Brief Principles of Macroeconomics (MindTap Course List)
8th Edition
ISBN: 9781337091985
Author: N. Gregory Mankiw
Publisher: Cengage Learning
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Chapter 9, Problem 5CQQ
To determine
Based ondiversification and its benefit.
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3. The risk free rate is 3%. The optimal risky portfolio has an expected return of 9% and standard deviation of 20%. Answer the following questions.
(a) Assume the utility function of an investor is U = E(r) − 0.5Aσ2. What is condition of A to make the investors prefer the optimal risky portfolio than the risk free asset?
(b) Assume the utility function of an investor is U = E(r) − 2.5σ2. What is the expected return and standard deviation of the investor’s optimal complete portfolio?
When you are long an option and you delta hedge, you want
A.
traders talking a lot about other asset classes and ignore your underlying
B.
volatility to increase and the underlying to move around a lot
C.
the cost of carry to narrow
D.
volatility to decrease and the underlying to just stop moving
a) Explain the practical relevance of the mean-variance model of portfolio selection
Chapter 9 Solutions
Brief Principles of Macroeconomics (MindTap Course List)
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- 6. Risk-averse people will choose different asset portfolios than people who are not risk averse. Over a long period of time, we would expect thatA.every risk-averse person will earn a higher rate of return than every non-risk averse person.B.every risk-averse person will earn a lower rate of return than every non-risk averse person.C.the average risk-averse person will earn a higher rate of return than the average non-risk averse person.D.the average risk-averse person will earn a lower rate of return than the average non-risk averse person. 7.The real exchange rate equals the relative A.price of domestic and foreign currency.B.price of domestic and foreign goods.C.rate of domestic and foreign interest. D.None of the above is correct. 8.According to the theory of liquidity preference, an increase in the price level causes theA.interest rate and investment to rise.B.interest rate and investment to fall.C.interest rate to rise and investment to fall.D.interest rate to fall and…arrow_forwardANSWER E PLEASE ONLY Consider the following portfolio choice problem. The investor has initial wealth w andutility u(x) = (x^n) / n. There is a safe asset (such as a US government bond) that has netreal return of zero. There is also a risky asset with a random net return that has onlytwo possible returns, R1 with probability 1 − q and R0 with probability q. We assumeR1 < 0, R0 > 0. Let A be the amount invested in the risky asset, so that w − A isinvested in the safe asset.a) What are risk preferences of this investor, are they risk-averse, riskneutral or risk-loving?b) Find A as a function of w. c) Does the investor put more or less of his portfolio into the risky assetas his wealth increases? d) Now find the share of wealth, α, invested in the risky asset. How doesα change with wealth? e) Calculate relative risk aversion for this investor. How does relativerisk aversion depend on wealth?arrow_forwardWhich statement about portfolio diversification is CORRECT? i) Typically, as more securities are added to a portfolio, total risk would be expected to decrease at an increasing rate.ii) Proper diversification can reduce or eliminate total risk.iii) The risk-reducing benefits of diversification do not occur meaningfully until at least 50-60 individual securities have been purchased.iv) Because diversification reduces a portfolio's total risk, it necessarily reduces the portfolio's expected return.arrow_forward
- B. Richard's nickname is "No-Risk Rick" because he is an extremely risk-averse individual. His utility function is given by U(W) = √W. where W represents his current wealth in dollars. He currently has $100 worth of property, but there is a 50% chance that all of it will be stolen. What is Richard's expect wealth and expected utility of wealth? An insurance company offers to reimburse Richard for his loss if the money is stolen. What is the most that Richard would pay for such a policy? Explain. Please solve this with in 1 hourarrow_forwardAssume that you manage a risky portfolio with an expected return of18% and a standard deviation of 28%. The T-note rate is 2.7%. If your client chooses to invest 75% of a portfolio in your fund and 25% in a T-note bond fund. a. What is the expected return of your client's portfolio? b. What is the standard deviation of your client's prtfolio?arrow_forwardInvestors have different preferences with regards to the risk: they can be risk averse, risk neutral and risk seeking. What do we mean by risk averse, risk neutral, and risk seeking?arrow_forward
- Suppose you have a house worth $200,000 (wealth). Your utility of wealth is given by U(w) = ln(w). There is a small chance that a fire will damage your house causing a loss of $75,000. You estimate there is a 2% chance of fire. a) What is your expected wealth? b) What is your expected utility from owning the house? c) Suppose you can add a fire detection/prevention system to your house. This would reduce the chance of a bad event to 0 but it would cost you $C to install. What is the most you are willing to pay for the security system? (Here is an identity you will find usefularrow_forwardSam, after taking a $200 loan from the bank to finance an investment that pays $1000 50% of the time and $0 50% of the time at a 100% interest, discovers another riskier investment that pays out $5,000 but only 10% of the time, while the other 90% of the time it pays zero. Would the he want to switch to the riskier investment? Question 4 options: Yes because his return has increased No because his liability to the bank has increased No because his return has decreased None of the abovearrow_forwardDefine the term Expected return on a risky asset?arrow_forward
- ANSWER C AND D PLEASE ONLY Consider the following portfolio choice problem. The investor has initial wealth w andutility u(x) = (x^n) / n. There is a safe asset (such as a US government bond) that has netreal return of zero. There is also a risky asset with a random net return that has onlytwo possible returns, R1 with probability 1 − q and R0 with probability q. We assumeR1 < 0, R0 > 0. Let A be the amount invested in the risky asset, so that w − A isinvested in the safe asset.a) What are risk preferences of this investor, are they risk-averse, riskneutral or risk-loving?b) Find A as a function of w. c) Does the investor put more or less of his portfolio into the risky assetas his wealth increases? d) Now find the share of wealth, α, invested in the risky asset. How doesα change with wealth?arrow_forwardplease show steps on financail calculator if possible? The real risk-free rate is 3.25%. Inflation is expected to be 2.00% this year and 3.75% during the next 2 years. Assume that the maturity risk premium is zero. What is the yield on 2 year Treasury securities? Do not round Intermediate calculations. Round your answer to two decimal places. % What is the yield on 3-year Treasury securities? Do not round intermediate calculations. Round your answer to two decimal places.arrow_forwardDiscuss: i) diversifiable risk; ii) market risk; iii) systematic risk iv) unsystematic risk;arrow_forward
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