Relative Valuation and Bond Pricing

Relative Valuation

• In relative valuation, asset prices are compared to market prices of similar assets.
• Market prices are standardized to create price multiples.

Bond Pricing

• As time to maturity decreases, bond price increases or decreases (contradictory statements).
• When yield to maturity (YTM) decreases, bond price increases, decreasing effective annual return.
• When YTM increases, bond price decreases, increasing effective annual return.

Risks

Reinvestment Risk

• Occurs when interest rates decrease (bond prices are at a premium).
• Good for investors if yields increase, bad if yields decrease.

Price Risk

• Occurs when interest rates increase (bond price is low).
• Good for investors if yields decrease, bad if yields increase.
• Investors only subject to price risk if they need to sell before maturity.

Inflation Risk

• Inflation causes bond prices to decrease, decreasing returns.
• Investors subject to price risk are affected.

Liquidity Risk

• Occurs when investors need to sell bonds before maturity at a discounted price due to high yields and low prices.

Pure Expectations Theory

• Assumes current yield curve reflects investors' expectations of future short-term interest rates.
• Predicts future short-term rates based on current long-term rates.
• Long-term interest rates are determined by expected future short-term interest rates.

Yield Curve

Normal - Upward Sloping

• Short-term yields are lower than long-term yields.
• Investors expect stronger economic growth and higher inflation in the future.
• Higher yields are demanded for long-term bonds due to higher uncertainty and inflation risk.

Inverted - Downward Sloping

• Short-term yields are higher than long-term yields.
• Investors expect slower economic growth or recession in the future.
• Lower returns are expected for long-term bonds due to lower uncertainty and inflation risk.

Liquidity Preference Theory

• Investors are compensated for time and take on more risk with longer-term investments.
• Reinvestment risk is a concern for investors who don't need to sell, while price risk is a concern for those who need to sell.

Market Segmentation Theory

• Investors have a preferred time frame for investments.
• Supply and demand shift yields for each market segment.

Preferred Habitat Theory

• Investors have preferred time maturities, but may take other opportunities.
• Preferences include investment duration, price risk tolerance, and more.

Macaulay's Duration

• Measures a bond's price sensitivity to interest rate changes.
• Duration increases with time to maturity (TTM) and decreases with coupon rate and YTM.
• Properties: Dmac ≤ TTM, Dmac increases with lower Crate and YTM, and higher TTM.

Implications of Duration

• Positive relationship between duration and price sensitivity to interest rate changes.
• Positive relationship between TTM and duration.
• Negative relationship between coupon rate and duration.
• Two bonds with the same Dmod have the same percentage price change sensitivity to yields.

Convexity

• Measures the sensitivity of a bond's duration to interest rate changes.
• Captures the non-linear relationship between a bond's price and yield.
• Properties: convexity increases with lower Crate and YTM, and higher TTM.
• More convexity means more curvature, which is desirable for investors.

Summary of Duration and Convexity

• Positive relationship between duration and convexity.
• Convexity is good, providing more gains when yields decrease and fewer losses when yields increase.
• Duration increases with TTM, but investors want more convexity without more duration.

Relative Valuation

• Relative valuation involves comparing the price of an asset to the prices of similar or comparable assets.
• Market prices are standardized to create price multiples.

Bond Pricing

• Bond price decreases as time to maturity decreases.
• Bond price increases as time to maturity increases.
• When yield to maturity (YTM) decreases, bond price increases, reducing the effective annual return.
• When YTM increases, bond price decreases, increasing the effective annual return.

Risks

Reinvestment Risk

• Occurs when interest rates decrease and bond prices are at a premium.
• Investors can reinvest coupons at the market yield.

Price Risk

• Occurs when interest rates increase and bond prices are low.
• Investors are only subject to price risk if they need to sell before maturity.

Inflation Risk

• Inflation causes bond prices to decrease, ultimately decreasing the return of bonds.

Liquidity Risk

• Occurs when investors need to sell their bond before maturity and cannot liquidate it at a reasonable price.
• Investors may have to sell at a discounted price.

Pure Expectations Theory

• Assumes the current yield curve solely reflects investors' expectations of future short-term interest rates.
• Predicts future short-term rates based on current long-term rates.
• If the market anticipates short-term rates will increase, the yield curve will slope upwards.
• If the market anticipates short-term rates will decrease, the yield curve will slope downwards.

Yield Curve

Normal (Upward Sloping)

• Short-term yields are lower than long-term yields.
• Long-term bonds have higher yields compared to short-term bonds.
• Indicates that investors expect stronger economic growth and potentially higher inflation in the future.

Inverted (Downward Sloping)

• Short-term bonds have higher yields compared to long-term bonds.
• Indicates that investors expect slower economic growth or a recession in the future.

Liquidity Preference Theory

• Investors are compensated for time but get extra if they invest for longer.
• Investors take more risk for longer-term investments.

Market Segmentation Theory

• Investors will never change their preference and will only invest in a bond for a certain time frame.
• Supply and demand shift the yield for each market segment.

Preferred Habitat Theory

• Investors have preferred time maturity to bonds, but may take other opportunities if available.
• Preference is based on investment duration, price risk, or tolerance.

Macaulay's Duration

• Measures the sensitivity of a bond's price to changes in interest rates.
• Duration is a measure of price risk.
• Properties:
  • Duration is less than or equal to time to maturity (TTM).
  • Duration is higher for bonds with lower coupon rates.
  • Duration is higher for bonds with lower YTM.
  • Duration is higher for bonds with higher TTM.

Implications of Duration

• Positive relationship between a bond's duration and price sensitivity to interest rate changes.
• Positive relationship between TTM and duration.
• Negative relationship between coupon rate and duration.
• Two bonds with the same duration have the same percentage price change sensitivity to yields.

Convexity

• Measures the sensitivity of a bond's duration to changes in interest rates.
• Captures the non-linear relationship between a bond's price and yield.
• Properties:
  • Convexity is higher for bonds with lower coupon rates.
  • Convexity is higher for bonds with lower YTM.
  • Convexity is higher for bonds with higher TTM.

Summary of Duration and Convexity

• Duration and convexity have a positive relationship.
• Convexity is beneficial for investors.
• Duration increases interest rate risk, while convexity reduces price changes in response to interest rate movements.
• Investors want more convexity, but it requires taking on more duration.

Relative Valuation

• The price of an asset is compared to the prices of similar or comparable assets in the market.
• Market prices are standardized to create price multiples.

Bond Pricing

• As time to maturity decreases, bond price increases.
• As time to maturity increases, bond price decreases.
• When yield to maturity (YTM) decreases, the bond price increases, decreasing the effective annual return.
• When YTM increases, the bond price decreases, increasing the effective annual return.

Risks Associated with Bonds

Reinvestment Risk

• Occurs when interest rates go down, and bond prices are at a premium.
• Investors can reinvest coupons at the market yield, benefiting from increasing yields.

Price Risk

• Occurs when interest rates go up, and bond prices are low.
• Investors are only subject to price risk if they need to sell before maturity.
• Decreasing yields benefit investors, while increasing yields harm them.

Inflation Risk

• Inflation causes bond prices to decrease, ultimately decreasing the return of bonds.

Liquidity Risk

• Investors may suffer a loss if they need to sell their bond before maturity.
• They may not be able to liquidate their bond at a reasonable price, especially if yields are high and the price has dropped.

Pure Expectations Theory

• The current yield curve reflects investors' expectations of future short-term interest rates.
• Long-term interest rates are determined by the market's expectation of future short-term interest rates.

Yield Curve

Normal - Upward Sloping

• Short-term yields are lower than long-term yields.
• Long-term bonds have higher yields compared to short-term bonds.
• An upward-sloping yield curve indicates that investors expect stronger economic growth and potentially higher inflation in the future.

Inverted - Downward Sloping

• Short-term bonds have higher yields compared to long-term bonds.
• An inverted yield curve suggests that investors expect slower economic growth or a recession in the future.

Liquidity Preference Theory

• Investors are compensated for time and take on more risk.
• Reinvestment risk is a concern if interest rates decrease.
• Price risk is a concern if interest rates increase.

Market Segmentation Theory

• Investors will never change their preference and only invest in bonds with specific time frames.

Preferred Habitat Theory

• Investors have preferred time maturity for bonds, but may take other opportunities if available.

Macaulay's Duration

• Measures the sensitivity of a bond's price to changes in interest rates.
• Duration looks at price risk; if yields increase, price decreases.
• Properties: • Dmac is less than or equal to TTM • Dmac is higher for bonds with lower Crate (all else equal) • Dmac is higher for bonds with lower YTM (all else equal) • Dmac is higher for bonds with higher TTM (all else equal)

Implications of Duration

• Positive relationship between a bond's duration and price sensitivity to interest rate changes.
• Positive relationship between Time to Maturity (TTM) and Duration.
• Negative relationship between the coupon rate and duration.

Convexity

• Measures the sensitivity of a bond's duration to changes in interest rates.
• Captures the non-linear relationship between a bond's price and yield.
• Properties: • Convexity is higher for bonds with lower Crate (all else equal) • Convexity is higher for bonds with lower YTM (all else equal) • Convexity is higher for bonds with higher TTM (all else equal)

Summary of Duration and Convexity

• Duration and Convexity have a positive relationship.
• Convexity is beneficial as it provides more gains when yields decrease and fewer losses when yields increase.
• Duration increases interest rate risk, while Convexity reduces it.