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CFA® Level II · Fixed Income · free lesson
The Term Structure and Interest Rate Dynamics
The yield curve is the starting point for valuing every bond and for every active fixed income decision. This module links spot rates, forward rates, par yields and realised returns, shows how managers use forward rates as a hurdle and ride the curve, explains the swap curve and short-term funding spreads, compares the theories that explain the curve's shape, measures exposure to level, slope and curvature, and turns economic views into duration, curve and convexity positions. Level II vignettes combine bootstrapping, forward rates, holding-period returns and key rate durations.
What you will learn
1. Relate spot rates, forward rates, yields to maturity and realised returns, and bootstrap spot rates from par rates.
- Spot rates discount single cash flows; forward rates link spot rates: (1 + z_(j+k))^(j+k) = (1 + z_j)^j [1 + f(j,k)]^k.
- Upward-sloping spot curve implies forward rates above spot rates.
- Bootstrap spot rates from par rates one maturity at a time, using earlier spot rates for earlier coupons.
- YTM equals the realised return only if held to maturity, paid in full and coupons reinvested at the YTM.
- Price bonds with spot rates; YTM is a summary of them.
2. Explain rolling down the yield curve and how active managers use forward rates as a break-even hurdle.
- If future spot rates equal today's forwards, all bonds earn the same short-term rate over the period.
- Expect future spot rates below forwards: buy bonds maturing after the horizon; above forwards: stay short.
- Riding the curve: with a stable, upward-sloping curve, a bond's yield falls as it ages, adding a price gain.
- Return from riding the curve exceeds the initial YTM only if the curve does not rise or flatten.
- The strategy relies on the curve's slope reflecting a term premium, not just expected rate increases.
3. Explain the swap curve, swap spreads and short-term credit and liquidity spreads, and why market participants use them.
- Swap rate = fixed rate that gives a swap zero value at inception; swap rates form the swap curve.
- Swap curves are liquid, available at many maturities and free of government-bond supply effects.
- Swap spread = swap rate - government yield; I-spread = bond yield - swap rate; G-spread = bond yield - government yield.
- TED spread (unsecured bank rate - T-bill) and MRR-OIS spread measure bank credit and funding stress.
- Long-dated US dollar swap spreads have been negative since 2008.
4. Compare traditional term structure theories and measure a portfolio's exposure to level, slope and curvature shifts with effective and key rate durations.
- Pure expectations: forwards = expected spot rates; local expectations: equal returns over short horizons only.
- Liquidity preference: term premium makes forwards exceed expected spot rates.
- Segmented markets: separate supply and demand by maturity; preferred habitat: investors move for a premium.
- Level, slope and curvature explain most curve moves; level dominates.
- Estimated % price change = -sum(KRD_i x change in rate_i); KRDs sum to effective duration.
5. Explain how yield volatility varies by maturity and how economic views translate into duration, curve and convexity positioning.
- Short-term yields are usually more volatile than long-term yields; long-end volatility can spike in stress.
- Expect lower yields: extend duration; expect higher yields: shorten it.
- Steepening view: long short maturities, short long maturities (duration-neutral); flattening: the reverse.
- Barbells have more convexity than bullets of equal duration and gain from large moves.
- Low expected volatility favours selling convexity (callables, MBS); high volatility favours buying it.
Module at a glance
- Forward rates link spot rates: (1 + z_(j+k))^(j+k) = (1 + z_j)^j [1 + f(j,k)]^k; bootstrap spot rates from par rates.
- YTM equals the realised return only if held to maturity with coupons reinvested at the YTM.
- Forward rates are the break-even path: expect lower future rates than the forwards and extend maturity.
- Riding a stable, upward-sloping curve earns more than the initial yield.
- Swap spread = swap rate - government yield; I-spread is measured against swaps; MRR-OIS and TED spreads gauge bank stress.
- Pure expectations, liquidity preference, segmented markets and preferred habitat explain curve shape differently.
- Key rate durations show exposure to level, slope and curvature; barbells add convexity, steepeners and flatteners express slope views.
This free module has 5 lessons, 16 practice questions with full explanations.