a) Do you think the variables x and y are independent? Explain your answer. No. Interest rates probably has no effect on the investment returns.No. Interest rate probably affects both investment returns. Yes. Interest rates probably has no effect on the investment returns.Yes. Interest rate probably affects both investment returns. (b) Suppose you decide to put 75% of your investment in bonds and 25% in real estate. This means you will use a weighted average w = 0.75x + 0.25y. Estimate your expected percentage return ?w and risk ?w. ?w = ?w = (c) Repeat part (b) if w = 0.25x + 0.75y. ?w = ?w =
Previously, you studied linear combinations of independent random variables. What happens if the variables are not independent? A lot of mathematics can be used to prove the following: Let x and y be random variables with means ?x and ?y, variances ?2x and ?2y, and population
σ2w = a2σ2x + b2σ2y + 2abσxσyρ
In this formula, r is the population correlation coefficient, theoretically computed using the population of all (x, y) data pairs. The expression ?x?y? is called the
Do you have to be rich to invest in bonds and real estate? No, mutual fund shares are available to you even if you aren't rich. Let x represent annual percentage return (after expenses) on the Vanguard Total Bond Index Fund, and let y represent annual percentage return on the Fidelity Real Estate Investment Fund. Over a long period of time, we have the following population estimates.
(a) Do you think the variables x and y are independent? Explain your answer.
(b) Suppose you decide to put 75% of your investment in bonds and 25% in real estate. This means you will use a weighted average w = 0.75x + 0.25y. Estimate your expected percentage return ?w and risk ?w.
?w =
?w =
(c) Repeat part (b) if w = 0.25x + 0.75y.
?w =
?w =
(d) Compare your results in parts (b) and (c). Which investment has the higher expected return? Which has the greater risk as measured by ?w?
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