Finance Chapter: Relative Valuation

Relative Valuation

• Compares the price of an asset to similar or comparable assets in the market
• Market prices are converted into standardized prices, creating price multiples

Advantages of Relative Valuation

• Easier to justify buying or selling decisions using relative valuation
• Quicker and requires fewer assumptions about the future compared to discounted cash flow valuation
• More likely to reflect market perceptions and moods

Median Preference in Relative Valuation

• Median is a more reliable comparison point than the mean
• Median is unaffected by extreme outliers or non-symmetric distributions of scores
• Generally a better representation of the true average if the sample has outliers

Issues in Relative Valuation

Choice of Comparable

• Selecting appropriate comparable is subjective and can significantly affect the valuation
• Inaccurate valuation if chosen comparable are not truly similar to the asset being valued

Market Conditions

• Market conditions can influence the prices of comparable
• Valuations based on comparable might reflect temporary market conditions rather than the intrinsic value of the asset

Differences in Growth Rates

• Companies or assets with different growth rates might be compared
• High-growth companies may appear overvalued compared to low-growth companies, leading to misleading conclusions

Scale and Size of Companies

• Comparable may differ significantly in scale and size
• Smaller companies might trade at different multiples compared to larger companies, leading to valuation discrepancies

Limitations of Regression Analysis

• Non-linearity: assumes a linear relationship between the multiple and its fundamentals
• Non-stationarity: the relationship between the multiple used and the financial variables may not be stable
• Multi-collinearity: independent variables are correlated with each other, making coefficients unreliable

Bonds

• Bonds are used by corporations and governments to raise long-term capital.
• When investing in bonds, the initial cost is paid, and then coupon (interest) is received periodically.
• When the bond matures, the face value is returned.
• Types of bonds include:
  • Zero-coupon bonds: no coupon payments during the bond's life, only face value at maturity.
  • Convertible bonds: can be converted into a predetermined number of stocks in the future.
  • Indexed bonds: coupon rate is related to movements in inflation.
  • Callable bonds: the seller can buy the bond back from the buyer in the future.
  • Perpetual bonds: last forever.
  • Treasury bonds: issued by the federal government.
  • Municipal bonds: issued by state governments or government agencies.

Bond Pricing and YTM

• YTM (Yield to Maturity) reflects the market's required return on the bond.
• If market return > coupon rate, bond price drops (discount).
• If market return < coupon rate, bond price increases (premium).
• Changes in market interest rates affect YTM, leading to changes in bond prices.

Relationship Between YTM, Coupon Rate, and Time to Maturity

• Premium bond:
  • Coupon rate > YTM, sold at price above face value.
  • As time to maturity decreases, bond price decreases.
  • As time to maturity increases, bond price increases.
• Discount bond:
  • Coupon rate < YTM, sold at price below face value.
  • As time to maturity decreases, bond price increases.
  • As time to maturity increases, bond price decreases.

Characteristics of Bonds

• Par value bond: coupon rate = YTM.
• Discount bond: coupon rate < YTM.
• Premium bond: coupon rate > YTM.

Strips

• Strips are separate trading of registered interest and principal securities.
• Investors can sell components of their bonds.
• Generally common in Treasury bonds.
• The total PV of interest and principal cash flows should equal the bond's face value price.

Arbitrage

• If PV bond = PV of all strips: no arbitrage opportunities.
• If PV bond > PV of all strips: arbitrage opportunities present, market is inefficient.
• If PV bond < PV of all strips: arbitrage opportunities present, market is inefficient.

Risks

• Reinvestment risk: occurs when interest rates go down (bond prices are at a premium).
  • Investors can reinvest coupons at market yield.
• Price risk: occurs when interest rates go up (bond price is low).
  • Investors are only subject to price risk if they need to sell before maturity.
• Inflation risk: inflation causes bond prices to decrease, affecting return on bonds.
• Liquidity risk: suffers loss if desperately needing to sell bond before maturity at a reasonable price.

Bonds

• Bonds are used by corporations and governments to raise long-term capital.
• When investing in bonds, the initial cost is paid, and then coupon (interest) is received periodically.
• When the bond matures, the face value is returned.
• Types of bonds include:
  • Zero-coupon bonds: no coupon payments during the bond's life, only face value at maturity.
  • Convertible bonds: can be converted into a predetermined number of stocks in the future.
  • Indexed bonds: coupon rate is related to movements in inflation.
  • Callable bonds: the seller can buy the bond back from the buyer in the future.
  • Perpetual bonds: last forever.
  • Treasury bonds: issued by the federal government.
  • Municipal bonds: issued by state governments or government agencies.

Bond Pricing and YTM

• YTM (Yield to Maturity) reflects the market's required return on the bond.
• If market return > coupon rate, bond price drops (discount).
• If market return < coupon rate, bond price increases (premium).
• Changes in market interest rates affect YTM, leading to changes in bond prices.

Relationship Between YTM, Coupon Rate, and Time to Maturity

• Premium bond:
  • Coupon rate > YTM, sold at price above face value.
  • As time to maturity decreases, bond price decreases.
  • As time to maturity increases, bond price increases.
• Discount bond:
  • Coupon rate < YTM, sold at price below face value.
  • As time to maturity decreases, bond price increases.
  • As time to maturity increases, bond price decreases.

Characteristics of Bonds

• Par value bond: coupon rate = YTM.
• Discount bond: coupon rate < YTM.
• Premium bond: coupon rate > YTM.

Strips

• Strips are separate trading of registered interest and principal securities.
• Investors can sell components of their bonds.
• Generally common in Treasury bonds.
• The total PV of interest and principal cash flows should equal the bond's face value price.

Arbitrage

• If PV bond = PV of all strips: no arbitrage opportunities.
• If PV bond > PV of all strips: arbitrage opportunities present, market is inefficient.
• If PV bond < PV of all strips: arbitrage opportunities present, market is inefficient.

Risks

• Reinvestment risk: occurs when interest rates go down (bond prices are at a premium).
  • Investors can reinvest coupons at market yield.
• Price risk: occurs when interest rates go up (bond price is low).
  • Investors are only subject to price risk if they need to sell before maturity.
• Inflation risk: inflation causes bond prices to decrease, affecting return on bonds.
• Liquidity risk: suffers loss if desperately needing to sell bond before maturity at a reasonable price.

Bonds

• Bonds are issued by corporations and governments to raise long-term capital.
• Investors pay the initial cost (face value) and receive periodic interest (coupon) and the face value back when the bond matures.
• Types of bonds include:
  • Zero-coupon bonds: no coupon payments, only face value at maturity.
  • Convertible bonds: can be converted into a predetermined number of stocks.
  • Indexed bonds: rate of return is affected by inflation.
  • Callable bonds: seller can buy the bond back from the investor.
  • Perpetual bonds: last forever.
  • Treasury bonds: issued by the federal government.
  • Municipal bonds: issued by state governments or government agencies.

Bond Pricing and YTM

• YTM (Yield to Maturity) reflects the market's required return on the bond.
• If YTM is higher than the coupon rate, the bond's price drops (discount).
• If YTM is lower than the coupon rate, the bond's price increases (premium).
• Changes in market interest rates affect YTM:
  • When interest rates rise, YTM increases, and bond prices fall.
  • When interest rates fall, YTM decreases, and bond prices rise.

Relationship Between YTM, Coupon Rate, and Time to Maturity

• Premium bonds: sold at a price above face value if coupon rate is higher than YTM.
• Discount bonds: sold at a price below face value if coupon rate is lower than YTM.
• Characteristics of bonds:
  • Par value bond: coupon rate equals YTM.
  • Discount bond: coupon rate is less than YTM.
  • Premium bond: coupon rate is greater than YTM.

Strips

• Strips are separate trading of registered interest and principal securities.
• Investors can sell components of their bonds.
• Strips are common in Treasury bonds.
• The total PV of interest and principal cash flows should equal the bond's face value price.

Arbitrage

• If PV Bond = PV of all Strips, no arbitrage opportunities are present.
• If PV Bond > PV of all Strips, arbitrage opportunities are present.
• If PV Bond < PV of all Strips, arbitrage opportunities are present.

Risks

• Reinvestment risk: occurs when interest rates go down (bond prices are at a premium).
• Price risk: occurs when interest rates go up (bond price is low).
• Inflation risk: inflation causes bond prices to decrease, ultimately decreasing the return.
• Liquidity risk: investors suffer a loss if they need to sell their bond before maturity at a discounted price.

Pure Expectations Theory

• The current yield curve solely reflects investors' expectations of future short-term interest rates.
• The theory predicts future short-term rates (forward rates) based on current long-term rates.
• If the market anticipates short-term rates will increase (decrease) in the future, the yield curve will slope upwards (downwards).
• Long-term interest rates are determined by the market's expectation of future short-term interest rates (forward rates).

Yield Curve Shape

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 typically suggests that investors expect stronger economic growth and potentially higher inflation in the future.
• Investors demand higher yields for long-term bonds to compensate for risks.
• It indicates that market participants expect interest rates to rise 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.
• Investors prefer long-term bonds to lock in current yields, anticipating that interest rates will fall due to economic weakness.
• It indicates that market participants expect interest rates to decrease in the future.

Flat Yield Curve

• Rarely seen, only occurs when the economy is changing.
• A flat curve indicates a transition from an upward or downward sloping curve.

Discount Factors/Spot Rates/Forward Rates

• Discount Factors are determined from the market price and cashflows of a bond.
• Spot rates are obtained from discount factors and used to create a yield curve.
• Forward rates are market expectations of interest rates in the future.
• Comparing forward rates to spot rates indicates what the market thinks will happen in the future.
• Use spot rate vs forward rate curve to understand market expectations.
• Short-term bonds have less interest rate risk, while long-term bonds are more sensitive to risk.
• Changes in interest rates affect bond prices: up = down, and vice versa.

Arbitrage Opportunity - Negative Rates

• A negative rate implies mispricing.
• Buy underpriced bonds and sell overpriced bonds to take advantage of the opportunity.

Interest Rates

High Interest Rates

• Decrease in bond prices, providing an opportunity for investors.

Low Interest Rates

• Increase in bond price, making them more valuable.
• The shape of the yield curve is determined by market expectations of future interest rate movements.

Liquidity Preference Theory

• Investors are compensated for time, but also take on more risk.
• Reinvestment risk occurs when interest rates decrease, resulting in higher bond prices.
• Price risk occurs when interest rates increase, resulting in lower bond prices.

Market Segmentation Theory

• Investors have fixed preferences and only invest in bonds with specific time frames.
• 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.
• Preferences include investment duration, price risk, or tolerance.

Pure Expectations Theory

• The current yield curve solely reflects investors' expectations of future short-term interest rates.
• The theory predicts future short-term rates (forward rates) based on current long-term rates.
• If the market anticipates short-term rates will increase (decrease) in the future, the yield curve will slope upwards (downwards).
• Long-term interest rates are determined by the market's expectation of future short-term interest rates (forward rates).

Yield Curve Shape

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 typically suggests that investors expect stronger economic growth and potentially higher inflation in the future.
• Investors demand higher yields for long-term bonds to compensate for risks.
• It indicates that market participants expect interest rates to rise 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.
• Investors prefer long-term bonds to lock in current yields, anticipating that interest rates will fall due to economic weakness.
• It indicates that market participants expect interest rates to decrease in the future.

Flat Yield Curve

• Rarely seen, only occurs when the economy is changing.
• A flat curve indicates a transition from an upward or downward sloping curve.

Discount Factors/Spot Rates/Forward Rates

• Discount Factors are determined from the market price and cashflows of a bond.
• Spot rates are obtained from discount factors and used to create a yield curve.
• Forward rates are market expectations of interest rates in the future.
• Comparing forward rates to spot rates indicates what the market thinks will happen in the future.
• Use spot rate vs forward rate curve to understand market expectations.
• Short-term bonds have less interest rate risk, while long-term bonds are more sensitive to risk.
• Changes in interest rates affect bond prices: up = down, and vice versa.

Arbitrage Opportunity - Negative Rates

• A negative rate implies mispricing.
• Buy underpriced bonds and sell overpriced bonds to take advantage of the opportunity.

Interest Rates

High Interest Rates

• Decrease in bond prices, providing an opportunity for investors.

Low Interest Rates

• Increase in bond price, making them more valuable.
• The shape of the yield curve is determined by market expectations of future interest rate movements.

Liquidity Preference Theory

• Investors are compensated for time, but also take on more risk.
• Reinvestment risk occurs when interest rates decrease, resulting in higher bond prices.
• Price risk occurs when interest rates increase, resulting in lower bond prices.

Market Segmentation Theory

• Investors have fixed preferences and only invest in bonds with specific time frames.
• 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.
• Preferences include investment duration, price risk, or tolerance.

Macaulay's Duration

• Measures a bond's price sensitivity to changes in interest rates (yields)
• Duration increases as Time to Maturity (TTM) increases, exposing the bond to more price risk
• Properties:
  • Less than or equal to TTM
  • Higher for bonds with lower coupon rates (all else equal)
  • Higher for bonds with lower Yield to Maturity (YTM) (all else equal)
  • Higher for bonds with higher TTM (all else equal)

Modified Duration

• Adjusts Macaulay's Duration for a bond's yield
• Represents a percentage change in a bond's price
• Example: Dmod of 2.23 means a 1% increase (decrease) in yield results in a 2.23% decrease (increase) in bond price

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 modified duration have the same percentage price change sensitivity to yields
• Duration represents a negative linear relationship, with small changes having little impact but larger changes affecting the yield curve

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:
  • Higher for bonds with lower coupon rates (all else equal)
  • Higher for bonds with lower YTM (all else equal)
  • Higher for bonds with higher TTM (all else equal)
• Convexity accounts for the curvature of the yield curve, providing a more accurate estimate of price changes
• The more convexity, the less price change when yields increase, and more price change when yields decrease

Summary of Duration and Convexity

• Duration and Convexity have a positive relationship
• Convexity is desirable, as it provides more gains when yields decrease and less losses when yields increase
• Duration increases interest rate risk, while convexity reduces it
• To achieve more convexity, one must invest in longer bonds, which increases duration.

Macaulay's Duration

• Measures a bond's price sensitivity to changes in interest rates (yields)
• Duration increases as Time to Maturity (TTM) increases, exposing the bond to more price risk
• Properties:
  • Less than or equal to TTM
  • Higher for bonds with lower coupon rates (all else equal)
  • Higher for bonds with lower Yield to Maturity (YTM) (all else equal)
  • Higher for bonds with higher TTM (all else equal)

Modified Duration

• Adjusts Macaulay's Duration for a bond's yield
• Represents a percentage change in a bond's price
• Example: Dmod of 2.23 means a 1% increase (decrease) in yield results in a 2.23% decrease (increase) in bond price

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 modified duration have the same percentage price change sensitivity to yields
• Duration represents a negative linear relationship, with small changes having little impact but larger changes affecting the yield curve

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:
  • Higher for bonds with lower coupon rates (all else equal)
  • Higher for bonds with lower YTM (all else equal)
  • Higher for bonds with higher TTM (all else equal)
• Convexity accounts for the curvature of the yield curve, providing a more accurate estimate of price changes
• The more convexity, the less price change when yields increase, and more price change when yields decrease

Summary of Duration and Convexity

• Duration and Convexity have a positive relationship
• Convexity is desirable, as it provides more gains when yields decrease and less losses when yields increase
• Duration increases interest rate risk, while convexity reduces it
• To achieve more convexity, one must invest in longer bonds, which increases duration.