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

How does relative risk aversion change as γ decreases?

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

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

<p>$1$ (A)</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) (B)</p> Signup and view all the answers

What does the second term of (5) represent?

<p>Risk premium on the asset (B)</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 (A)</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 (D)</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 (A)</p> Signup and view all the answers

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

<p>Additional return for bearing risk (A)</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 (C)</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 (D)</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>$E(1+Rt+1) = 1 - Cov(St+1Rt+1)$ (B)</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 (C)</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 (A)</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 (A)</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 (C)</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 (A)</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) (C)</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 (A)</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 (C)</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) (C)</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. (B)</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). (C)</p> Signup and view all the answers

Which function represents a higher preference for low consumption volatility?

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

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

<p>They save more. (C)</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. (B)</p> Signup and view all the answers

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