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What characteristic of the Security Market Line (SML) makes it relevant for individual assets?

  • It calculates risk based on historical data alone.
  • It depicts expected return as a function of systematic risk. (correct)
  • It applies only to efficient portfolios.
  • It measures total risk of the portfolio.

    • Which statement accurately reflects the relationship between beta (β) and risk in the context of the Security Market Line?

  • Beta is proportional to the systematic risk an individual asset adds to the portfolio. (correct)
  • A lower beta affects the individual asset's return independently of the market return.
  • Beta measures total risk including both systematic and unsystematic risk.
  • A higher beta indicates less systematic risk and therefore lower expected return.

    • In what way does the Capital Market Line (CML) differ from the Security Market Line (SML)?

  • CML indicates that only systematic risk influences expected returns.
  • CML is applicable only to individual assets, unlike SML which covers portfolios.
  • CML measures total risk using beta while SML uses standard deviation.
  • CML depicts efficient portfolios' risk premium based on total risk, while SML bases it on systematic risk. (correct)

    • Why is beta (β) considered a suitable risk measure in a well-diversified portfolio?

    <p>It effectively measures the contribution of systematic risk to the portfolio's overall risk.</p> Signup and view all the answers

    What is the primary function of the equation derived from the Security Market Line?

    <p>To express expected return based on the asset's beta in relation to market return.</p> Signup and view all the answers

    What does the correlation coefficient indicate when assessing the risk-return relationship between two assets?

    <p>It illustrates the degree to which asset returns move in relation to each other.</p> Signup and view all the answers

    In efficient diversification, what is considered the primary benefit of combining two assets?

    <p>Achieving a higher return for a given level of risk through diversification.</p> Signup and view all the answers

    What is the minimum variance portfolio characterized by?

    <p>It has the lowest possible variance for any given correlation.</p> Signup and view all the answers

    How is covariance between two asset returns related to the correlation coefficient?

    <p>Covariance can be calculated directly from the correlation coefficient and asset standard deviations.</p> Signup and view all the answers

    What would happen to the efficient frontier if the correlation between two assets approaches -1?

    <p>The efficient frontier would expand outward, allowing for higher returns with reduced risk.</p> Signup and view all the answers

    Which of the following statements about the risks involved in portfolio diversification is true?

    <p>Diversification can reduce unsystematic risk associated with individual assets.</p> Signup and view all the answers

    What does the coefficient of determination assess in the context of asset returns?

    <p>The percentage of variance in one asset's returns explained by the other asset's returns.</p> Signup and view all the answers

    What characterizes the 'efficient frontier' in investment theory?

    <p>A line representing the set of portfolios that maximize return for a given level of risk.</p> Signup and view all the answers

    In the context of portfolio selection, what do the investor-specific preferences influence?

    <p>The final choice of the optimal portfolio on the Capital Allocation Line (CAL).</p> Signup and view all the answers

    Why may investors select different complete portfolios according to their risk aversion?

    <p>Different aversions affect how investors respond to risk-return trade-offs.</p> Signup and view all the answers

    What element must exist for an optimal portfolio to be determined?

    <p>There must be restrictions on possible assets and allocations.</p> Signup and view all the answers

    What is the result of the mean-variance criterion in investment decisions?

    <p>Investors will strive for portfolios that provide higher returns for the same risk level.</p> Signup and view all the answers

    What does the tangency point between the efficient frontier and an indifference curve represent?

    <p>It is the optimal portfolio that maximizes utility for a given risk level.</p> Signup and view all the answers

    Which of the following statements about feasible portfolios is correct?

    <p>Many feasible portfolios may exist without being optimal in terms of return.</p> Signup and view all the answers

    What is the role of computers in portfolio selection according to the content?

    <p>Computers assist in identifying possible portfolios and optimal selections.</p> Signup and view all the answers

    What typically leads to a different set of optimal portfolios for investors?

    <p>Variations in risk preferences and investment constraints.</p> Signup and view all the answers

    What does the intercept term, $\alpha_i$, in a regression equation represent?

    <p>The expected return when the independent variable is zero</p> Signup and view all the answers

    In the context of the single-factor model, which of the following correctly describes $\beta_i$?

    <p>The slope, or regression coefficient, indicating the asset's sensitivity to market changes</p> Signup and view all the answers

    What does $e_i$ represent in the regression equation?

    <p>The unexplained residual of the regression</p> Signup and view all the answers

    How can the beta factor of a portfolio, $\beta_P$, be determined?

    <p>As the product of the asset weights and their respective betas</p> Signup and view all the answers

    What is the expected value of the error term $e_i$ in the regression model?

    <p>Equal to zero</p> Signup and view all the answers

    In the single-factor model, what is the meaning of $\rho_{ii}$ in the beta formula?

    <p>Correlation coefficient between the asset and the market returns</p> Signup and view all the answers

    What type of relationship does the regression equation $R_i = \alpha_i + \beta_i R_M + e_i$ describe?

    <p>A straight line illustrating linear relationships between asset and market returns</p> Signup and view all the answers

    What does $\sigma_M^2$ represent in the beta formula?

    <p>The variance of the market returns</p> Signup and view all the answers

    Which statement best describes the quality of the regression in the context of the coefficient of determination?

    <p>It assesses the proportion of variance in the dependent variable explained by the independent variable</p> Signup and view all the answers

    What does the risk premium of an individual asset depend on?

    <p>The risk premium of the market and the asset's beta</p> Signup and view all the answers

    Which of the following reflects the relationship between systematic risk and expected return according to CAPM?

    <p>Expected return increases linearly with beta.</p> Signup and view all the answers

    The equation for expected return in CAPM can be reformulated in multiple ways. What is the standard form of this equation?

    <p>E(Ri) = rf + βi * (E(Rm) - rf)</p> Signup and view all the answers

    What does a high risk premium on the market portfolio indicate?

    <p>Investors expect higher returns due to increased risk.</p> Signup and view all the answers

    Which statement best describes systematic risk in the context of CAPM?

    <p>It refers to market-related risk that cannot be eliminated through diversification.</p> Signup and view all the answers

    What does the beta coefficient represent in the CAPM framework?

    <p>The sensitivity of an asset's return to the market return</p> Signup and view all the answers

    In CAPM, when is the market considered to be in equilibrium?

    <p>When the expected return is equal to the CAPM required return.</p> Signup and view all the answers

    Why is there a reward for taking systematic risk according to CAPM?

    <p>Investors cannot avoid systematic risk, so they demand a risk premium.</p> Signup and view all the answers

    What would happen if the risk premium of the market portfolio is too low?

    <p>Investors would quickly seek higher returns elsewhere.</p> Signup and view all the answers

    What does the Capital Market Line (CML) represent?

    <p>The return versus risk trade-off for efficient portfolios including the risk-free asset.</p> Signup and view all the answers

    Study Notes

    Portfolio Theory and Behavioral Finance

    • This course covers portfolio theory and behavioral finance.
    • The course is titled, "Portfolio Theory and Behavioral Finance (w.IN.23HS.V)".
    • Included is Chapter 3 on optimal asset combination and single factor asset models.
    • The course materials were developed by Dr.-Ing. Martin Schnauss, CFA, FRM / Dr. Jan-Alexander Posth / Dr. Marcus Wunsch.

    Asset Combination

    • Insertion: Splitting the risk
    • Discusses diversification and portfolio risk.
    • How portfolio risk changes with increasing assets.

    Diversification and Portfolio Risk

    • A portfolio of N securities is considered.
    • Standard deviations are equal.
    • Correlations are equal.
    • Portfolio's standard deviation tends to a certain value.
    • The value of p and the value of s are asked for in this section.

    Diversification and Portfolio Risk - Interpretation

    • Variance (risk) of a portfolio decreases rapidly with more assets.
    • Significant reduction in specific risk is achievable with 15-20 assets.
    • A note about how many assets some types of investment strategies may utilize (e.g. CTAs may have up to 200).

    Splitting the Risk - Systematic Risk

    • A risk affecting an entire class of assets or a global economy.
    • Cannot be eliminated through diversification.
    • Example: Risk in the overall stock market index.
    • It can, however, be mitigated by investing in different asset classes or different markets/countries.

    Splitting the Risk - Question

    • How to understand risk reduction and remaining systematic risk?
    • Risk emerges at different levels (e.g., market-level, sector-level, company-level).
    • Some examples include GDP growth, rates, geopolitical events, commodity prices, regulations, CEO changes, and internal fraud.

    Splitting the Risk - Additional Details

    • Risk is in the uncertainty of future developments.
    • Company and sector-specific risk factors neutralize with more assets; only systematic/market risk remains.

    Splitting the Risk - Components

    • Risk of a single asset or a portfolio can be split into systematic (non-diversifiable) and unsystematic (diversifiable) risk.
    • The latter is composed of company-specific or idiosyncratic risk.
    • The systematic part is split into the market risk component.

    Splitting the Risk - Systematic Risk

    • Systematic risk mostly derives from macroeconomic influences, impacting all assets.
    • Unsystematic risk relates to company-specific conditions, impacting only the particular company.

    Modern PF-Theory (MPT)

    • Only systematic risk is rewarded with a risk premium.
    • Systematic risk shows an asset's and portfolio's response to market fluctuations.
    • The beta factor shows how sensitive individual assets or portfolios are to market/macroeconomic fluctuations.

    Chapter 3: The Capital Asset Pricing Model

    • The text has arrived at Chapter 3 of the capital asset pricing model.

    Learning Outcomes

    • Students will understand and apply concepts such as efficient diversification, single-factor models, portfolio asset correlations, and performance measures like Treynor, Sharpe, and Jensen's Alpha.
    • The course will also cover Capital Asset Pricing Models (CAPM).

    Efficient Diversification

    • Questions regarding potential portfolios and how those change depending on correlation levels (between −1 and +1).
    • A link to an app illustrating possible portfolios and their correlations.

    Efficient Diversification

    • The efficient frontier with two assets.
    • An exercise on diversification from the FinanceLab.
    • A link to the FinanceLab.

    Efficient Diversification

    • Relationship between correlation and covariance.
    • Formulas to determine the correlation and the covariance of assets.

    Efficient Diversification

    • For any given correlation, the portfolio with the lowest variance is the minimum variance portfolio.
    • Formulas for finding this minimum variance portfolio.

    Efficient Diversification

    • Finding the Sharpe ratio of specified market portfolios and minimum variance portfolios.

    Efficient Diversification - The Optimal Risky Portfolio

    • Adding a risk-free investment to risky portfolios.
    • The resulting graph shows a Capital Market Line (CML).
    • The efficient frontier is beat by the optimal frontier because of risk-free investment.

    Efficient Diversification - The Optimal Risky Portfolio

    • The reward-to-variability ratio (Sharpe Ratio) of Portfolio 3 is greater than that of Portfolio 1.
    • The optimal portfolio lies on the tangent to the efficient frontier.
    • The optimal portfolio has the highest possible Sharpe Ratio.

    Efficient Diversification - Calculating Optimal Portfolio Weights

    • Calculating the weights of the optimal portfolio composed of two assets (A and B).
    • Formulas for finding the weights, including asset risk premiums.

    The Optimal Risky Portfolio with Many Assets

    • Combining a risk-free investment with numerous risky assets.
    • The graph illustrates the tangency portfolio, efficient frontier, and individual assets.

    The Optimal Risky Portfolio with Many Assets

    • Calculating assets' expected return using matrix notation.
    • Portfolio's expected return formula.
    • Weights and vectors of portfolio and asset returns used in the formula.

    The Optimal Risky Portfolio with Many Assets

    • Covariance matrix formula, and alternative notations.
    • Variance, Var(Rp) or σ².

    Efficient Diversification - Mean-Variance Criterion and Efficient Frontier

    • Investors are risk-averse, and only take risk for higher expected returns.
    • Investors choosing between options with equal returns will prefer the lower-risk option.
    • Investors choosing between options with equal risk will prefer the higher-return option.
    • The resulting "northwest" direction is called the mean-variance criteria.

    Efficient Diversification - Mean-Variance Criterion and Efficient Frontier

    • The "northwest" aspect of the criteria is called the efficient frontier.
    • All investors will only choose portfolios on the efficient frontier.

    Efficient Diversification - The Optimal Risky Portfolio

    • The graph illustrates the relationship between standard deviation and expected return.
    • Key parts of the graph include the market portfolio, and Portfolios 1, 2, and 3.

    Efficient Diversification - The Optimal Risky Portfolio with Many Assets - Remarks

    • Restrictions in assets and allocation choices may result in different efficient frontiers.
    • Optimal portfolios depend on possible portfolios.
    • Investors choose portfolios on the optimal Capital Allocation Line (CAL) to fit individual risk and return goals.

    Efficient Diversification - The Optimum Risky Portfolio with Many Assets

    • The first two steps for finding portfolios are technical tasks, done by computer.
    • Only investor-specific risk aversion needs to be considered in the final step, along with the optimal CAL.

    Efficient Diversification - The Optimum Risky Portfolio with Many Assets

    • Portfolios like P1 and P2 are feasible but don't maximize utility.
    • Portfolios on indifference curve 3 might be desirable but aren't feasible.
    • The optimal portfolio is the point of tangency between the efficient frontier and indifference curve 2.
    • Investors with differing risk aversions may choose different complete portfolios.

    Efficient Diversification - The Optimum Risky Portfolio with Many Assets -Practical

    • Investors select optimal portfolios.
    • Investors with differing risk aversions will choose different complete portfolios.

    Efficient Diversification - The Optimum Risky Portfolio with Many Assets -Practical

    • Beta is not constant over time; its components of volatility and correlation can change dramatically.
    • Underlying transaction and hedge maturity differences must be addressed.
    • Suitable futures for different underlying assets are needed, and may be hard to find.

    Efficient Diversification - The Optimum Risky Portfolio with Many Assets -Practical

    • Cross-hedging is problematic due to the absence or similarity with ideal hedging instruments.
    • In using similar instruments, the counterparty risk is reduced with the use of exchanges.
    • In using forwards (OTC), however, counterparty risk must be considered.

    Capital Asset Pricing Model (CAPM)

    • The CAPM is an equilibrium model for valuing risky assets.
    • The CAPM explains the relation between risk and return in a single-factor model.
    • The CAPM is a foundational model in modern finance.

    Capital Asset Pricing Model (CAPM) - Assumptions

    • Investors are as "equal" as possible, although starting with varying funds and risk tolerance degrees.
    • Investors cannot alter the pricing of assets by their trades, and perfect competition exists.
    • Investors agree on the same investment horizon.
    • Investors can borrow and lend risk-free sums of money in unlimited amounts.

    Capital Asset Pricing Model (CAPM) - Assumptions on Investors

    • All investors should not have to pay taxes or transaction costs.
    • Investors should be rational and choose optimal portfolios based on the efficient frontier.
    • Investors should use identical economic models, probability calculations, and correlation assumptions, leading to a singular optimal portfolio based on homogenous expectations.

    Capital Asset Pricing Model (CAPM) - Introduction (cont.).

    • The market portfolio serves as the only risky investment for all investors.
    • The Market portfolio (M) is the optimal portfolio O, with CAL becoming CML.

    Capital Asset Pricing Model (CAPM) - Introduction (cont.)

    • Market portfolio risk premium is proportional to the market standard deviation.
    • Individual asset risk premium = the market risk premium * asset beta coefficient.

    Capital Asset Pricing Model (CAPM) - Introduction (cont.)

    • Discussion: Why do all investors hold market portfolios?
    • A passive strategy is efficient based on the CAPM and mutual fund theorem.
    • The market risk premium: what happens if it's too high or too low?

    Capital Asset Pricing Model (CAPM) - Introduction (cont.)

    • Reward is only for taking systematic risk.
    • Ratio of risk premium to systematic risk is constant for all assets and portfolios.

    Capital Asset Pricing Model (CAPM) - Central Conclusion

    • Market equilibrium causes expected return (CAPM required return) calculations from a risk-free rate, plus ẞ, and the market's risk premium.
    • The expected return is the "CAPM required return".
    • The expected return compensates the asset's systematic risk in a diversified portfolio.

    Capital Asset Pricing Model (CAPM) - Central Conclusion

    • The CAPM expected return equation can be re-formulated in various approaches.
    • The ratio of an asset's risk premium to the market's risk premium should equal the asset's ẞ.
    • The risk premium's ratio to systematic risk is consistent across all assets, and portfolios

    Capital Asset Pricing Model (CAPM) - The Capital Market Line

    • All rational investors hold the market portfolio.
    • The market portfolio is efficient and on the efficient frontier.
    • Therefore, the market portfolio is the optimal portfolio.
    • All efficient and complete portfolios are a mix of the portfolio O and risk-free assets; these reside along a straight line.
    • The investment decision is a function of the risk aversion of the investor.

    Capital Asset Pricing Model (CAPM) - The Capital Market Line - Definition

    • The straight line between the risk-free asset and the optimum market portfolio is called the Capital Market Line (CML).
    • The equation of the CML.

    Capital Asset Pricing Model (CAPM) - The Capital Market Line - Application

    • The CML describes the risk-return relationship for a complete portfolio, including the optimum risky portfolio.
    • It is used for strategic asset allocation.
    • The CML is invalid for individual assets or for portfolios that are not efficient.
    • The equation for CML.

    Capital Asset Pricing Model (CAPM) - The Security Market Line

    • The SML shows the expected return as a function of systematic risk β.
    • Beta is a suitable risk metric as it is proportional to the systematic risk a given individual asset adds to the market portfolio.
    • In a well-diversified portfolio, only systematic risk is rewarded with excess return.

    Capital Asset Pricing Model (CAPM) - The Security Market Line - Cont.

    • Individual asset returns in a well diversified portfolio are proportional to the portfolio's systematic risk.
    • The expected return is a function of β.

    Capital Asset Pricing Model (CAPM) - The Security Market Line - Equation

    • The equation for the SML.
    • The market portfolio lies on the Security Market Line.

    Capital Asset Pricing Model (CAPM) - Differences between CML and SML

    • The CML showcases the risk premium of efficient portfolios as functions of total risk (standard deviation).
    • The SML shows the risk premium for individual or portfolio assets.
    • The assets' premium is affected by systematic risk, measured using β.

    Capital Asset Pricing Model (CAPM) - Differences between CML and SML - Discussion

    • Standard deviation is the relevant metric for portfolio risk in the CML, and the relevant risk measure is the asset's contribution to portfolio risk (β), expressed by the SML.
    • SML is sufficient for individual assets and portfolios.
    • Properly or fairly priced assets lie on the SML; those that are undervalued lie above it, while underpriced ones lie below it.

    Capital Asset Pricing Model (CAPM) - CAPM-Based Performance Measures - Treynor Ratio

    • The Treynor ratio measures risk premium per unit of systematic risk.
    • It answers the question "what is the reward of taking systematic risk?"
    • The equation for the Treynor Ratio.

    Capital Asset Pricing Model (CAPM) - CAPM-Based Performance Measures - Sharpe Ratio

    • The Sharpe Ratio measures the risk premium per unit of total risk.
    • It answers the question "what is the reward for taking total risk?"
    • The equation for the Sharpe ratio.

    Capital Asset Pricing Model (CAPM) - CAPM-Based Performance Measures - Jensen's alpha

    • Jensen's alpha measures the difference between realized and expected return.
    • It is positive for undervalued assets and negative for overvalued assets.

    Single Factor Models - Conceptual background

    • A single-factor model explains an asset's excess return through a single determinant (e.g., interest rates, money supply, financial index, business cycle).
    • This differentiation leads to the consideration of systematic and unsystematic risk.
    • The single-factor-model is less comprehensive than including multiple factors to determine returns.

    Single Factor Models - Index Model

    • The market return is the most appropriate single determinant variable.
    • A single factor model based on an index is an index model.
    • This model splits up an asset’s excess return into three components: α, β, RM, and e.

    Single Factor Models - Index Model - Equation

    • Ri = ai + bi * RM + ei
    • Alpha (a) is the excess return of the asset that is not related to the market or company-specific risk.
    • Beta (b) is the sensitivity the asset has to market movements, based on macroeconomic factors.
    • ei is the component that reflects unexpected company-specific events.

    Single Factor Models - Graphic Representation

    • Ri versus RM are graphically represented.
    • These plots depict the relationship between return on an asset and return on the market.

    Single Factor Models - Systemic and Diversifiable Risks

    • Total variance is split into systemic and company-specific (idiosyncratic) risk in a single index model.
    • The β coefficient of an asset reflects its sensitivity to market movements; the average beta across all assets equals one.
    • Defensive assets' beta levels are below one; aggressive assets' beta levels are above one.

    Single Factor Models - Approach

    • The calculation of β provides a useful approach to explain the return of assets based on market rates.
    • The equation shows that the calculation of assets based on market risk and a return-based on its sensitivity to market rates.

    Single Factor Models - Coefficient of Determination

    • The precision of a regression is measured by the coefficient of determination or R-squared.
    • Systemic risk variance (related to market movements) is a portion of a total asset return's variance.
    • The formula expresses the coefficient of determination for the single-factor model.

    Single Factor Models - Example Hedging with Futures

    • Hedging long equity index positions involves shorting future contracts on appropriate index futures.
    • Number of contracts for a perfect hedge is calculated.

    Single Factor Models - Example Hedging with Futures - Practical Problems

    • Beta is not constant over time.
    • Maturity of underlying transaction and hedge are different.
    • Suitable futures for different underlying instruments are required.

    Single Factor Models - Example Hedging with Futures - Practical Problems

    • Cross-hedging may lack hedging instruments in some situations.
    • Counterparty risk with future instruments traded in exchanges is often minimal due to the clearing mechanism.
    • In forwards, however, counterparty risk is affected by OTC trades.

    Capital Asset Pricing Model (CAPM)

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    Description

    Test your knowledge on the Security Market Line (SML) and its relevance for individual assets. This quiz explores the relationship between beta (β) and risk, and highlights the differences between the SML and the Capital Market Line (CML). Additionally, you'll learn about the role of beta in a well-diversified portfolio and the functions of the SML equation.

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