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Questions and Answers
What does the duration of a coupon bond reflect?
What does the duration of a coupon bond reflect?
Which bond might be more difficult to find in the market when trying to match a future liability?
Which bond might be more difficult to find in the market when trying to match a future liability?
How does an increase in interest rates benefit an investor with reinvestment risk?
How does an increase in interest rates benefit an investor with reinvestment risk?
What is the relationship between bond price and interest rate changes?
What is the relationship between bond price and interest rate changes?
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Which risk is associated with holding a longer-term bond?
Which risk is associated with holding a longer-term bond?
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What assumptions are made in the static analysis of investment returns?
What assumptions are made in the static analysis of investment returns?
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What is true about the expected return on any investment?
What is true about the expected return on any investment?
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In the context of interest rates, what is a primary concern for investors in bonds?
In the context of interest rates, what is a primary concern for investors in bonds?
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What is the goal of combining assets with low correlations in a portfolio?
What is the goal of combining assets with low correlations in a portfolio?
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What does the Minimum Variance Frontier (MVF) represent in portfolio management?
What does the Minimum Variance Frontier (MVF) represent in portfolio management?
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Why is it indicated that more assets in a portfolio lead to reduced risk?
Why is it indicated that more assets in a portfolio lead to reduced risk?
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What is the ideal correlation between assets to maximize diversification benefits?
What is the ideal correlation between assets to maximize diversification benefits?
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What is the first step in deriving the Minimum Variance Frontier?
What is the first step in deriving the Minimum Variance Frontier?
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How is the duration of a zero-coupon bond defined?
How is the duration of a zero-coupon bond defined?
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What happens to a bond's duration when the coupon rate increases?
What happens to a bond's duration when the coupon rate increases?
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Which rule states that a bond's duration increases with time to maturity?
Which rule states that a bond's duration increases with time to maturity?
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What occurs when the yield to maturity (YTM) of a bond decreases?
What occurs when the yield to maturity (YTM) of a bond decreases?
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How is the duration of a perpetuity calculated?
How is the duration of a perpetuity calculated?
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What does a greater convexity in bonds indicate about the price-yield relationship?
What does a greater convexity in bonds indicate about the price-yield relationship?
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Why is the duration-price relationship considered a good approximation only for small changes in bond yields?
Why is the duration-price relationship considered a good approximation only for small changes in bond yields?
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How can a coupon bond be conceptualized in terms of zero-coupon bonds?
How can a coupon bond be conceptualized in terms of zero-coupon bonds?
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What is the primary purpose of forward rates in finance?
What is the primary purpose of forward rates in finance?
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Which hypothesis explains the typically upward sloping yield curve?
Which hypothesis explains the typically upward sloping yield curve?
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How does the liquidity preference hypothesis (LPH) affect investor behavior?
How does the liquidity preference hypothesis (LPH) affect investor behavior?
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What does a liquidity premium in bond pricing indicate?
What does a liquidity premium in bond pricing indicate?
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In the context of the expectations hypothesis, under what condition is liquidity premium considered zero?
In the context of the expectations hypothesis, under what condition is liquidity premium considered zero?
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What does E(r2) represent in financial terms?
What does E(r2) represent in financial terms?
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What is the implication of most individuals being short-term investors?
What is the implication of most individuals being short-term investors?
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How are forward rates described in relation to the actual future interest rates?
How are forward rates described in relation to the actual future interest rates?
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What does a β value greater than 1 indicate about an asset's risk compared to the market?
What does a β value greater than 1 indicate about an asset's risk compared to the market?
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Which of the following describes systematic risk?
Which of the following describes systematic risk?
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Unsystematic risk is characterized as which of the following?
Unsystematic risk is characterized as which of the following?
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As more assets are added to a portfolio, the resulting effect on unsystematic risk is to:
As more assets are added to a portfolio, the resulting effect on unsystematic risk is to:
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Which of the following is NOT an example of systematic risk?
Which of the following is NOT an example of systematic risk?
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The Capital Asset Pricing Model (CAPM) specifically prices which type of risk?
The Capital Asset Pricing Model (CAPM) specifically prices which type of risk?
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Market-wide events such as interest rate rises are classified as:
Market-wide events such as interest rate rises are classified as:
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Which of the following statements about diversification is true?
Which of the following statements about diversification is true?
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What does the CAPM primarily account for when pricing assets?
What does the CAPM primarily account for when pricing assets?
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According to the CAPM, what compensation do investors receive for taking on unsystematic risk?
According to the CAPM, what compensation do investors receive for taking on unsystematic risk?
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How is systematic risk represented in the CAPM model?
How is systematic risk represented in the CAPM model?
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What is the main implication of holding well-diversified portfolios according to the CAPM?
What is the main implication of holding well-diversified portfolios according to the CAPM?
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Which of the following statements about the Security Market Line (SML) is true?
Which of the following statements about the Security Market Line (SML) is true?
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What differentiates the CML from the SML?
What differentiates the CML from the SML?
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What is the significance of an asset having a β value of 2?
What is the significance of an asset having a β value of 2?
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Where do individual assets typically plot in relation to the Capital Allocation Line (CAL)?
Where do individual assets typically plot in relation to the Capital Allocation Line (CAL)?
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Study Notes
Bond Characteristics
- A bond is a debt obligation between an issuer (borrower) and bondholder (lender)
- The coupon rate, maturity date, and par value are part of the bond indenture (contract)
- Default risk is the risk that the issuer will not repay their debt
Bond Pricing
- Two approaches to pricing debt: Fundamental and Arbitrage
- Prices are set in supply-demand equilibrium
- Arbitrage replicates future cash flows of an asset using similar assets with known prices (replicating portfolio or synthetic asset)
- The market value of the asset to be priced should be equal to the market value of the replicating portfolio
Yield/Return Measures
- Bond price is inversely proportional to interest rates (YTM)
- If actual interest rates are constant and equal to YTM, the annualized actual return over any holding period will be YTM
- Actual market rates do not usually equal and stay constant as YTM
- Holding Period Return (HPR) and Realised Compound Yield (HPR Annualised) measure actual return on bonds
Term Structure of Interest Rates
- Term structure of interest rates refers to how rates vary over different investment horizons (maturities)
- Shown on a yield curve
- Yield curve plots yields (interest rates) of bonds with equal credit rating but varying maturities
- The slope of the yield curve helps predict the direction of interest rates/economic expansion or contraction
Future Interest Rates
- When given a series of spot rates, we can derive forecasted interest rates
- For example, using the 1-year and 2-year spot rates we can predict the 2-year rate
Spot Rates vs Short Rates
- Spot rate: interest rate today for a t-period zero coupon bond (starting today and ending at time t)
- The spot rate is the geometric average of its component short rates
Forward Rates
- Under uncertainty, forecasted interest rates are known as forward rates
- Forward rates are agreed upon interest rates for a defined future time period
- The forward rate for period n is denoted fn, and is derived from the equation
Term Structure Hypotheses
- Expectations Hypothesis: The forward rate equals the market's expected future short-interest rate
- Liquidity Preference Hypothesis: Forward rates are market expectations of future spot rates plus a liquidity rate premium (or a discount) for long-term investments
Interest Rate Risk
- Bond prices and yields are inversely related (P ↑ YTM ↓)
- Long-term bonds are more price sensitive to changes in interest rates than short-term bonds
- Low coupon bonds are more sensitive than high coupon bonds to changes in interest rates
- Bonds with lower YTM are more sensitive to interest rate changes than those with higher YTM
Duration
- Duration is the “effective” maturity of a bond
- Duration is a measure of a bond’s interest rate sensitivity
- Duration is higher when the coupon rate is lower
- Higher when the bond's yield to maturity is lower
- Duration is a measure of interest rate risk
Portfolio Duration
- Portfolio duration is the weighted average of the durations of its component bonds
Asset-Liability Matching
- Matching a known future liability by buying zero-coupon bonds
- Buying coupon bonds may also be required and exposes investors to interest rate risk
Factor Models
- A general factor model expresses the excess return of an asset using multiple factors
- Fama-French-Carhart four-factor model is commonly used. Includes four portfolio returns as factors
Behaviour Finance
- Investors may commit systematic errors that may never wash out (behavioral biases)
- Behavioral biases may lead to suboptimal investment decisions based on their assumptions
Efficient Market Hypothesis
- Current Prices of securities fully reflect available information
- Three versions: Weak form, Semi-strong form, Strong form
- Weak form: Current prices reflect all past trading (historical) data
- Semistrong form: Current prices reflect all publicly available information about a firm
- Strong form: Current prices reflect all available information, including non-public
Option Introduction
- Options are derivatives that give the holder a right, but no obligation, to trade an underlying asset.
- Call options give the right to buy and Put options give the right to sell
- Exercise price: The price at which the underlying asset can be bought or sold
- Intrinsic value: The value an option would have if exercised today
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