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We all learned in our economics classes that the way to think about the price of anything is through the forces of demand and supply. That's how market economies are supposed to work – at least when there are no government price controls or other impediments to the free flow of goods and services. The market-clearing price will be such that demand equals supply, that is, where the two curves cross in the classic economics diagram. We'll soon use those diagrams to determine the level of bond prices and yields.

Consider first Figure 3.1 illustrating a bond transaction. To force this example a bit, suppose there is only one specific bond that can be bought or sold – a 4%, annual payment, 4-year fixed-income security. On the “buy side” of the trade we have investors who are willing and able to lend money for four years. On the “sell side” there are the bond issuers who need to borrow money, such as governments that have to finance a budget deficit or businesses that are expanding production capabilities. We can include on the sell side those who already own the bond and for liquidity reasons need to divest. The two arrows describe the transaction, the exchange of money for the security.

The point of Figure 3.1 is that we can track either arrow in our analysis. The demand and supply of money in Figure 3.2a determine the equilibrium interest rate. The horizontal axis is the quantity of money; the vertical axis is the price of money (i.e., the interest rate). The bond issuers need money, so they constitute the demand curve. The curve is downward sloping because the lower the cost of borrowed funds, the more money they want. To be more technical, we could appeal to corporate finance theory and say that at

Exchange Diagram

FIGURE 3.1 Exchange Diagram

The Interest Rate Diagram

FIGURE 3.2A The Interest Rate Diagram

a lower cost of capital, more investment projects have positive net present value. The investors' willingness to lend money, the more so the higher the rate of return, is apparent in the upward-sloping supply of money. In equilibrium, the interest rate turns out to be 4.2%.

The words “interest rate,” “bond yield,” and “rate of return” require some attention at this point. Often in bond math they can be used interchangeably. Sometimes “interest rate” stands for the level of market interest rates for some degree of credit risk and time to maturity. Because the graph plots money demand and supply, “interest rate” is the most natural term here, although we could use “bond yield” as well. The point is that at 4.2% lenders are willing to lend the same amount of money that borrowers want to borrow. A rate of return of 4.2% to investors, or a 4.2% cost of funds to borrowers, is the market-clearing interest rate.

The Bond Price Diagram

FIGURE 3.2B The Bond Price Diagram

The same ideas are expressed in Figure 3.2b, which tracks the bond arrow in the Figure 3.1 exchange diagram. Here the horizontal axis is the quantity of 4%, 4-year bonds; the vertical axis is the bond price. The motives driving the demand for money are now represented by the supply of bonds. It's an upward-sloping line because issuers will supply more bonds when they fetch a higher price. The demand for bonds from buy-side investors slopes downward because a lower price on a fixed-coupon bond corresponds to a higher yield. The equilibrium bond price turns out to be 99.3, a small discount off par value because the 4.2% required rate of return is higher than the 4% coupon rate.

Now suppose that suddenly there is unexpected news about global commodity prices, lowering the expected inflation rate from 2% to 1%. If the nominal interest rate stays at 4.2%, the expected real rate of interest goes up from about 2.2% to 3.2% – that's good for lenders, but bad for borrowers. That statement uses the standard decomposition of a nominal interest rate into the expected real rate and the expected inflation rate.


When the inflation rate is low, the cross-product term often is neglected.


Some economists will quibble with these expressions, arguing that there should be a term for a risk premium on the right side of both. Their idea is that the nominal rate should include compensation for the expected real rate of return and inflation as well as uncertainty about those expectations.

In any case, when expected inflation goes down because of breaking news about global commodity prices, the nominal interest rate is not likely to remain unchanged. Instead, it typically changes because the demand and supply curves in both graphs will react. The idea is that lenders and borrowers make decisions based on the expected real rate of return and real cost of borrowed funds. Economists call this the “no money illusion.”

The impact of a new level of expected inflation is illustrated in Figures 3.3a and 3.3b. In the interest rate diagram, lower inflation produces a lower equilibrium nominal interest rate, as would be expected. Given the new outlook for commodity prices, borrowers would want to borrow less and lenders would want to lend more for each nominal rate on the vertical axis because the real rate would be higher. The combination of weaker demand for funds and stronger supply pushes the nominal interest rate down to less

The Interest Rate Diagram

FIGURE 3.3A The Interest Rate Diagram

than 4.00%. In the bond price diagram, the two curves shift upward so that the bond price is now at a premium above par value. In general, lower expected inflation shifts the demand for fixed-income bonds out and the supply of bonds in.

Figure 3.3a and Figure 3.3b resolve the timing issue regarding bond prices and yields. We see the inverse relation between the two visually in the diagrams without resorting to a bond pricing equation – yields go down and prices go up, and vice versa. So, which drives which? The answer is that the curves in the upper and lower panels shift simultaneously. The point is that the same market forces responding to the news about expected inflation impact both the demand and supply of money and therefore the equilibrium interest rate, and the demand and supply of bonds and therefore the equilibrium price.

That's enough economics for now; let's move to the bond math.

The Bond Price Diagram

FIGURE 3.3B The Bond Price Diagram

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