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Summary of Some Lesson from the Yield Curve (Campbell)

  • Structure and focus of article is to “I first summarize recent research on the term

structure of interest rates and then relate it to recent swings in the bond market and the government's choice of debt maturity.”

  • Zero-coupon security – makes a single payment at a specified future date
  • Coupon-bearing securities – make a series of small coupon payments and then a larger final payment of face value
  • “The difference between the long-term yield and the short yield is known as the yield spread; the difference between the 1-year return on a long bond and the short yield is known as the excess return.”
  • “Over time, the short-term yields at the left of Figure 1 move more than the long-term yields at the right of the figure. But long yields do vary, and as shown in the equation above, small movements in long yields produce big changes in long bond prices and volatile returns on long bonds.”
  • Forward Rate – the amount that it will cost to deliver a currency, commodity, or some other asset some time in the future; used to determine the price of a futures contract--it accounts for holding costs, appreciation and demand for the good.
  • “The forward rate curve lies above the yield curve when the yield curve is upward-sloping and below it when the yield curve is downward-sloping. The two curves cross when the yield curve is flat. These of course are the standard properties of marginal and average cost curves.”
  • “An investor who buys a zero-coupon bond knows with certainty that its price at maturity will equal its face value. This means that any unexpected price change that may occur in the near future must be compensated by opposite price changes in the more distant future to bring the price back to face value on the maturity date. The variation in nominal returns on a given bond must therefore be negatively serially correlated and hence forecastable.”
  • Cannot directly compare bonds with different time horizons (e.g., 1 vs. 30 year bond)
  • “The pure expectations hypothesis of the term structure is the theory that interest rates are expected to move in exactly this way, to equalize expected returns on short- and long-term investment strategies. The expectations hypothesis is the slightly weaker proposition that the difference between the expected returns on short- and long-term investment strategies is constant, although it need not be zero as required by the pure hypothesis.”
  • “The pure expectations hypothesis says that whenever a long bond yield exceeds a short yield, the yield on the long bond subsequently tends to rise over the life of the short bond; this generates expected capital losses on the long bond, which offset the current yield advantage.”
  • “The pure expectations hypothesis also says that whenever a long bond yield exceeds a short yield, short yields tend to rise to equate returns over the life of the long bond; the average short rate over the life of the long bond must equal the current yield on the long bond, which requires that the difference between the average short rate over the remaining m - 1 periods and the current short rate must be m/(m - 1) times the current yield spread.”
  • “These theories have an implication that is counterintuitive for many of those studying them for the first time. When long rates are unusually high relative to short rates, long rates do not decline to restore the usual yield curve, as one might suppose. Instead long rates tend to rise; the yield spread falls only because short rates rise even faster. The pure expectations hypothesis also implies that instantaneous forward rates equal expected future short rates; for the expectations hypothesis, the two are equal after being adjusted by a constant. Thus, both theories imply that one can read investors' expectations about future interest rates off the forward rate curve.”
  • He compares these theories to data and has somewhat mixed results; however, the data better supports the expectations hypothesis for very short and very long maturities.
  • “In general, however, the yield spread will reflect changing rational expectations of both excess long bond returns and future short-term interest rates.”
  • Federal Funds Rate – FFR, the overnight rate paid by a bank that borrows reserves to a bank that lends them; example below is his discussion regarding the bond market in 1994 as a reaction to a 1.25 percentage point increase in the FFR over 4 months
  • “To understand why the behavior of the bond market was surprising, recall that normally long yields are less variable than short rates. An increase in the short rate is typically associated with a smaller increase in the long rate. In spring 1994, however, the first Fed policy move drove up the federal funds rate by a quarter of a percentage point, but the 6-month, 5-year, and 10-year yields each rose by a half point, and the 30-year yield rose by about a quarter point. The response to the second policy move was similar. From January to early April, then, the short and long ends of the yield curve both rose by a half percentage point while the middle of the yield curve rose by a full percentage point.”
    • One way to understand would be via the expectations theory, but he supports a theory on excess bond returns. “An alternative view is that the increases in 5- and 10-year zero-coupon bond yields were driven in part by increases in required excess returns on long bonds. Required excess returns may have gone up because of increases in risk, manifested in greater bond market volatility but attributable ultimately to uncertainty about Fed policy, or because losses incurred by highly leveraged bond traders increased the effective risk aversion of some market participants.”
  • Should the Govt borrow Short or Long? “The government might be able to reduce average interest costs with extremely short-term Treasury bill financing, but there is no strong evidence that the government can cut costs by shortening the maturity of its longer-term debt.” “A government may also be able to use debt management to reduce interest costs in circumstances where it has superior information about the likely future path of interest rates.”
  • “the argument runs, long-term borrowing is less risky for the government. There are two problems with this argument. First, it confuses bond yields with bond returns. To measure the risks of an investment or debt management policy, one should look at the returns on the policy measured over some uniform horizon. Second, the argument confuses nominal returns with real returns-the latter, presumably, being of primary concern to the government. But in real terms, it turns out that long bond returns are more volatile than short bond returns at all horizons.”
  • “Third, if the government wishes to limit the variability of real returns on its debt over long horizons, it can do so most effectively with long-term indexed bonds of the type issued in Britain. Such bonds guarantee investors a fixed long-run real rate of return regardless of variations in inflation and short-term real interest rates.”
  • “The analogous irrelevance theorem for the government says that debt management policy has no real effects, given spending policy, if markets are complete and the government can levy nondistortionary taxes.”
  • Summary. “This brief review suggests that shortening the maturity of the government debt, or issuing indexed debt, has several potential advantages. First, the government can reduce its average interest costs if it shortens maturity when the yield curve is steep (as it has been in the early 1990s). Second, shortening maturity or issuing indexed debt reduces the variability of the real returns on government debt, and therefore reduces the variability of the government's real financing costs. Finally, shortening maturity or issuing indexed debt may lower inflationary expectations if it improves the credibility of anti-inflationary monetary policy.”

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