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Questions and Answers

What does the duration of a coupon bond reflect?

  • The total time to maturity of the bond
  • The average of the coupon rates
  • The total cash flow from all coupon payments
  • The weighted average of the durations of its component zeros (correct)

Which bond might be more difficult to find in the market when trying to match a future liability?

  • Convertible bond
  • Zero-coupon bond (correct)
  • Variable-rate bond
  • Inflation-linked bond

How does an increase in interest rates benefit an investor with reinvestment risk?

  • Bonds can be sold at a higher price
  • Future cash flows can be reinvested at a better rate (correct)
  • The liquidity risk premium diminishes
  • The bond duration decreases

What is the relationship between bond price and interest rate changes?

<p>Inverse relationship (A)</p> Signup and view all the answers

Which risk is associated with holding a longer-term bond?

<p>Liquidity risk premium (B)</p> Signup and view all the answers

What assumptions are made in the static analysis of investment returns?

<p>One period and normally distributed returns (A)</p> Signup and view all the answers

What is true about the expected return on any investment?

<p>It is uncertain and variable (D)</p> Signup and view all the answers

In the context of interest rates, what is a primary concern for investors in bonds?

<p>Interest rate risk (B)</p> Signup and view all the answers

What is the goal of combining assets with low correlations in a portfolio?

<p>To reduce overall portfolio risk while maintaining return (B)</p> Signup and view all the answers

What does the Minimum Variance Frontier (MVF) represent in portfolio management?

<p>The lowest risk portfolio for each level of expected return (B)</p> Signup and view all the answers

Why is it indicated that more assets in a portfolio lead to reduced risk?

<p>More assets create more opportunity for negative correlations (A)</p> Signup and view all the answers

What is the ideal correlation between assets to maximize diversification benefits?

<p>Low or ideally negative correlation (B)</p> Signup and view all the answers

What is the first step in deriving the Minimum Variance Frontier?

<p>Set a target expected portfolio return (B)</p> Signup and view all the answers

How is the duration of a zero-coupon bond defined?

<p>It equals its time to maturity. (C)</p> Signup and view all the answers

What happens to a bond's duration when the coupon rate increases?

<p>The duration decreases. (D)</p> Signup and view all the answers

Which rule states that a bond's duration increases with time to maturity?

<p>Rule 3 (B)</p> Signup and view all the answers

What occurs when the yield to maturity (YTM) of a bond decreases?

<p>The value of cash flows in later periods increases relatively more. (A)</p> Signup and view all the answers

How is the duration of a perpetuity calculated?

<p>(1 + y) / y (D)</p> Signup and view all the answers

What does a greater convexity in bonds indicate about the price-yield relationship?

<p>There is more curvature in the relationship. (D)</p> Signup and view all the answers

Why is the duration-price relationship considered a good approximation only for small changes in bond yields?

<p>Due to the curvature created by convexity. (C)</p> Signup and view all the answers

How can a coupon bond be conceptualized in terms of zero-coupon bonds?

<p>As a portfolio of zero-coupon bonds. (A)</p> Signup and view all the answers

What is the primary purpose of forward rates in finance?

<p>To infer expected future interest rates under uncertainty (C)</p> Signup and view all the answers

Which hypothesis explains the typically upward sloping yield curve?

<p>Expectations hypothesis (D)</p> Signup and view all the answers

How does the liquidity preference hypothesis (LPH) affect investor behavior?

<p>Investors favor short-term investments to minimize liquidity risk (A)</p> Signup and view all the answers

What does a liquidity premium in bond pricing indicate?

<p>Compensation for uncertainty in bond resale prices (D)</p> Signup and view all the answers

In the context of the expectations hypothesis, under what condition is liquidity premium considered zero?

<p>When future cash flows from investments are expected to be equal (D)</p> Signup and view all the answers

What does E(r2) represent in financial terms?

<p>The expected future short interest rate (B)</p> Signup and view all the answers

What is the implication of most individuals being short-term investors?

<p>Prices must ensure f<del>2</del> is greater than E(r<del>2</del>) (A)</p> Signup and view all the answers

How are forward rates described in relation to the actual future interest rates?

<p>They reflect the consensus expectation of future rates (D)</p> Signup and view all the answers

What does a β value greater than 1 indicate about an asset's risk compared to the market?

<p>The asset contributes more risk than the average asset. (D)</p> Signup and view all the answers

Which of the following describes systematic risk?

<p>Market-wide risks that affect all firms. (A)</p> Signup and view all the answers

Unsystematic risk is characterized as which of the following?

<p>Specific to an individual asset and can be diversified away. (C)</p> Signup and view all the answers

As more assets are added to a portfolio, the resulting effect on unsystematic risk is to:

<p>Converge toward systematic risk level. (D)</p> Signup and view all the answers

Which of the following is NOT an example of systematic risk?

<p>A retail store's poor sales due to bad management. (C)</p> Signup and view all the answers

The Capital Asset Pricing Model (CAPM) specifically prices which type of risk?

<p>Systematic risk that cannot be diversified away. (B)</p> Signup and view all the answers

Market-wide events such as interest rate rises are classified as:

<p>Systematic risks. (D)</p> Signup and view all the answers

Which of the following statements about diversification is true?

<p>It only reduces firm-specific risks. (A)</p> Signup and view all the answers

What does the CAPM primarily account for when pricing assets?

<p>Only systematic risk (D)</p> Signup and view all the answers

According to the CAPM, what compensation do investors receive for taking on unsystematic risk?

<p>They receive no compensation (D)</p> Signup and view all the answers

How is systematic risk represented in the CAPM model?

<p>By the beta coefficient (β) (A)</p> Signup and view all the answers

What is the main implication of holding well-diversified portfolios according to the CAPM?

<p>Only systematic risk needs to be considered (C)</p> Signup and view all the answers

Which of the following statements about the Security Market Line (SML) is true?

<p>Movements up the SML suggest higher returns for increased systematic risk (A)</p> Signup and view all the answers

What differentiates the CML from the SML?

<p>CML includes only efficient/optimal assets (D)</p> Signup and view all the answers

What is the significance of an asset having a β value of 2?

<p>It implies the asset contributes double the risk of an average asset and earns double the reward (D)</p> Signup and view all the answers

Where do individual assets typically plot in relation to the Capital Allocation Line (CAL)?

<p>Under the CAL, indicating unsystematic risk exists (B)</p> Signup and view all the answers

Flashcards

Short Rate

The interest rate for a specific time interval at a particular point in time.

Forward Rate

An agreed-upon interest rate for a future time period, starting at a future date.

Forward Rate Premium

The extra compensation for accepting uncertainty about future bond prices, when the forward rate is greater than the expected short rate.

Expectation Hypothesis (EH)

A theory where the forward rate equals the market's expectation for the future short rate, and assumes liquidity premiums are zero.

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Yield Curve

A graph that plots the yield on bonds of varying maturities. It typically shows the relationship between the maturity and yield of a bond.

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Liquidity Preference Hypothesis (LPH)

Investors prefer short-term bonds to long-term bonds because they avoid liquidity risk.

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Liquidity Risk

The risk that an asset cannot be readily sold at a fair market value when needed.

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Upward Sloping Yield Curve

A yield curve where longer maturities have higher yields than shorter maturities.

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Bond Duration

Bond duration measures a bond's sensitivity to interest rate changes. It indicates how much the bond price will change for a given change in interest rates.

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Zero-Coupon Bond Duration

The duration of a zero-coupon bond is equal to its time to maturity.

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Coupon Rate & Duration

Lower coupon rates lead to higher bond durations, all else equal.

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Time to Maturity & Duration

Generally, bond duration increases with time to maturity, though at a decreasing rate.

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Yield to Maturity & Duration

Lower yields to maturity generally lead to higher bond durations, all else equal.

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Perpetuity Duration

The duration of a perpetuity is calculated as (1 + y) / y, where y is the yield to maturity.

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Duration and Interest Rate Risk

Bond duration is a key measure of interest rate risk. It quantifies the potential price change of a bond due to interest rate fluctuations.

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Duration and Convexity

Duration is an approximation of price sensitivity to yield changes, best for small yield changes. Bonds with higher convexity deviate more from linearity in price-yield relationships, requiring a more accurate measure than duration for larger yield changes.

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Duration of a Coupon Bond

The weighted average of the durations of its component zero-coupon bonds.

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Asset-Liability Matching

A strategy where one purchases bonds with maturities and payments that match future liabilities to minimize interest rate risk.

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Reinvestment Risk

The risk that interest rates will decline, forcing reinvestment of coupon payments at lower rates, reducing future returns.

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Inverse Relationship: Duration & Coupon Rate

Higher coupon rates result in shorter durations, because more cash flows are received earlier, making the bond less sensitive to interest rate changes.

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Sensitivity of Bond Price to Interest Rates

Duration measures how much the market value of a bond changes in response to a change in interest rates.

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Key Assumption: Static Portfolio

The portfolio's composition is held constant over a single investment period, meaning there is no rebalancing.

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Normal Distribution Assumption

The returns on investments are assumed to follow a normal distribution, allowing probability calculations to be made.

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Diversification

The strategy of investing in various assets to reduce risk and potential losses. By spreading investments across different asset classes, the overall portfolio becomes less volatile.

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Asset Correlation

The extent to which the prices or returns of two assets move together. A high positive correlation means they move in the same direction, while a low or negative correlation means they move independently or in opposite directions.

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Low Correlated Assets

Assets that tend to move independently of each other, minimizing the overall portfolio risk. When one asset performs poorly, the other might perform well, providing some protection.

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Minimum Variance Frontier (MVF)

A curve that represents the set of portfolios with the lowest possible risk for each level of expected return. Every point on the MVF contains the optimal portfolio for its corresponding return level.

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Optimal Portfolio (No Risk-Free Asset)

A portfolio for an investor that offers the most favorable risk-return trade-off. It is a point on the MVF, providing the lowest possible risk for the desired level of return.

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Beta (β)

A measure of an asset's volatility relative to the market. It indicates how much an asset's price is likely to change in response to changes in the market.

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Positive Beta

An asset's price is expected to move in the same direction as the market. A beta greater than 1 indicates the asset is more volatile than the market.

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Negative Beta

An asset's price is expected to move in the opposite direction to the market. A beta less than 0 indicates the asset is negatively correlated with the market.

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Systematic Risk

The risk that is inherent in the overall market and cannot be diversified away. It's also known as market risk or non-diversifiable risk.

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Unsystematic Risk

The risk that is specific to a particular asset or company. This risk can be diversified away by investing in a portfolio of assets.

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CAPM (Capital Asset Pricing Model)

A model that describes the relationship between risk and expected return for an asset. It states that the expected return of an asset is equal to the risk-free rate plus a risk premium that is proportional to the asset's beta.

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Total Risk = Systematic Risk + Unsystematic Risk

The total risk of an asset can be decomposed into two components: systematic risk and unsystematic risk. Systematic risk is the risk that cannot be diversified, while unsystematic risk can be diversified.

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CAPM & Unsystematic Risk

The Capital Asset Pricing Model (CAPM) assumes all rational investors hold diversified portfolios, eliminating unsystematic risk. Therefore, the CAPM only prices systematic risk. Investors are not compensated for taking on unsystematic risk because it can be diversified away.

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CAPM & Systematic Risk

The CAPM states that the expected return of an asset is determined by its beta (β), which measures the asset's systematic risk relative to the market.

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CAPM & Passive Strategy

The CAPM suggests a passive investment strategy, meaning investors should hold a well-diversified portfolio, such as the market portfolio, instead of trying to beat the market.

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Security Market Line (SML)

The SML is a graphical representation of the relationship between the expected return of an asset and its beta (systematic risk). The SML slopes upwards because higher risk is rewarded with higher expected returns.

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SML & Beta

An asset's beta (β) determines its position on the SML. An asset with a beta of 1 has the same risk as the market, while a beta of 0.5 means half the risk, and a beta of 2 means double the risk.

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SML vs. CAL

Individual assets typically plot below the Capital Allocation Line (CAL) because the CAL represents efficient portfolios where unsystematic risk is diversified away. Thus, the total risk of an asset on the CAL is equal to its systematic risk.

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SML vs. CML

Both the SML and the Capital Market Line (CML) start at the risk-free rate (rf), but the CML considers total risk (σ) while the SML only considers systematic risk (β). The CML only includes efficient assets/portfolios.

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What risk earns a reward?

Only systematic risk earns a reward under the CAPM. Unsystematic risk can be diversified away and does not contribute to expected returns.

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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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