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Weigh the main theories of how interest rates vary with maturity against each other, namely the term structure of interest rates theories.

FRM® Part I · Financial Markets and Products · Properties of Interest Rates · FRM1.FM.16.k

The idea

Four theories explain why yields vary with maturity. Pure expectations says a long rate is an average of expected future short rates. So forward rates equal expected spot rates, and an upward slope signals expected rate rises. Liquidity preference says investors prefer short maturities. So forward rates exceed expected spot rates by a premium that grows with maturity. This explains why curves usually slope upward even when rate expectations are flat. Market segmentation says each maturity range has its own supply and demand, with no substitution between ranges. Preferred habitat is a middle view. Investors prefer a maturity range but will move for extra yield, so premiums arise when supply and demand are unbalanced. Only pure expectations implies that the maturity mix of debt supply has no effect on the term structure.

A practice question

From the question bank, with the reason each wrong option is wrong.

According to the pure expectations theory of the term structure, which statement is correct?

  1. Long-term rates are determined by expected future short-term rates, so forward rates equal expected future spot rates - correct
  2. Long-term rates include a premium that rewards investors for tying up money for longerWhy not: This is the liquidity preference theory; pure expectations has no term premium.
  3. Rates at each maturity are set independently by supply and demand in that maturity segmentWhy not: This is market segmentation, where maturities are not linked through expectations.
  4. Investors prefer a particular maturity but will move out of it if offered enough extra yieldWhy not: This is the preferred habitat theory, which adds a premium for leaving a habitat.

Under pure expectations the yield curve is a statement about expected future short rates: an upward-sloping curve means short rates are expected to rise and a downward-sloping one means they are expected to fall. Forward rates are unbiased predictors of future spot rates.

A harder one

The 1-year spot rate is 2.5% and the 2-year spot rate is 3.2%, annually compounded. Under pure expectations theory, the market's expected 1-year rate one year from now is closest to:

  1. 3.20%Why not: Takes the 2-year spot rate as the expected future 1-year rate.
  2. 3.90% - correct
  3. 0.70%Why not: Subtracts the 1-year spot rate from the 2-year spot rate.
  4. 2.85%Why not: Averages the two spot rates rather than solving for the forward rate.

Under pure expectations the forward rate equals the expected spot rate: (1.032)²/1.025 - 1 = 3.90%.

The hardest tier

The 1-year spot rate is 2.5% and the 2-year spot rate is 3.2%, annually compounded. Under liquidity preference theory, investors demand a 0.50 percentage point premium on the second year. The expected 1-year rate one year from now is closest to:

  1. 3.90%Why not: Ignores the liquidity premium and treats the forward rate as the expected rate, as in pure expectations.
  2. 4.40%Why not: Adds the premium to the forward rate; the forward rate already includes the premium, so the expected rate is lower.
  3. 3.40% - correct
  4. 2.70%Why not: Subtracts the premium from the 2-year spot rate rather than from the forward rate.

Forward rate = 1.032²/1.025 - 1 = 3.90%. Under liquidity preference, forward rate = expected future spot rate + premium, so expected = 3.90% - 0.50% = 3.40%.

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