CONCEPT CHECK
7
The liquidity premium hypothesis also holds that issuers of bonds prefer to issue long-term bonds to lock in borrowing costs. How would this pref- erence contribute to a positive liquidity premium?
Forward rates derived from conventional bonds are nomi- nal interest rates. But using price-level-indexed bonds such as TIPS, we can also calculate forward real interest rates.
Recall that the difference between the real rate and the nominal rate is approximately the expected inflation rate.
Therefore, comparing real and nominal forward rates might give us a glimpse of the market’s expected future inflation rates. The real versus nominal spread is a sort of forward inflation rate.
As part of its monetary policy, the Federal Reserve Board periodically reduces its target federal funds rate in an attempt to stimulate the economy. The following page capture from a Bloomberg screen shows the minute- by-minute spread between the 5-year forward nominal interest rate and forward real rate on one day the Fed announced such a policy change. The spread immediately widened at the announcement, signifying that the market expected the more expansionary monetary policy to even- tually result in a higher inflation rate. The increase in the inflation rate implied by the graph is fairly mild, about
.05%, from about 2.53% to 2.58%, but the impact of the announcement is very clear, and the speed of adjustment to the announcement was impressive.
By the way, nothing limits us to nominal bonds when using the expectations hypothesis.
The nearby box points out that we can apply the theory to the term structure of real interest rates as well, and thereby learn something about market expectations of coming inflation rates.
Liquidity Preference
We noted in our discussion of the long- and short-term investors that short-term investors will be unwilling to hold long-term bonds unless the forward rate exceeds the expected short interest rate, f 2 > E ( r 2 ), whereas long-term investors will be unwilling to hold short bonds unless E ( r 2 ) > f 2 . In other words, both groups of investors require a premium to induce them to hold bonds with maturities different from their investment horizons.
Advocates of the liquidity preference theory of the term structure believe that short-term investors dominate the market so that the forward rate will generally exceed the expected short rate. The excess of f 2 over E ( r 2 ), the liquidity premium, is predicted to be positive.
To illustrate the differing implications of these theories for the term structure of inter- est rates, consider a situation in which the short interest rate is expected to be con- stant indefinitely. Suppose that r 1 5 5% and that E ( r 2 ) 5 5%, E ( r 3 ) 5 5%, and so on.
Under the expectations hypothesis the 2-year yield to maturity could be derived from the following:
(11y2)25(11r1)311E(r2)4 5(1.05)(1.05)
so that y 2 equals 5%. Similarly, yields on bonds of all maturities would equal 5%.
In contrast, under the liquidity preference theory f 2 would exceed E( r 2 ). To illustrate, suppose the liquidity premium is 1%, so f 2 is 6%. Then, for 2-year bonds:
(11y2)25(11r1)(11f2) 51.0531.0651.113
implying that 1 1 y 2 5 1.055. Similarly, if f 3 also equals 6%, then the yield on 3-year bonds would be determined by
(11y3)35(11r1)(11f2)(11f3) 51.0531.0631.0651.17978
Forward Rate Interest Rate (%)
Year Constant
Liquidity Premium
Forward Rate
Expected short rate is constant Yield curve is upward- sloping
0 1 2 3 4
Interest Rate (%)
Year A
B Yield Curve
Expected short rate is falling Liquidity premium increases with maturity 7
6 5 4
Figure 15.4 Yield curves. Panel A, Constant expected short rate. Liquidity pre- mium of 1%. Result is a rising yield curve. Panel B, Declining expected short rates. Increasing liquidity premiums. Result is a rising yield curve despite falling expected interest rates. (continued on next page)
Interest Rate (%)
D
Expected short rate is rising
Liquidity premium increases with maturity
Forward
Rate Yield curve
rises steeply Constant Liquidity Premium
Yield curve is humped
Forward Rate Expected Short Rate C
Interest Rate (%)
Year
Year
Figure 15.4 (Concluded) Panel C , Declining expected short rates. Constant liquidity premiums. Result is a hump-shaped yield curve. Panel D , Increasing expected short rates. Increasing liquidity premiums. Result is a sharply rising yield curve.
implying that 1 1 y 3 5 1.0567. The plot of the yield curve in this situation would be given as in Figure 15.4 , panel A. Such an upward-sloping yield curve is commonly observed in practice.
If interest rates are expected to change over time, then the liquidity premium may be overlaid on the path of expected spot rates to determine the forward interest rate. Then the yield to maturity for each date will be an average of the single-period forward rates.
Several such possibilities for increasing and declining interest rates appear in Figure 15.4 , panels B to D.