Relative Valuation in Finance

Relative Valuation

• In relative valuation, an asset's price is compared to the prices of similar or comparable assets in the market.
• Market prices are standardized to create price multiples.
• Relative valuation is popular due to its ease of use and ability to reflect market perceptions and moods.

Advantages of Relative Valuation

• Easier to justify buying or selling decisions using relative valuation.
• Faster and requires fewer assumptions about the future compared to discounted cash flow valuation.

Issues in Relative Valuation

• Selecting comparable assets can be subjective and affect valuation accuracy.
• Market conditions can influence comparable prices, leading to inaccurate valuations.
• Differences in growth rates and company scale can lead to misleading conclusions.

Bonds

• Bonds are a type of debt security used to raise long-term capital.
• Bond characteristics:
  • Par Value Bond: Coupon rate = YTM
  • Discount Bond: Coupon rate < YTM
  • Premium Bond: Coupon rate > YTM

Types of Bonds

• 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: Issuer can buy the bond back from the investor in the future.
• Perpetual bonds: Lasts forever.
• Treasury bonds: Issued by the federal government.
• Municipal bonds: Issued by state governments or government agencies.

Relationship Between YTM, Coupon Rate, and Time to Maturity

• Expensive/Premium bond: Sold at a price above face value, decreasing in price as time to maturity decreases.
• Cheap/Discount bond: Sold at a price below face value, increasing in price as time to maturity decreases.

Strips

• Separate trading of registered interest and principle securities.
• Common in Treasury bonds, allowing investors to sell components of their bonds.

Arbitrage

• No arbitrage opportunities if PV Bond = PV of all strips, indicating an efficient market.
• Arbitrage opportunities exist if PV Bond ≠ PV of all strips, indicating an inefficient market.

Risks Associated with Bonds

• Reinvestment risk: Occurs when interest rates decrease, affecting coupons and principal repayment.
• Price risk: Occurs when interest rates increase, affecting bond prices.
• Inflation risk: Causes bond prices to decrease, ultimately decreasing returns.
• Liquidity risk: Selling bonds before maturity at a discounted price due to high yields.

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.

Yield Curve Shape

• Normal/Upward Sloping: Indicates expectations of stronger economic growth and higher inflation in the future.
• Inverted/Downward Sloping: Indicates expectations of slower economic growth or recession.

Discount Factors/Spot Rates/Forward Rates

• Discount factor: Determined from market price and cashflows of a bond, used to obtain spot rates and create a yield curve.
• Forward rates: Market expectations of interest rates in the future, used to hedge risk.

Macaulay's Duration

• Measures sensitivity of bond price to changes in interest rates (yields).
• Properties:
  • Dmac ≤ TTM
  • Dmac is higher for bonds with lower coupon rates and lower YTM.
  • Dmac is higher for bonds with higher TTM.

Modified Duration

• A modified version of Dmac, adjusting for the bond's yield.
• Represents a percentage change in bond price in response to a 1% change in yield.

Convexity

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

Active and Passive Trading Strategies

• Active management: Forecast yield curve changes and adjust portfolio accordingly.
• Passive management: Buy and hold bonds until maturity.

Duration Management

• Increase or decrease portfolio duration based on forecasted changes in interest rates.

Relative Valuation

• In relative valuation, the price of an asset is compared to the prices of similar or comparable assets to determine its value.
• Market prices are standardized to create price multiples, allowing for comparison between assets.
• Relative valuation is popular due to its ease of justification in buying or selling assets, and its ability to reflect market perceptions and moods.

Issues with Relative Valuation

• Selecting comparable assets can be subjective and significantly affect the valuation.
• Market conditions can influence the prices of comparable assets, leading to inaccurate valuations.
• Differences in growth rates between companies or assets can lead to misleading conclusions.
• Scale and size differences between comparable assets can result in valuation discrepancies.

Bonds

• Bonds are long-term debt securities issued by corporations and governments to raise capital.
• Investors pay the initial cost and receive coupon (interest) payments periodically, and the face value of the bond when it matures.
• Types of bonds include:
  • Convertible bonds: can be converted into a predetermined number of stocks in the future.
  • Indexed bonds: the coupon rate is related to movements in inflation.
  • Callable bonds: the seller can buy the bond back from the investor in the future.
  • Perpetual bonds: the bond has no maturity date.
  • Treasury bonds: issued by the federal government.
  • Municipal bonds: issued by state governments or government agencies.

Relationship Between YTM, Coupon Rate, and Time to Maturity

• If the coupon rate is higher than YTM, the bond is sold at a price above face value.
• As time to maturity decreases, the bond price decreases, and as time to maturity increases, the bond price increases.
• When YTM decreases, the bond price increases, decreasing the effective annual return.
• If interest rates go down, YTM decreases, increasing the bond price.

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, 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 present, and the market is efficient.
• If PV Bond > PV of all Strips, or PV Bond < PV of all Strips, arbitrage opportunities are present, and the market is inefficient.

Risks

• Reinvestment Risk: occurs when interest rates go down, and an investor can reinvest coupons at the market yield.
• Price Risk: occurs when interest rates go up, and investors are only subject to price risk if they need to sell before maturity.
• Inflation Risk: causes bond prices to decrease, decreasing the return of bonds.
• Liquidity Risk: suffers a loss if selling a bond before maturity 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.

Yield Curve Shape

• Normal (Upward Sloping): short-term yields are lower than long-term yields, indicating economic growth and potentially higher inflation.
• Inverted (Downward Sloping): short-term yields are higher than long-term yields, indicating slower economic growth or a recession.

Discount Factors, Spot Rates, and Forward Rates

• Discount Factor: determined from the market price and cash flows 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 indicates what the market thinks will happen in the future.

Theories of the Term Structure

• Pure Expectations Theory: long-term interest rates are determined by the market's expectation of future short-term interest rates.
• Liquidity Preference Theory: investors are compensated for time, but get extra if they invest for longer.
• Market Segmentation Theory: investors have preferred time frames for bonds, and supply and demand shift the yield for each market segment.
• Preferred Habitat Theory: investors have a preferred time maturity to bonds, but may take other opportunities.

Macaulay's Duration and Convexity

• Macaulay's Duration: measures the sensitivity of a bond's price to changes in interest rates.
• Modified Duration: a modified version of Macaulay's duration, adjusting for the bond's yield.
• Convexity: measures the sensitivity of a bond's duration to changes in interest rates, capturing the non-linear relationship between price and yield.

Duration and Convexity Properties

• Duration is higher for bonds with lower coupon rates and lower yields.
• Duration is higher for bonds with longer maturity periods.
• Convexity is higher for bonds with lower coupon rates, lower yields, and longer maturity periods.

Active and Passive Trading Strategies

• Active management: requires investors to forecast yield curve changes or divest depending on the prediction.
• Passive management: aims to buy and hold bonds until maturity, with little involvement from the investor.
• Duration management: investors modify their portfolio allocation to increase or decrease its duration, depending on forecasted changes in interest rates.