest, should come down.
- However, if the market rate of interest is already low enough so that everybody expects it to rise in future, causing capital losses, nobody will wish to hold bonds. Everyone in the economy will hold their wealth in money balance and if additional money is injected within the economy it will be used up to satiate people’s craving for money balances without increasing the demand for bonds and without further lowering the rate of interest below the floor rmin. Such a situation is called a liquidity trap. The speculative money demand function is infinitely elastic here.
Total demand for money in an economy is composed of transaction demand and speculative demand. The former is directly proportional to real GDP and price level, whereas the latter is inversely related to the market rate of interest. The aggregate money demand in an economy can be summarised by the following equation –
Bibliography : NCERT – Introductory Macroeconomics