answer as many as you can please thank you

Questions for Thought . If you repeat the dice game several times, or 4. A portfolio can contain more than two items, perhaps in a class, you might find that Red oc- such as a mixture of Red, White, and Green. casionally comes out the winner. Seeing that all Consider the portfolio that has 40% Red, 50% of the others lose with Red, how might it be that Green, and 10% White. some team comes out ahead with Red?1 Is Pink the best mix of Red and White? There's (a) Find the mean and variance of this portfolio. no rule that says a portfolio has to be an equal (b) Compare the long-run performance of this mix of two investments. portfolio to a Pink. (c) Is this the best mixture of the three invest- (a) Find the mean and variance of a portfolio ments, from a long-run point of view? (Keep that has 60% invested in White and 40% all of the shares between 0 and 1.) invested in Red. 5. Red is artificial; we don't know an investment (b) Does the portfolio in (a) outperform Pink in that would work so well if paired with returns the long run? on Treasuries (White). What other attribute of (c) How might you find a better mixture of Red the simulation is artificial? (Hint: This attribute and White? makes it easy to find the variance of Pink.) 3. The example portfolio Pink mixes Red and 6. The role of randomness in investing has paral- White. Might an investment that mixed Green lels in gambling, such as in the following game. and Red perform better? Consider a slot machine. When you put in x dol- (a) Find the mean and variance of a portfolio lars and pull the handle, it randomly pays out that mixes half Red and half Green. either 0.7x, 0.8x, 0.9x, 1.1x, 1.2x, or 1.5x. The (b) Does this new mixture outperform Pink in payouts are equally likely. Here are two ways to the long run? play with the machine. (a) Put in $1, pull the handle, and keep what you get. Repeat. (b) First, put in $1 and pull the handle. Then put back into the machine whatever the For more on this perspective, see our paper D. P. Foster and R. A. machine pays. Repeat. Stine (2006). " Warren Buffett: A Classroom Simulation of Risk and (c) Can you win money with either approach? Wealth When Investing in the Stock Market." The American Statisti- Which is the better way to play? (We suggest cian, 60, 53-60. using dice to simulate these methods.)