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Show, using equations or a diagram, that an expected utility maximizer requires a higher return for a riskier asset
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- 2. Consider an individual with a current wealth of $100,000 who faces the prospect of a 25% chance of losing $20,000 through theft of her car during the next year. If the person’s utility function is U(X) = ln(X), where X is wealth: a. calculate expected utility without insurance, b. calculate the actuarially fair premium for full insurance, c. calculate expected utility with full insurance at the actuarially fair premium d. calculate the maximum amount the individual would pay for full insurance.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…Now assume an investor is negotiating with the bank to pay either a 1.5% interest rate or a 2.0% interest rate on loans advanced. Will she/he be better off with the first or second option? Explain carefully.
- 1. In terms of the Markowitz portfolio model, explain how an investor identifies his / her optimal portfolio. What specific information does an investor need to identify an optimal portfolio?INV 1 5aiv Suppose that you have the following utility function: U=E(r) – ½ Aσ2 and A=3 Suppose that you have $10 million to invest for one year and you want to invest that money into ETFs tracking the S&P 500 (US) and S&P/TSX 60 (Canada) index, which are often used as proxies for the US and Canadian stock markets, respectively, and the Canadian one-year T-bill. Assume that the interest rate of the one-year T-bill is 0.35% per annum. You have found two ETFs that you are interested in. From a set of their historical data between 2001 and 2019, you have estimated the annual expected returns, standard deviations, and covariance as follows: ETFUS : E(r)= 0.070584 standard deviation = 0.173687 ETFCDA : E(r)= 0.073763 standard deviation = 0.16816 Covariance between ETFUS and ETFCDA = 0.02397 What is the standard deviation for ETFCDA?Sam, 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 above
- Suppose Maria prefers to buy a bond with a 7%expected return and 2% standard deviation of itsexpected return, while Jennifer prefers to buy a bondwith a 4% expected return and 1% standard deviationof its expected return. Can you tell if Maria is more orless risk-averse than Jennifer?Jamal has a utility function U = W1/2, where W is his wealth in millions of dollars and U is the utility he obtains from that wealth. In the final stage of a game show, the host offers Jamal a choice between (A) $4 million for sure, or (B) a gamble that pays $1 million with probability 0.6 and $9 million with probability 0.4. (1) Does A or B offer Jamal a higher expected utility? Explain your reasoning with calculations. (2) Should Jamal pick A or B? Why? I would like help with the unanswered last parts of the questions.5. Finding the interest rate and the number of years The future value and present value equations also help in finding the interest rate and the number of years that correspond to present and future value calculations. A. If a security currently worth $2,000 will be worth $2,809.86 three years in the future, what is the implied interest rate the investor will earn on the security—assuming that no additional deposits or withdrawals are made? 9.60% 0.47% 12.00% 7.12% B. If an investment of $30,000 is earning an interest rate of 8.00%, compounded annually, then it will take for this investment to reach a value of $37,791.36—assuming that no additional deposits or withdrawals are made during this time. C. Which of the following statements is true—assuming that no additional deposits or withdrawals are made? An investment of $25 at an annual rate of 10% will return a higher value in five years than $50 invested at an…
- 3. Suppose the investment yield on a 91-day T-bill is 3%. What is its discount- basis yield? Show your solutionINV 1 5ai Suppose that you have the following utility function: U=E(r) – ½ Aσ2 and A=3 Suppose that you have $10 million to invest for one year and you want to invest that money into ETFs tracking the S&P 500 (US) and S&P/TSX 60 (Canada) index, which are often used as proxies for the US and Canadian stock markets, respectively, and the Canadian one-year T-bill. Assume that the interest rate of the one-year T-bill is 0.35% per annum. You have found two ETFs that you are interested in. From a set of their historical data between 2001 and 2019, you have estimated the annual expected returns, standard deviations, and covariance as follows: ETFUS : E(r)= 0.070584 standard deviation = 0.173687 ETFCDA : E(r)= 0.073763 standard deviation = 0.16816 Covariance between ETFUS and ETFCDA = 0.02397 What is the portfolio expected return for ETFUS?What is compute forward-looking expected return and risk and how does it influence financial decisions regarding risk and return?