THE IMPACT OF THE CAPITAL MARKET
2.3 DETERMINATION OF THE MARKET RATE OF INTEREST
than lenders (depositors). Taxes are discriminatory. Nevertheless, we would contend that, whilst these assumptions are not likely to be met completely, the analysis still provides a useful basis for evaluating the role of the capital market. The analysis is demonstrated more formally in Box 2.1.
This theory explains how ¢nancial intermediation improves an individual’s welfare by enabling him to save and increase his utility in the future or borrow from his future resources so as to increase his utility in the current period above what was available under autarky. But where does this interest rate come from?
Who decides what’s the market rate of interest? This question can only be answered when we move from the individual analysis to the market as a whole.
Funds Theory explains how the rate of interest is determined by the interaction of savers and investors. Figure 2.4 illustrates the equilibrium rate of interest determined by the interaction of savings and investment decisions by agents in the economy.
Investment varies inversely with the rate of interest, and saving varies positively with the rate of interest. The higher the rate of interest the higher the level of saving induced by agents prepared to sacri¢ce current consumption for future consumption. The equilibrium rate of interest is the point where investment equals savings shown as pointr0in Figure 2.4, in other words where:
SðrÞ ¼IðrÞ Sr >0
Ir <0
The theory was criticized by Keynes (1936) both as a theory of interest rate deter- mination and as a theory of savings. Because this theory enabled the Classicals to argue that investment was equal to savings at all times, then the macroeconomy was always at full employment. Whatever the merits or otherwise of Keynes’s critique, we can show how the theory can be used to explain how a market can produce ¢nancial intermediation. Nowadays the saver has a myriad of savings instruments o¡ered to them: mutual funds and PEPs are but two of a number of such savings instruments. We can use the Loanable Funds Theory to examine the modern-day equivalent in the form of savings instruments that act as alternatives to the conventional bank deposit.
In the Loanable Funds Theory, the ¢nancial counterpart to the savings and investment decision is the £ow supply and demand for ¢nancial securities. The
FIGURE 2.4
Determination of the equilibrium rate of interest
r
S
I r0
S, I
£ow supply is the increase/decrease in supply of securities and, correspondingly, the
£ow demand is the increase/decrease in demand for securities. Investors borrow by supplying securities that act as claims to capital goods. We can think of investors as
¢rms that wish to borrow funds to invest in projects that yield a positive rate of return. They borrow funds by issuing new securities (equity, bonds, commercial paper), which represent liabilities to the ¢rm. Households (and even other ¢rms and nonbank ¢nancial institutions such as pension funds and insurance companies) will channel savings by demanding new securities to add to their portfolio of assets.
So, savings represent the £ow demand for securities (DBd) and investment represents the £ow supply of securities (DBs) whereDis the change in the level of stock andB represents the stock of bonds as a proxy for all securities and the superscripts represent demand and supply. In other words:
S¼DBd I ¼DBs
The £ow demand for securities is positively related to the rate of interest because the
£ow demand is negatively related to the price of securities. Hence, as the rate of interest rises, the price of securities falls and the £ow demand increases. Box 2.2 explains why the price of a security and the rate of interest are inversely related.
The £ow supply of securities is negatively related to the rate of interest because supply is positively related to the price of securities. Hence, the demand and supply equations can be speci¢ed formally as:
DBd ¼fðrÞ DBs ¼gðrÞ
f0>0; g0<0 Figure 2.5 illustrates the case.
Consider what happens if there is an increased desire to invest by ¢rms. The investment schedule shifts up to the right fromI0toI1and the equilibrium rate of interest increases fromr0tor1as shown in Figure 2.6. To attract funds for invest- ment, ¢rms will increase the £ow supply of securities. At every level of the rate of interest, the £ow supply of securities would increase, shifting theDBs schedule to the right. The increase in the £ow supply of securities will drive down the price of securities and drive up the rate of interest fromr0tor1.
Consider what happens when there is an increased desire to save by savers. How is the message that savers wish to save more transmitted to investors? The change in savings preference shifts the saving schedule in Figure 2.7 fromS0toS1and the rate of interest falls fromr0tor1. The increased desire for savings is translated into an increase in the £ow demand for securities. TheDBd schedule shifts to the right for every given level of the rate of interest. The increase in the £ow demand for securities drives up the price of securities and drives down the rate interest fromr0tor1.
DETERMINATION OF THE MARKET RATE OF INTEREST 27
BOX 2.2
The yield (r) on a security is given by its dividend yield and expected capital gain. If the dividend is denotedDand the price of the security is denotedP, the yield at a point in time is described by:
r¼Dt
PtþtEPtþ1Pt
Pt
wheretEPtþ1is the rational expectation at timetfor the price of the security in periodtþ1. Rearranging this equation and solving forPt, we have:
Pt¼ Dt
ð1þrÞþ tEPtþ1 ð1þrÞ
Taking expectations of this expression and pushing the time period one stage forward:
tEPtþ1¼ tEDtþ1
ð1þrÞþ tEPtþ2 ð1þrÞ Substituting this expression intoPt we have:
Pt¼ Dt
ð1þrÞþ tEDtþ1
ð1þrÞ2þ tEPtþ2 ð1þrÞ2
By continuous forward substitution the expression forPt becomes:
Pt¼Xn
i¼0
tE Dtþi
ð1þrÞiþ tEPtþn ð1þrÞn
We don’t know the true value of future dividends and the best guess for them is the current value of dividends. So, the expected value forDtþ1and all future values ofDis simplyDt. Let’s assume for arguments sake that the maturity of the security is infinite, meaning that it is an irredeemable asset, then the second term on the right-hand side of the equation goes to zero asn! 1.
After substitutingDt for expected future values ofD, the first term on the right-hand side can be expressed as:
Pt¼ Dt
ð1þrÞ
1þ 1
ð1þrÞþ 1
ð1þrÞ2þ
The term in parentheses is nothing other than the sum of a geometric series, which can be expressed as:
Pt¼ Dt
ð1þrÞ 1 1 1
1þr 0
@
1 A ) Dt
ð1þrÞ 1þr
r
¼Dt
r
So at any point in time the price of a security is inversely related to its yield or rate of return. In an efficient capital market, the yield on the security will represent the rate of interest in the economy. The price will change only if the rate of interest changes or if the expected future dividend stream changes.
The Loanable Funds Theory is self-contained. For ¢nancial intermediation to exist, it would appear that all that is needed is an e⁄cient capital market. So, why do we need ¢nancial intermediaries and banks?
We have so far established that the introduction of a capital market increases welfare, but the question still remains as to why funds £ow through a ¢nancial intermediary rather than being transferred directly from the surplus units. In a Walrasian world of perfect frictionless markets, there would be no need for ¢nancial intermediaries, as lenders and borrowers would be able to contact each other to arrange for loans. Patently, the view does not accord with the world we observe, so
DETERMINATION OF THE MARKET RATE OF INTEREST 29
FIGURE 2.5
Equivalence of the savings and investment schedules to the flow and demand for securities
r
I, S r
∆Bs,∆Bd I0
S0
∆Bs0
∆Bd0
r0
FIGURE 2.6
Increased desire to invest by firms r
I, S r
∆Bs,∆Bd I0
S
∆Bs0
∆Bd
r0
I1 ∆Bs1
r1
we must be able to provide sensible reasons for the existence of ¢nancial intermediaries and in particular banks. This is the subject of Chapter 3.