$1.$ What is the key difference between speculation and gambling?

$2.$ Is investing in the equity market a gamble? Is it a fair game?

$3.$ What does it mean for investors to have homogeneous expectations?

$4.$ Assume two investors A & B have essentially the same belief that US stocks are trading at fair value $$ meaning they expect to earn the historical risk premium over the next $5-10$ years. Use utility theory to explain why investor A might sell his holding in an ETF that tracks the S&P $500,$ while investor B might buy it$.$

$5.$ The Vampguard Fund is a risky portfolio with an expected return $=12\%$ and std deviation $=18\%.$ T$-$Bills offer a risk$-$free return of $7\%.$ What is the level of risk aversion that would make the investor indifferent between the risky portfolio and T$-$Bills?

$6.$ Fill in the table below for the indifference curve that corresponds to a Utility $=0\mathrm{.}05$ and risk aversions of A$=3$ and A$=4.$

Standard deviation Variance E $($r$)($A$=3)$ E $($r$)($A$=4)$

$0\mathrm{.}0$

$0\mathrm{.}05$

$0\mathrm{.}10$

$0\mathrm{.}15$

$0\mathrm{.}20$

$0\mathrm{.}25$

$7.$ The table below shows four investments of varying risk and return. If your risk aversion coefficient A $=4,$ which investment would you select and why?

Investment E$($r$)$ Std Deviation Utility for $($A$=4)$

$1\mathrm{.}12\mathrm{.}3$

$2\mathrm{.}15\mathrm{.}5$

$3\mathrm{.}21\mathrm{.}16$

$4\mathrm{.}24\mathrm{.}21$

$8.$ In the example above, if the investor was risk neutral $($A$=0)$ which investment would he select and why?

$9.$ You have a chance to play a coin flip game where if the coin comes up heads you get $$5,000$; but lose $$1,000$ if it comes up tails. If you are risk averse $($A$>0),$ how much would you need to be paid to walk away and not play the game? Explain.