The speculative demand for money is introduced in the literature by Keynes who defines the speculative motive of holding money as "the object of securing profit from knowing better than the market what the future will bring forth"(Keynes, 1936: 170). In his The General Theory, Keynes asserted that the speculative demand for money resulted from the uncertainty as to the future of the rate of interest. Assuming that there are two assets: (i) either individuals can hold money that does not have any yield, or (ii) they can keep bonds that have a positive yield. Since people have different views on the future interest rate, those who believe that the interest rate will be higher in the future than the one assumed by the market will tend to hold money in order to make profit. In fact, for this group of people who believe that the interest rate will rise and the price of bonds will fall, they prefer to sell their bonds now and hold money in order to avoid capital losses in the future. On the other hand, individuals who think that the interest rate will be the one assumed by the market will tend to hold bonds instead of money, since as they think that the interest rate will fall thus raising bond prices. Therefore, they choose to hold bonds now rather than money (Keynes, 1936). Hence, in Keynes view, the
speculative demand for money can be written as:Msp = L(r) where,Msp is the speculative demand for money, r is the market rate of interest and L(r) is Keynes' degree of the liquidity preference. This explanation applies to a single individual. Now concerning the aggregate
demand function, Keynes argues that since investor's expectations as to the future interest rate differ, then at high rates of interest more investors will expect them to fall and few will hold cash. Conversely, at rather low rates of interest, only a few investors will expect them to fall further and most investors will hold cash. This implies that the aggregate demand for money is a continuous downward sloping curve Msp as shown in Figure 2.3 below.
M sp Figure 2.3 Keynes' degree of liquidity preference
Source: Handa (2000: 39)
2.10.2 Formalization of Keynes' speculative demand for money by Tobin
Tobin (1958) postulates that an individual chooses to hold money as part of a portfolio because the rate of return on holding money is more certain than the rate of return on holding earning assets. In other words, holding assets other than money is riskier than holding just
money alone. This difference in riskness can be explained by the fact that alternative assets (bonds and equities) are subject to market price volatility, while money is not (Sriram, 1999).
Tobin (1958) formalizes Keynes' approach of the speculative demand for money. He assumed like Keynes that people have only two assets in which to invest: (i) money which does not provide any yield and is risk free and (ii) bonds which have a non-zero yield and the yield has a positive standard deviation indicating these bonds are risky. He further assumes that, the bond is a consol, which is unredeemable. A consol pays a fixed coupon c indefinitely. Thus, in perfect capital markets, the market price pb of a consol paying a coupon c per period is given by its present discounted value at the market rate of interest, x, on loans as follows (Handa, 2000):
c c
+ -. 7T + .
l + X (\ + xf
00 1
y
l= c
00 1
y
1= c - 1 V l + x J
= c \xj
x
(For c=x A,=l)Assuming r to be the current return on consols, or the coupon payment and regarding re, as the future expected market rate of return on consols as the expected rate of discount, then Pb
is r/re. It is usual to consider the expected capital gain or loss on the consol as g, which can be written as g = ye -1. Then, the sum of the coupon (r) and the capital gain (g) is the expected yield (r + g) given by r + g = r-\ 1. If the yield (r + g) is positive, (r + g) > 0, rational
re
individuals will purchase the consol instead of holding money, which has a yield equal to zero.
Conversely, for a negative yield or (r + g) < 0, it is rational to hold money which in this case has a great yield. Between the positive yield (r + g)> 0 and the negative one (r + g) < 0, there is a zero yield (r + g = 0), which is known as the switch point concerning the choice between keeping money or consols. We can derive a critical return rc indicating that interest rate at which an individual will switch from holding consols to money. This critical switching yield is or rc. Thus if the individual makes the correct guess as to re, any r above rc indicates l + re
positive yields can be made on consols. The individual will hold no money.
This situation is illustrated in Figure 2.4 below.
A
rc , B
W M>
Figure 2.4 Tobin's formalization of Keynes' version of the speculative demand for money Source: Handa (2000: 39)
For any current interest rate greater than the critical level (r > rc), the whole portfolio W o£
rational individuals will be held in consols, so that money balances will be equal to zero for interest rates along AB. On the other hand, for a current interest rate less than the critical level i.e. (r < rc), rational individuals will hold their entire portfolio W as money. This is represented in Figure 2.4 by the portion of the demand for money CW. Thus, the individual's demand for money appears to be the discontinuous step function (AB, CW). A smooth downward sloping money demand function is obtained by assuming many investors who do not have the same critical level of the interest rate.