a. Suppose you forecast that the standard deviation of the market return will be 20% in the coming year. If the measure of risk aversion in Equation 5.16 is A = 4, what would be a reasonable guess for the expected market risk premium? b. What value of A is consistent with a risk premium of 9%? C. What will happen to the risk premium if investors become more risk tolerant? (LO 5-4) 0.0256 We call the ratio of a portfolio's risk premium to its variance the price of risk. Later in the section, we turn the question around and ask how an investor with a given degree of risk aver- sion, say, A = 3.91, should allocate wealth between the risky and risk-free assets. To get an idea of the risk aversion exhibited by investors in U.S. capital markets, we can look at a representative portfolio held by these investors. Assume that all short-term borrowing offsets lending; that is, average net borrowing and lending are zero. In that case, the average investor holds a complete portfolio represented by a stock market index such as the S&P 500; call it M. Using a long-term series of historical returns on the S&P 500 to estimate investors' expectations about mean and variance, we can recast Equation 5.15 with these stock market data to obtain an estimate of average risk aversion. Roughly speaking, the average excess return on the market has been .08, and variance has been nearly .04. Therefore, we infer average risk aversion as: price of The ratio pnlau premium Average (rM)-r 0.08 0.04 (5.16) Sample oi, The price of risk of the market index portfolio, which reflects the risk aversion of the aver- age investor, is sometimes called the market price of risk. Conventional wisdom holds that plausible estimates for the value of A lie in the range of 1.5 – 4. The Sharpe Ratio Risk aversion implies that investors will demand a higher reward (as measured by their port- folio risk premium) to accept higher portfolio volatility. A statistic commonly used to rank portfolios in terms of this risk-return trade-off is the Sharpe ratio, defined as Sharpe
a. Suppose you forecast that the standard deviation of the market return will be 20% in the coming year. If the measure of risk aversion in Equation 5.16 is A = 4, what would be a reasonable guess for the expected market risk premium? b. What value of A is consistent with a risk premium of 9%? C. What will happen to the risk premium if investors become more risk tolerant? (LO 5-4) 0.0256 We call the ratio of a portfolio's risk premium to its variance the price of risk. Later in the section, we turn the question around and ask how an investor with a given degree of risk aver- sion, say, A = 3.91, should allocate wealth between the risky and risk-free assets. To get an idea of the risk aversion exhibited by investors in U.S. capital markets, we can look at a representative portfolio held by these investors. Assume that all short-term borrowing offsets lending; that is, average net borrowing and lending are zero. In that case, the average investor holds a complete portfolio represented by a stock market index such as the S&P 500; call it M. Using a long-term series of historical returns on the S&P 500 to estimate investors' expectations about mean and variance, we can recast Equation 5.15 with these stock market data to obtain an estimate of average risk aversion. Roughly speaking, the average excess return on the market has been .08, and variance has been nearly .04. Therefore, we infer average risk aversion as: price of The ratio pnlau premium Average (rM)-r 0.08 0.04 (5.16) Sample oi, The price of risk of the market index portfolio, which reflects the risk aversion of the aver- age investor, is sometimes called the market price of risk. Conventional wisdom holds that plausible estimates for the value of A lie in the range of 1.5 – 4. The Sharpe Ratio Risk aversion implies that investors will demand a higher reward (as measured by their port- folio risk premium) to accept higher portfolio volatility. A statistic commonly used to rank portfolios in terms of this risk-return trade-off is the Sharpe ratio, defined as Sharpe
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
Related questions
Question
Transcribed Image Text:a. Suppose you forecast that the standard deviation of the market return will be 20%
in the coming year. If the measure of risk aversion in Equation 5.16 is A = 4, what
would be a reasonable guess for the expected market risk premium?
b. What value of A is consistent with a risk premium of 9%?
C. What will happen to the risk premium if investors become more risk tolerant? (LO 5-4)
Transcribed Image Text:0.0256
We call the ratio of a portfolio's risk premium to its variance the price of risk. Later in the
section, we turn the question around and ask how an investor with a given degree of risk aver-
sion, say, A = 3.91, should allocate wealth between the risky and risk-free assets.
To get an idea of the risk aversion exhibited by investors in U.S. capital markets, we can
look at a representative portfolio held by these investors. Assume that all short-term borrowing
offsets lending; that is, average net borrowing and lending are zero. In that case, the average
investor holds a complete portfolio represented by a stock market index such as the S&P 500;
call it M. Using a long-term series of historical returns on the S&P 500 to estimate investors'
expectations about mean and variance, we can recast Equation 5.15 with these stock market
data to obtain an estimate of average risk aversion. Roughly speaking, the average excess
return on the market has been .08, and variance has been nearly .04. Therefore, we infer
average risk aversion as:
price of
The ratio
pnlau premium
Average (rM)-r
0.08
0.04
(5.16)
Sample oi,
The price of risk of the market index portfolio, which reflects the risk aversion of the aver-
age investor, is sometimes called the market price of risk. Conventional wisdom holds that
plausible estimates for the value of A lie in the range of 1.5 – 4.
The Sharpe Ratio
Risk aversion implies that investors will demand a higher reward (as measured by their port-
folio risk premium) to accept higher portfolio volatility. A statistic commonly used to rank
portfolios in terms of this risk-return trade-off is the Sharpe ratio, defined as
Sharpe
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 4 steps with 3 images
Recommended textbooks for you
Principles of Economics (12th Edition)
Economics
ISBN:
9780134078779
Author:
Karl E. Case, Ray C. Fair, Sharon E. Oster
Publisher:
PEARSON
Engineering Economy (17th Edition)
Economics
ISBN:
9780134870069
Author:
William G. Sullivan, Elin M. Wicks, C. Patrick Koelling
Publisher:
PEARSON
Principles of Economics (12th Edition)
Economics
ISBN:
9780134078779
Author:
Karl E. Case, Ray C. Fair, Sharon E. Oster
Publisher:
PEARSON
Engineering Economy (17th Edition)
Economics
ISBN:
9780134870069
Author:
William G. Sullivan, Elin M. Wicks, C. Patrick Koelling
Publisher:
PEARSON
Principles of Economics (MindTap Course List)
Economics
ISBN:
9781305585126
Author:
N. Gregory Mankiw
Publisher:
Cengage Learning
Managerial Economics: A Problem Solving Approach
Economics
ISBN:
9781337106665
Author:
Luke M. Froeb, Brian T. McCann, Michael R. Ward, Mike Shor
Publisher:
Cengage Learning
Managerial Economics & Business Strategy (Mcgraw-…
Economics
ISBN:
9781259290619
Author:
Michael Baye, Jeff Prince
Publisher:
McGraw-Hill Education