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- Suppose the expected return on the tangent portfolio is 12% and its volatility is 30%.The risk-free rate is 3%.(a) What is the equation of the Capital Market Line (CML)?(b) What is the standard deviation of an efficient portfolio whose expected return of16.5%? How would you allocate $3,000 to achieve this positionWhich 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.Suppose you have just inherited $10,500 and are considering different options for investing the money to maximize your return. If you are risk-neutral (that is, neither seek out or shy away from risk), which of the following options should you choose to maximize your expected return? A. Hold the money in cash and earn zero return. B. Invest the money in a corporate bond, with a stated return of 4%, but there is a chance of 9% the company could go bankrupt. C. Put the money in an interest-bearing checking account, which earns 3%. The FDIC insures the account against bank failure. D. Loan the money to one of your friends' roommates, Mike, at an agreed upon interest rate of 7%, but you believe there is a 5% chance that Mike will leave town without repaying you.
- 1. Tanner is choosing between two investment options. He can invest $500 now and get (guaranteed) $550 in one year, or invest $500 now and get (guaranteed) $531.40 back later today. The risk-free rate is 3.5%. Which investment should Tanner prefer? A) $531.40 later today, since $1 today is worth more than $1 in one year. B) $550 in one year, since it is $50 more than he invested rather than $31.40 more than he invested. C) Neither - both investments have a negative NPV. D) Tanner should be indifferent between the two investments, since both are equivalent to the same amount of cash today.Suppose you visit with a financial adviser, and you are considering investing some of your wealth in one of three investment portfolios stocks, bonds, or commodities. Your financial adviser provides you with the following table, which gives the probabilities of possible returns from each investment To maximize your expected return, you should choose: Stocks Bonds Probability Return Probability Return 0.15 20% 0.15 16.7% 06 10% T 04 7.5% 0.25 8% 0.45 3.3% OA bonds OB stocks OC. commodities OD. All of the portfolios have the same expected return. If you are risk-averse and had to choose between the stock or the bond investments, you would choose OA the stock portfolio because there is less uncertainty over the outcome OB. the bond portfolio because there is less uncertainty over the outcome. OC. the stock portfolio because of greater expected return. OD. the bond portfolio because of greater expected return. Commodities Probability Return 02 20% 0.2 15% 0.2 8% 02 02 5% 0%10. Which one of the following measures may be used to measure the risk of an investment on its own? a) Expected return of the investment. b) Expected utility of the investment for an investor. c) Standard deviation of the possible outcomes of the investment. d) The Bernoullian utility function's value of a good investment outcome.
- 3) A risk-loving individual has $1000 to invest. The individual maximizes his/her expected utility and has a monotonic utility function. Show that he/she will never choose a diversified portfolio - that is, show that he/she will either keep the entire $1000 in a safe, or invest the entire $1000 in a risky assesst, for which each $1 invested yields $] with probability p, and SB with probability (1-p), where $B<$1<$J.1. Consider an insurance contract with the premium r=$200 and payout q=$800 a.) John has healthy-state income IH = $900 and sick-state income IS = $100. He has a probability of illness p = 0.2. Is the contract fair and/or full for John? b.) What is John’s expected income without this insurance contract? What is John’s expected income with this insurance contract?Suppose you are considering buying $5,000 worth of Canada savings bonds (risk-free) and a portfolio of perfectly risk- balanced stocks so that the portfolio is also "risk-free". The stocks portfolio is "risk-free" because it has some stocks that rise in value during a recession (such as McDonald's, chocolate bars, etc.) and some stocks that fall in value during a recession (Samsung, Tesla, etc.) Both choices offer to pay a 5% annual return. However, you also know that 100% of interest income from bonds is taxed as regular income while only 50% of stock income is taxed as regular income. The discount rate you use to evaluate the stocks portfolio should be a. Equal to 5% b. Higher than 5% c. Lower than 5% d. Equal to your income tax rate.
- 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?5. Priyanka has an income of £90,000 and is a von Neumann-Morgenstern expected utility maximiser with von Neumann-Morgenstern utility index u(x) = √x. There is a 1 % probability that there is flooding damage at her house. The repair of the damage would cost £80,000 which would reduce the income to £10,000. I Would Priyanka be willing to spend £500 to purchase an insurance policy that would fully insure her against this loss? Explain. What would be the highest price (premium) that she would be willing to pay for an insurance policy that fully insures her against the flooding damage?Q. 4 Suppose you, owner and CEO of a corporation, are considering a $25 million project that constructs a building in the downtown area of Toronto. The current market price of the similar building is about $20 million. The future price is uncertain. It may be either $28 million or $22 million in one year from now, depending on the economic situation. The company can borrow at a risk-free rate of 5 percent per year. What is the value of this project? Use a binomial model to value this real option.