Relative Valuation in Finance

Relative Valuation

• In relative valuation, an asset's price is compared to the prices of similar or comparable assets
• Market prices are standardized to create price multiples
• Reasons for popularity: easier to justify and reflects market perceptions and moods
• Median is preferred over mean due to its reliability and resistance to extreme outliers

Issues in Relative Valuation

• Choice of comparables: subjective selection can significantly affect valuation
• Market conditions: can influence prices of comparables and lead to inaccurate valuations
• Differences in growth rates: comparing companies with different growth rates can be misleading
• Scale and size of companies: comparing companies of different sizes can lead to valuation discrepancies

Bonds

• Bonds raise long-term capital for corporations and governments
• Investors pay the initial cost, receive coupon (interest) periodically, and face value when the bond matures
• Types of bonds: convertible, indexed, callable, perpetual, treasury, and municipal
• Bond pricing and YTM: YTM reflects market's required return on the bond

Yield to Maturity (YTM)

• If market requires higher return than coupon rate, bond price drops (discount)
• If market requires lower return than coupon rate, bond price increases (premium)
• Changes in market interest rates affect YTM and bond prices
• Relationship between YTM, coupon rate, and time to maturity:
  • Bond price increases when YTM decreases
  • Bond price decreases when YTM increases
  • Bond price increases as time to maturity increases
  • Bond price decreases as time to maturity decreases

Characteristics of Bonds

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

Pure Expectations Theory

• Assumes yield curve reflects investors' expectations of future short-term interest rates
• Long-term interest rates determined by market's expectation of future short-term interest rates (forward rates)
• Investors indifferent between holding short-term or long-term securities with the same total return

Yield Curve Shape

• Normal (upward sloping): long-term bonds have higher yields, indicating expectations of stronger economic growth and inflation
• Inverted (downward sloping): short-term bonds have higher yields, indicating expectations of slower economic growth or recession
• Flat yield curve: rarely seen, indicates changes in the economy

Discount Factors, Spot Rates, and Forward Rates

• Discount factor: determined from market price and cash flows of a bond
• Forward rates: market expectations of interest rates in the future
• Comparing forward rates to spot rates indicates market expectations of future interest rate changes
• Short-term bonds have less interest rate risk, while long-term bonds are more sensitive to risk

High and Low Interest Rates

• High interest rates: decrease in bond prices, providing an opportunity for investors
• Low interest rates: increase in bond price, making bonds more valuable
• Shape of yield curve determined by market expectations of future interest rate movements

Liquidity Preference Theory

• Investors are compensated for time and take on more risk when investing for longer periods
• Liquidity preference theory assumes current yield curve reflects investors' expectations of future short-term interest rates and their preference for liquidity
• Investors prefer shorter-term securities, which are exposed to less interest rate risk, and require a premium for investing in long-term securities with higher risk

Relative Valuation

• Relative valuation compares the price of an asset to the prices of similar or comparable assets.
• Market prices are converted into standardized prices, creating price multiples.
• Reasons for popularity:
  • Easier to justify using relative valuation.
  • More likely to reflect market perceptions and moods.
  • Advantage when market perceptions are important.
• Median is preferred over mean:
  • Median is a more reliable comparison point.
  • Median is unaffected by extreme outliers or non-symmetric distributions.
  • Median is a better representation of the true average with outliers.

Issues in Relative Valuation

• Choice of comparables:
  • Selecting appropriate comparables is subjective and affects valuation.
  • Inaccurate valuation if comparables are not similar.
• Market conditions:
  • Market conditions influence prices of comparables.
  • Valuations may reflect temporary market conditions rather than intrinsic value.
• Differences in growth rates:
  • Comparing companies with different growth rates.
  • High-growth companies may appear overvalued compared to low-growth companies.
• Scale and size of companies:
  • Comparables may differ significantly in scale and size.
  • Smaller companies may trade at different multiples compared to larger companies.

Non-linearity Regression

• Assumes a linear relationship between the multiple and its fundamentals.
• Issues:
  • Non-stationarity: relationship between multiple and financial variables may not be stable.
  • Multi-collinearity: independent variables are correlated, making coefficients unreliable.

Bonds

• Issued by corporations and governments to raise long-term capital.
• Bond characteristics:
  • Par value: coupon rate equals yield to maturity (YTM).
  • Discount bond: coupon rate is less than YTM.
  • Premium bond: coupon rate is greater than YTM.

Bond Pricing and YTM

• YTM reflects the market's required return on the bond.
• Bond price changes:
  • If market requires a higher return than the bond's coupon rate, bond price drops.
  • If market requires a lower return than the bond's coupon rate, bond price increases.
• Interest rate changes:
  • When market interest rates rise, YTM increases, and bond prices fall.
  • When market interest rates fall, YTM decreases, and bond prices rise.

Relationship Between YTM, Coupon Rate, and Time to Maturity

• (Expensive/Premium) Bond:
  • If coupon rate is higher than YTM, bond is sold at a price above face value.
  • As time to maturity decreases, bond price decreases.
  • As time to maturity increases, bond price increases.
• (Cheaper/Discount) Bond:
  • If coupon rate is lower than YTM, bond is sold at a price below face value.
  • As time to maturity decreases, bond price increases.
  • As time to maturity increases, bond price decreases.

Pure Expectations Theory

• Assumes current yield curve reflects investors' expectations of future short-term interest rates.
• Long-term interest rates are determined by market expectations of future short-term interest rates.
• Investors are indifferent between holding short-term or long-term securities, provided the same total return is given over the same investment period.

Yield Curve Shapes

• Normal (Upward Sloping):
  • Long-term bonds have higher yields compared to short-term bonds.
  • Investors expect stronger economic growth and potentially higher inflation in the future.
  • Yield curve indicates market participants expect interest rates to rise in the future.
• Inverted (Downward Sloping):
  • Short-term bonds have higher yields compared to long-term bonds.
  • Investors expect slower economic growth or a recession in the future.
  • Yield curve indicates market participants expect interest rates to decrease in the future.
• Flat Yield Curve:
  • Rarely seen, only during economic changes.
  • Indicates a shift towards either an upward or downward sloping yield curve.

Discount Factors, Spot Rates, and Forward Rates

• Discount Factor: determined from the market price and cashflows of a bond, used to obtain the corresponding spot rate and create a yield curve.
• Forward Rates: market expectations of interest rates in the future.
• Comparing forward rates to spot rates: indicator of what the market thinks will happen in the future.

Liquidity Preference Theory

• Assumes the current yield curve reflects investors' expectations of future short-term interest rates and their preference for liquidity.
• Investors prefer shorter-term securities, which are exposed to less interest rate risk.
• Investors are willing to pay extra for reducing this risk exposure.
• Implications:
  • Shorter-term securities: lower risk, lower return (discount rate).
  • Long-term securities: higher risk, higher return (discount rate).

Relative Valuation

• Compares the price of an asset to the prices of similar or comparable assets in the market
• Market prices are converted into standardized prices, creating price multiples
• Preferred over discounted cash flow valuation because it reflects market perceptions and moods
• The median is preferred over the mean due to its reliability and immunity to extreme outliers and non-symmetric distributions

Issues in Relative Valuation

• Choice of comparables: selecting appropriate comparables can significantly affect the valuation
• Market conditions: temporary market conditions can influence the prices of comparables, affecting the valuation
• Differences in growth rates: comparing companies with different growth rates can lead to misleading conclusions
• Scale and size of companies: comparing companies of different sizes can lead to valuation discrepancies

Bonds

• Raises long-term capital for corporations and governments
• Investor pays initial cost, receives coupon (interest) periodically, and face value at maturity
• Types of bonds:
  • Convertible bonds: can be converted into a predetermined number of stocks
  • Indexed bonds: rate of return is eroded by inflation
  • Callable bonds: seller can buy the bond back from the investor
  • Perpetual bonds: has no maturity date
  • Treasury bonds: issued by the federal government
  • Municipal bonds: issued by state or government agencies

Bond Pricing and YTM

• YTM reflects the market's required return on the bond
• If the market requires a higher return, the bond's price drops; if the market requires a lower return, the bond's price increases
• Interest rate changes affect YTM and bond prices
• Relationship between YTM, coupon rate, and time to maturity:
  • Expensive/Premium bond: sold at a price above face value, with a higher coupon rate than YTM
  • Cheap/Discount bond: sold at a price below face value, with a lower coupon rate 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

Pure Expectations Theory

• Assumes 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
• Investors are indifferent between holding short-term or long-term securities, provided the same total return is achieved

Yield Curve Shape

• Normal/Upward-sloping: long-term bonds have higher yields, indicating expected stronger economic growth and higher inflation
• Inverted/Downward-sloping: short-term bonds have higher yields, indicating expected slower economic growth or recession
• Flat yield curve: rare, indicates a changing economy

Discount Factors, Spot Rates, and Forward Rates

• Discount factor: determined from the market price and cashflows of a bond
• Spot rate: used to create a yield curve
• Forward rate: market expectations of interest rates in the future
• Comparing forward rates to spot rates indicates market expectations
• Short-term bonds have less interest rate risk, while long-term bonds are more sensitive to risk

Liquidity Preference Theory

• Investors are compensated for time and take extra risk when investing for longer
• Liquidity preference: investors prefer shorter-term securities with lower interest rate risk
• Investors require a higher return premium for investing in long-term securities with higher interest rate risk
• Implications:
  • Shorter-term securities: lower risk, lower return, higher prices
  • Long-term securities: higher risk, higher return, lower prices

Relative Valuation

• In relative valuation, the price of an asset is compared to the prices of similar or comparable assets.
• Market prices are converted into standardized prices, creating price multiples.
• Reasons why relative valuations are popular:
  • Easier to justify using relative valuation
  • More likely to reflect market perceptions and moods than discounted cash flow valuation
• Median is preferred over the mean in relative valuation because:
  • The median is a more reliable comparison point
  • It's unaffected by extreme outliers or non-symmetric distributions of scores
  • The median is a better representation of the true average if the sample has outliers

Issues in Relative Valuation

• Choice of comparables:
  • Selecting appropriate comparables is subjective and can significantly affect the valuation
  • Impact: Inaccurate valuation if chosen comparables are not truly similar to the asset being valued
• Market conditions:
  • Impact: Valuations based on comparables might reflect temporary market conditions rather than the intrinsic value of the asset
• Differences in growth rates:
  • Impact: High-growth companies may appear overvalued compared to low-growth companies, leading to misleading conclusions
• Scale and size of companies:
  • Impact: Smaller companies might trade at different multiples compared to larger companies, leading to valuation discrepancies

Bonds

• Raise long-term capital for corporations and governments
• Bond characteristics:
  • Coupon rate (interest rate)
  • Face value (initial cost)
  • Maturity date
• Types of bonds:
  • Convertible bonds
  • Indexed bonds
  • Callable bonds
  • Perpetual bonds
  • Treasury bonds
  • Municipal bonds

Bond Pricing and YTM (Yield to Maturity)

• YTM reflects the market's required return on the bond
• If the market requires a higher return than the bond's coupon rate, the bond's price will drop (discount)
• If the market requires a lower return than the bond's coupon rate, the bond's price will increase (premium)
• Interest rate changes:
  • When market interest rates rise, YTM increases, and bond prices fall
  • When market interest rates fall, YTM decreases, and bond prices rise
• Relationship between YTM, coupon rate, and time to maturity:
  • (Expensive/Premium) bond: If coupon rate is higher than YTM, sold at a price above face value
  • (Cheaper/Discount) bond: If coupon rate is lower than YTM, sold at a price below face value

Pure Expectations Theory

• Assumes the current yield curve solely 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 (forward rates)
• Investors are indifferent between holding short-term or long-term securities provided any combination of investment gives the same total return over the same investment period

Yield Curve Shape

• Normal (Upward Sloping):
  • Long-term bonds have higher yields compared to short-term bonds
  • 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
  • Indicates that market participants expect interest rates to decrease in the future
• Flat Yield Curve:
  • Rarely seen, only when the economy is changing, as it either heads down or upwards sloping

Discount Factors/Spot Rates/Forward Rates

• Discount factor is determined from the market price and cash flows of a bond
• Forward rates are market expectations of interest rates in the future
• If you compare the forward rate to spot rate, it's a good indicator of what the market thinks will happen in the future

Liquidity Preference Theory

• Assumes the current yield curve reflects investors' expectations of future short-term interest rates and their preference for liquidity
• Investors prefer to hold shorter-term securities, which are exposed to less interest rate risk
• Investors are willing to pay extra for reducing this risk exposure
• Implications:
  • Shorter-term securities: Lower risk, lower return (discount rate)
  • Long-term securities: Higher risk, higher return (discount rate)