Suppose you have a portfolio that has a long position in call Ce(So, T, X1) and a short position in call Ce(So, T, X2), where X2 < X1. Your portfolio value is higher than zero O zero not higher than zero O none of the other choices
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- 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%4) You are a financial professional working in a corporate loan department. A company named Mitch Hedberg Inc. (MH) comes to you for a loan. MH has debt from a previous loan (given by a different firm than yours) of 200. Your company analysts say that MH is likely to earn either 180, 240, or 300 this year - each with a probability of 1/3. MH wants you to lend them 100. MH could use this borrowed 100 to do either project X or project Y. Project X has a guaranteed return of 125 if the 100 is put there. Project Y may return either 0 or 210; each has probability of 1/2 and also costs 100 to do. a) Which project, X or Y, has the larger expected value? b) If you lend MH the 100, what will they do with the money? Why? Show your math. c) Should you lend MH the money or not? Show your math. d) Why did I choose the letters "MH" for this problem? What financial economic concept with initials "MH" is important in this problem?You have $1,000 that you can invest. If you buy Ford stock, you face the following returns and probabilities from holding the stock for one year: with a probability of 0.2 you will get $1,500; with a probability of 0.4 you will get $1,100; and with a probability of 0.4 you will get $900. If you put the money into the bank, in one year’s time you will get $1,100 for certain. a) What is the expected value of your earnings from investing in Ford stock? b) Suppose you are risk-averse. Can we say for sure whether you will invest in Ford stock or put your money into the bank?
- 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?Suppose Caroline is choosing how to allocate her portfolio between two asset classes: risk-free government bonds and a risky group of diversified stocks. The following table shows the risk and return associated with different combinations of stocks and bonds.CombinationFraction of Portfolio in Diversified StocksAverage Annual ReturnStandard Deviation of Portfolio Return (Risk)(Percent)(Percent)(Percent)A 0 1.50 0B 25 3.00 5C 50 4.50 10D 75 6.00 15E 100 7.50 20There is a relationship between the risk of Caroline's portfolio and its average annual return.Suppose Caroline currently allocates 75% of her portfolio to a diversified group of stocks and 25% of her portfolio to risk-free bonds; that is, she chooses combination D. She wants to reduce the level of risk associated with her portfolio from a standard deviation of 15 to a standard deviation of 5. In order to do so, she must do which of the following? Check all that apply. Sell some of her stocks and use the proceeds to purchase…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.
- If investors want portfolios with small risk, should they look for investments that have positive covariance, have negative covariance, or are uncorrelated? Does a portfolio formed from the mix of three investments have more risk than a portfolio formed from two?3b. By investing in a particular stock, Mullins can in one year make a profit of $5000 with a probability 0.4 or lose $5000 with probability of 0.6. What is Mullins expected gain?Question 11 The beta of an active portfolio is 1.45. The standard deviation of the returns on the market index is 22%. The nonsystematic variance of the active portfolio is 3%. The standard deviation of the returns on the active portfolio is a) 36.30%. b) 5.84%. c) 19.60%. d) 24.17%. e) 26.0%.
- For a given option portfolio, you are long vega (value increases as volatility goes up), and short theta (as time passes your options portfolio loses money). Are you net long or short options? Net long, because as volatility goes up and it increases in value and as time passes you lose value. Net short, because as volatility goes up and it decreases in value and as time passes you increase value. not consistent you are long one and short the other, so can't tell completely independent derivatives, its apples and oranges and no reflection on your portfolio3. The day prior to the release of yearly profits, a stock has price equal to 1. An investor is deciding whether to buy the stock or not. The investor has a wealth equal to 10. Yearly profits can be high with probability 0.4 or low with probability 0.6. If profits are high, the price will double on the following day; if profits are low, the price will halve on the following day. If the investor does not buy the stock, her wealth remains unchanged. If the inverstors buys the stock, she will sell the stock on the following day (regardless of whether the profits are high or low) and she will accrue the relative profit or loss. In other words, she cannot hold the stock for more than one day. The investor does not discount the future and she abides von-Neumann and Morgenstern axioms. Her vNM utility index over money is u (x) = r with 3 E (0,2). • Write down the two possible gambles faced by the investor. • Does the investor buy the stock or not? Explain. • Compute the Arrow-Pratt measure of…Problem 2 Suppose a firm needs $100 to invest in a project. The firm can choose between two projects: S (safe) or R (risky). The bank cannot directly control the choice of project. If it is S, then it will yield a cash flow of $300 with probability 0.8 and zero with probability 0.2. If it is R., the project will yield a cash flow of $423 with probability 0.5 and zero with probability 0.5. Everybody is risk neutral. The riskless interest rate is 20%. The bank would like to induce the choice of project S. Assume that collateral worth $1 to the firm is worth $0.9 to the bank. The banking sector is perfectly competitive. a. Demonstrate that when the bank offers an unsecured loan, project S will never be chosen. b. Calculate the interest rate when the bank offers an unsecured loan. c. What kind of secured contract would the bank offer to induce the choice of project S? d. Calculate the collateral and interest rate associated with this secured contract.
