You have 2,000 to invest and are considering buying some combination of the shares of two companies Donkeylnc and ElephantInc. Shares of Donkeylnc will pay a return of 10 percent if the Democrats are elected, an event you believe to have a 25 percent probability;otherwise the shares pay a zero return. Shares of ElephantInc will pay 8 percent if the Republicans are elected (a probability of 75 percent), zero otherwise. Either the Democrats or the Republicans will be elected. Instructions: Enter your response as percentage rounded to one decimal place. a. If your only concern is maximizing your average expected return, with no regard for risk, you should invest your 2,000 in square and your expected return will be square % . b. What is your expected return if you invest 1,000 in each stock? (Hint:Consider what your return will be if the Democrats win and if the Republicans win, then weight each outcome by the probability that event occurs.) Instructions: Enter your response as percentage rounded to two decimal places. Expected rate of return: square % c. The strategy of investing 1,000 in each stock does not give the highest possible average expected return. You would: choose it anyway because the lower return is compensated by this strategy being less risky.as you receive a reasonable return no matter which party wins. not choose it because a less risky strategy cannot compensate for a lower expected return. not choose it because you should always choose the strategy with the highest average expected return. choose it anyway because this strategy guarantees the same return regardless of which party wins. d. Devise an investment strategy that is riskless that is, one in which the return on your 2,000 does not depend at all on which party wins. Instructions: Enter your responses rounded to two decimal places.

To solve this problem, we need to calculate the expected returns for different investment strategies and evaluate them based on risk and return.<br /><br />### a. Maximizing Average Expected Return<br /><br />1. **DonkeyInc:**<br /> - Probability of Democrats winning = 25%<br /> - Return if Democrats win = 10%<br /> - Expected return from DonkeyInc = \(0.25 \times 10\% = 2.5\%\)<br /><br />2. **ElephantInc:**<br /> - Probability of Republicans winning = 75%<br /> - Return if Republicans win = 8%<br /> - Expected return from ElephantInc = \(0.75 \times 8\% = 6\%\)<br /><br />Since the expected return from ElephantInc (6%) is higher than that from DonkeyInc (2.5%), you should invest your $2,000 in ElephantInc.<br /><br />- **Answer:** Invest in ElephantInc; expected return will be 6.0%.<br /><br />### b. Expected Return with $1,000 in Each Stock<br /><br />1. **If Democrats Win:**<br /> - Return from DonkeyInc = 10% of $1,000 = $100<br /> - Return from ElephantInc = 0% of $1,000 = $0<br /> - Total return = $100<br /><br />2. **If Republicans Win:**<br /> - Return from DonkeyInc = 0% of $1,000 = $0<br /> - Return from ElephantInc = 8% of $1,000 = $80<br /> - Total return = $80<br /><br />3. **Expected Return Calculation:**<br /> - Probability-weighted return = \(0.25 \times 100 + 0.75 \times 80 = 25 + 60 = 85\)<br /> - Expected rate of return = \(\frac{85}{2000} \times 100\% = 4.25\%\)<br /><br />- **Answer:** Expected rate of return: 4.25%<br /><br />### c. Strategy Evaluation<br /><br />The strategy of investing $1,000 in each stock results in a lower expected return (4.25%) compared to investing all in ElephantInc (6%). However, it provides some return regardless of which party wins.<br /><br />- **Answer:** Choose it anyway because the lower return is compensated by this strategy being less risky, as you receive a reasonable return no matter which party wins.<br /><br />### d. Riskless Investment Strategy<br /><br />To devise a riskless strategy, you need to ensure that the return is the same regardless of which party wins. This can be achieved by setting up equations where the returns from both stocks are equal under both scenarios.<br /><br />Let \( x \) be the amount invested in DonkeyInc, and \( 2000 - x \) be the amount invested in ElephantInc.<br /><br />1. **Democrats Win:**<br /> - Return from DonkeyInc = 10% of \( x \)<br /> - Return from ElephantInc = 0% of \( 2000 - x \)<br /><br />2. **Republicans Win:**<br /> - Return from DonkeyInc = 0% of \( x \)<br /> - Return from ElephantInc = 8% of \( 2000 - x \)<br /><br />Set the returns equal:<br /><br />\[ 0.10x = 0.08(2000 - x) \]<br /><br />Solve for \( x \):<br /><br />\[ 0.10x = 160 - 0.08x \]<br />\[ 0.18x = 160 \]<br />\[ x = \frac{160}{0.18} \approx 888.89 \]<br /><br />Invest approximately $888.89 in DonkeyInc and $1111.11 in ElephantInc.<br /><br />- **Answer:** Invest $888.89 in DonkeyInc and $1111.11 in ElephantInc for a riskless strategy.