Equities e. Suppose you are deciding between purchasing the two equities below, both of which are dependent on the state of the world (the economy either operates in a high or low capital world). Given their respective characteristics and there being equal probability that the world will be in each state, which equity would you purchase to maximize your expected return after one year? Stock 1, High Capital 2% Stock 1, Low Сapital 8% Stock 2, High Сapital Stock 2, Low Сapital 4% Required Return 3% Dividend $20 $10 $12 $5 Price of Equity Today $200 $200 $150 $150 f. The economy is just leaving a recession causing firms to have increased optimism in the profitability of research and development. Using rational expectations theory, how would you expect the returns to a representative firm's stock to change?
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- INV 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?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?Angie owns an endive farm that will be worth $90,000 or $0 with equal probability. Her Bernouilli utility function is u(w) =√w, where w is her wealth level (sum of initial wealth and the worth of the endive farm). 1. Suppose her firm is the only asset she has, that is, she has no initial wealth. What is the lowest price P at which she will agree to sell her endive farm before she knows how much it will be worth? 2. Redo part (1) assuming that she has $160,000 in her bank safe. 3. Compare and discuss your results in parts (1) and (2). What relationship can you find between Angie’s initial wealth level (zero versus $160,000) and her risk aversion?
- 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.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.1) What are risk preferences of this investor, are they risk-averse, riskneutral or risk-loving?2) Find A as a function of w.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. Calculate relative risk aversion for this investor. How does relative risk aversion depend on wealth?
- Suppose that, holding yield constant, investors are indifferent as to whether they hold bonds issued by the federal govemment or bonds issued by state and local governments (that is, they consider the bonds the same with respect to default risk, information costs, and liquidity) Suppose that state governments have issued perpetuities (or consoles) with $78 coupons and that the federal govemment has also issued perpetuities with $78 coupons. If the state and federal perpetuites both have after-tax yields of 8%, what are their pre-tax yields? (Assume that the relevant federal income tax rate is 31.13%) * The pre-tax yield on the state perpetuity will be______________% * The pre-tax yield on the federal perpetuity will be_______________%After careful analysis, you have determined that a firm’s dividends should grow at 15%, on average, in the foreseeable future. The firm’s last dividend was $1.5. Compute the current price of this stock, assuming the required return is 20%What is the difference if any between an individual gambling at a casino and gambling by buying a stock? What is the difference for society? For an individual, gambling at a casino or by buying a stock A. is the same because they have the same expected values. B. is the same insofar that both involve uncertain outcomes C. different because the expected value of gambling in a casino is higher. 2. For society, gambling at a casino or by buying a stock A. is the same because neither redistribute income. B. is different because buying a stock more directly provides capital for companies to make productive investments. C. is the same because both have no effect on the budget deficit.
- Suppose we have 2 countries: Home and Foregin. Each has one asset: a banana tree. The bananas go bad after every month, so they cannot be saved. The prouction is as follows: {Home, Foreign} {200, 100} with probability 1/4. {100, 150} with probablity 3/4. A) What would be the expected yield for each country without trade? B) Countries can now trade shares of stock of any size. How much Foreign stocks will Home buy? How much stocks will Home trade in return?Millicent’s utility function is U(w) = W0.5 , where W is her wealth. She owns a “pure water” producing firm that will be worth GH100 or 0 Ghana cedis next year with equal probability. a. Suppose her firm is the only asset she has. What is the lowest price at which she will agree to sell her pure water? (Hint: price=amount that will give her the same expected utility) b. Assume that she has GH200 safely stored under her mattress, find the new lowest price at which she will agree to sell her “pure water” producing firm c. From your answers in parts (a) and (b), what is the relationship between her wealth and her degree of risk aversion?Suppose Real Option Inc. has a product that generates the following cash flow. At t=1, the demand can be high or low. There is a probability of 0.6 that demand is high. If demand is high (low) the cash flow is CFH=400 (CFL=200). At t=2, the demand can also be high or low. If demand was high at t=1, then a high demand at t=2 arises with probability 0.7. If demand was low at t=1, then a high demand at t=2 arises with probability 0.2. If demand is high (low) at t=2 then CFH=400 (CFL=200). The interest rate for this project is 20%. (a) Draw the event and decision tree. (b) What is the market price (expected value) of Real Option Inc. at t=0? Now suppose Real Option Inc. can rent a platform to run a marketing campaign. For this purpose Real Option Inc. must sign a two year contract with the platform provider. The costs for using the platform are 180 per period. Marketing itself does not cost anything and has the following effect. In the high demand state, marketing doubles the demand. In…