Interpreting the Risk-Free Rate Formula
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Questions and Answers

How does the real risk-free rate change as individuals become more impatient?

  • Becomes negative
  • Rises (correct)
  • Remains the same
  • Falls
  • What is the impact on the real risk-free rate when the variance of consumption growth increases?

  • Falls (correct)
  • Rises
  • Remains the same
  • Becomes negative
  • How does an increase in γ affect the real risk-free rate according to the text?

  • Has no effect on the real risk-free rate
  • Increases it due to intertemporal substitution (correct)
  • Decreases it due to risk aversion
  • Causes the real risk-free rate to fluctuate
  • What does the parameter γ represent in a power utility function?

    <p>Risk aversion and intertemporal substitution</p> Signup and view all the answers

    How does relative risk aversion change as γ decreases?

    <p>Increases</p> Signup and view all the answers

    What is the Elasticity of Intertemporal Substitution (EIS) when γ equals 1?

    <p>$1$</p> Signup and view all the answers

    Which financial asset delivers the optimal amount of consumption smoothing?

    <p>Asset with positive Cov(St+1Rt+1)</p> Signup and view all the answers

    What does the second term of (5) represent?

    <p>Risk premium on the asset</p> Signup and view all the answers

    When is the risk-free asset return represented as E(1+Rt+1F)=1+Rt+1F=1/E(St+1)?

    <p>When R is non-stochastic</p> Signup and view all the answers

    What does equation (8) help us understand about the risk-free rate?

    <p>It's inversely proportional to expected consumption growth</p> Signup and view all the answers

    What happens to the relationship between SDF and R when Cov(St+1Rt+1) is negative?

    <p>Investor receives high return when labour income is high</p> Signup and view all the answers

    What does the risk premium represent in equation (7)?

    <p>Additional return for bearing risk</p> Signup and view all the answers

    What is the meaning of the covariance term in the context of asset pricing?

    <p>The covariance between S and R</p> Signup and view all the answers

    Based on the information provided, what does a positive Cov(St+1Rt+1) indicate?

    <p>High expected return on an asset</p> Signup and view all the answers

    How can the formula E(1+Rt+1) = 1/E(St+1)-Cov(St+1Rt+1)/E(St+1) be rearranged?

    <p>$E(1+Rt+1) = 1 - Cov(St+1Rt+1)$</p> Signup and view all the answers

    In the context of asset pricing, what does a high SDF value correspond to?

    <p>High return on the asset</p> Signup and view all the answers

    What do Figures 1 and 2 illustrate in terms of the relationship between Consumption and SDF?

    <p>Low Consumption leads to high SDF value</p> Signup and view all the answers

    If Cov(St+1Rt+1) is negative, what kind of relationship does it suggest between SDF and R?

    <p>Low SDF associated with high R</p> Signup and view all the answers

    What is the key aspect of an asset's risk identified using the SDF approach?

    <p>Covariance between the asset return and consumption</p> Signup and view all the answers

    For a log normally distributed random variable, what does E(en) = eE(n)+0.5Var(n) represent?

    <p>Expectation of the random variable</p> Signup and view all the answers

    What is the formula for U'(C) when U(C)=C^(1-γ)/(1-γ)?

    <p>(1-γ)C^(-γ)</p> Signup and view all the answers

    What does ln(St+1)=ln(θ)-γ(ln(Ct+1)-ln(Ct)) represent?

    <p>Consumption growth rate</p> Signup and view all the answers

    What does ln(θ)𝑒∆𝑐𝑡+1 = 𝛾2 - 𝛾𝐸∆𝑐𝑡+1 + 2𝑉𝑎𝑟(∆𝑐𝑡+1) calculate?

    <p>Expected variance of consumption growth</p> Signup and view all the answers

    What is the formula for 𝐹𝑅𝑡+1 in terms of ln(θ), 𝛾, 𝐸∆𝑐𝑡+1, and 𝑉𝑎𝑟(∆𝑐𝑡+1)?

    <ul> <li>ln(θ) + 𝛾2 - 𝛾𝐸∆𝑐𝑡+1 - 2𝑉𝑎𝑟(∆𝑐𝑡+1)</li> </ul> Signup and view all the answers

    Individuals with high $\gamma$ have a higher preference for low volatility of consumption because:

    <p>Low volatility leads to less utility volatility.</p> Signup and view all the answers

    Based on the information provided, how does an increase in $E(R_{t+1})$ affect an individual's savings (Ct)?

    <p>Decreases savings (Ct).</p> Signup and view all the answers

    Which function represents a higher preference for low consumption volatility?

    <p>The red function (high $\gamma$).</p> Signup and view all the answers

    In the context of the text, why do individuals with high $U''(C)/U'(C)$ respond more to changes in consumption growth volatility?

    <p>Because they value stability in consumption.</p> Signup and view all the answers

    How does an individual's saving decision change as $\gamma$ increases?

    <p>They save more.</p> Signup and view all the answers

    Based on the formula $U'(C) = C - \gamma$, what happens to $U'(C)$ if there is a given change in $C$ and $\gamma$ increases?

    <p>$U'(C)$ changes more.</p> Signup and view all the answers

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