Expectations Hypothesis and Term Structur Flashcards
What is the term structure of interest rates?
It is the relationship between the yields on risk-free bonds and their maturities. This relationship is usually visualized via the yield curve.
What shapes can the yield curve have, and what do they imply?
Upward sloping: market expects rates to rise, or risk premium is demanded.
Flat: market expects stable rates.
Inverted: market expects rates to fall (recession signal)
What is the Expectations Hypothesis (EH) of the term structure?
It states that the yield on a long-term bond equals the average of current and expected future short-term interest rates. It assumes investors are risk-neutral and that there are no risk or liquidity premiums.
What is the formula for the Expectations Hypothesis?
r(t,T) = Average of the current rate and expected short-term rates
Under EH, how is the forward rate related to future spot rates?
Under EH, the forward rate equals the expected future spot rate.
Why does the Expectations Hypothesis fail empirically?
Because in real life, investors are risk-averse, not risk-neutral. Future short rates are uncertain. Long-term bonds have interest rate risk so investors demand a risk premium, and there are convexity effects in the price-yield relation that are not covered by EH.
What is the risk premium in the term structure context?
It is the extra yield that investors require to hold long-term bonds instead of rolling over short-term bonds because long-term bonds carry higher risk.
What is convexity in bond pricing?
It refers to the curvature in the bond price-yield relationship. Higher interest rate volatility increases bond prices due to convexity. This leads to a small downward adjustment in yields.
Why is the yield curve typically upward sloping?
Expectations Effect: Market expects short-term rates to rise.
Risk Premium Effect: Long-term bonds are riskier so investors demand higher yield.
Convexity Effect: Higher rate uncertainty increases bond prices, which lowers yields slightly.
What are the three components in the full term structure model?
Expected Future Short Term Rates
Risk Premium
Convexity
What is Inflation Risk in fixed income?
The risk that the purchasing power of nominal bond payments decreases due to rising inflation.
What is a Treasury Inflation Protected Security (TIPS)?
A US Government bond where the principal is adjusted for inflation (CPI). Coupons are a fixed % of the adjusted principal - both coupon payments and principal grow with inflation.
How is a TIPS coupon payment calculated?
Coupon Payment = 0.5 * Coupon Rate * 100 * Index Ratio, which is the change in CPI
What is the Real Discount Factor?
The discount factor derived from the Real Interest Rate
What is Break-Even Inflation?
The difference between the nominal and real yields: r(t,T) - r real(t,T)
It reflects the average expected inflation rate over the bond’s life.
Is the break-even inflation rate a perfect measure of expected inflation?
No because it includes the expected inflation, inflation risk premium and TIPS liquidity premium.
r(t,T) - rTIPS(t,T) = Expected Inflation + Inflation Risk Premium - Liquidity Premium
What is the TIPS liquidity premium?
The extra yield investors demand to compensate for lower liquidity of TIPS compared to nominal bonds, it reduces the break-even inflation rate.
Which model is used to fit the real yield curve?
Nelson-Siegel
What factors complicate the relation between nominal and real yields?
Inflation risk premium
TIPS liquidity premium
Uncertainty about future inflation
Why does convexity lead to a lower adjustment of yields in an environment with high volatility?
Because of convexity, high volatility leads to an increase in prices. This is because if the rates fall hard, the bond prices will increase harder. If the rates increase hard, the bond prices will fall less hard. Therefore, on average, the bond prices increase which lowers the yields.
