Apply Capital Market Theories - Series 65

1. Which correlation value provides the greatest diversification benefit: $+1$, $0$, or $-1$?

   $-1$. A correlation of $-1$ indicates perfect negative movement, maximizing risk reduction when combining assets in a portfolio.

2. State the two-asset portfolio variance formula using $w_1,w_2,\sigma_1,\sigma_2$, and $\text{Cov}_{12}$.

   $\sigma_p^2=w_1^2\sigma_1^2+w_2^2\sigma_2^2+2w_1w_2\text{Cov}_{12}$. The two-asset variance formula captures individual variances and their interaction via covariance for precise risk calculation.

3. Using CAPM, find $\beta$ if $R_f=2\%$, $E(R_m)=8\%$, and $E(R_i)=11\%$.

   $1.5$. Solving CAPM rearranges to isolate beta as the ratio of security risk premium to market risk premium.

4. What is the interpretation of a negative beta, $\beta<0$?

   Tends to move opposite the market. Negative beta implies inverse correlation with the market, providing hedging potential in diversified portfolios.

5. Using CAPM, find $E(R_i)$ if $R_f=3\%$, $E(R_m)=9\%$, and $\beta=1.5$.

   $12\%$. CAPM calculation compensates for higher beta with increased expected return above the risk-free rate.

6. What is the definition of the global minimum-variance portfolio?

   The portfolio with the lowest possible variance. The global minimum-variance portfolio achieves the smallest risk among all possible portfolios on the efficient frontier.

7. What is the definition of an efficient portfolio in Modern Portfolio Theory?

   A portfolio on the efficient frontier. An efficient portfolio lies on the efficient frontier, providing the best risk-return tradeoff without dominated alternatives in Modern Portfolio Theory.

8. In CAPM, what is the market risk premium called and how is it written?

   Market risk premium: $E(R_m)-R_f$. The market risk premium represents compensation for bearing systematic risk over the risk-free rate in CAPM.

9. What is the interpretation of $\beta=1$ for a security?

   Expected to move one-for-one with the market. A beta of 1 indicates the security's returns match market movements, embodying average systematic risk in CAPM.

10. What is the semi-strong form Efficient Market Hypothesis (EMH)?

    Prices reflect all publicly available information. Semi-strong EMH implies fundamental analysis is ineffective as public information is instantly reflected in prices.

11. What does the Security Market Line (SML) graph in CAPM?

    Expected return versus beta ($\beta$). The Security Market Line illustrates the linear relationship between risk (beta) and required return in equilibrium under CAPM.

12. What is the definition of beta ($\beta$) in CAPM?

    Sensitivity of a security return to the market return. Beta measures systematic risk by quantifying how a security's returns respond to market fluctuations in the Capital Asset Pricing Model.

13. What is the definition of systematic (market) risk in Modern Portfolio Theory?

    Nondiversifiable risk from market-wide factors. Systematic risk arises from economy-wide events affecting all securities and cannot be eliminated through diversification in Modern Portfolio Theory.

14. State the formula for covariance using correlation $\rho_{12}$ and standard deviations $\sigma_1,\sigma_2$.

    $\text{Cov}_{12}=\rho_{12}\sigma_1\sigma_2$. Covariance measures joint variability and is derived from correlation and standard deviations for assessing portfolio risk.

15. State the CAPM expected return formula using $R_f$, $\beta$, and $E(R_m)$.

    $E(R_i)=R_f+\beta_i\left(E(R_m)-R_f\right)$. CAPM equates expected return to risk-free rate plus beta-adjusted market risk premium, pricing systematic risk.

16. What is the key diversification result of Modern Portfolio Theory for unsystematic risk?

    It can be reduced substantially by holding many securities. Diversification in Modern Portfolio Theory minimizes unsystematic risk by spreading investments across uncorrelated assets, approaching zero as the number of securities increases.

17. What is the efficient frontier in Modern Portfolio Theory?

    Portfolios with maximum return for a given risk level. The efficient frontier represents the set of optimal portfolios offering the highest expected return for any level of risk in Modern Portfolio Theory.

18. What is the interpretation of $\beta<1$ for a security?

    Less volatile than the market (lower systematic risk). Beta less than 1 signifies defensive securities with reduced sensitivity to market changes, implying lower systematic risk.

19. What is the definition of unsystematic (idiosyncratic) risk in Modern Portfolio Theory?

    Diversifiable risk specific to a company or industry. Unsystematic risk stems from factors unique to individual assets and can be mitigated through diversification in Modern Portfolio Theory.

20. On the SML, what does it imply if a security plots above the line?

    Undervalued (offers too high an expected return for its $\beta$). Plotting above the SML suggests the security is underpriced, as its return exceeds CAPM-predicted levels for its risk.

21. What is the weak-form Efficient Market Hypothesis (EMH)?

    Prices reflect all past market trading information. Weak-form EMH asserts that technical analysis cannot yield abnormal returns since historical price data is fully incorporated.

22. What does correlation measure in portfolio construction?

    The degree to which two returns move together. Correlation quantifies the linear relationship between asset returns, aiding in assessing diversification benefits in portfolio construction.

23. What does portfolio variance depend on besides individual security variances?

    Covariances (or correlations) among the securities. Portfolio variance incorporates covariances to account for how asset returns interact, beyond just individual variances.

24. State the formula for a portfolio expected return with weights $w_i$ and returns $E(R_i)$.

    $E(R_p)=\sum w_iE(R_i)$. Portfolio expected return is the weighted sum of individual asset expected returns, reflecting linear combination in Modern Portfolio Theory.

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