If we invest a proportion of the fortune in the American stock which has a rate of return X with standard deviation and
invest a proportion of the fortune in the Asian stock which has a rate of return Y with standard deviation
The variance of the return for the portfolio is
We want to minimize this variance (that is risk) by changing the value of .
The first first order condition for the minimization is to equate the first derivative of the portfolio variance w.r.t to 0
ans: The value of for which the risk is minimal is
4. Standard deviation and risk. The standard deviation o(X) of a random variable is the square...
Suppose x is a normal random variable with mean u and standard deviation o. If z is the standardized normal random variable of x, which of the following statements is false? (1) When r = y, the value of z=0. (2) When z is less than the mean y, the value of z is negative. (3) When r is greater than the mean y, the value of z is positive. (4) It is always the case that z <I.
Do bonds reduce the overall risk of an investment portfolio? Let x be a random variable representing annual percent return for Vanguard Total Stock Index (all stocks). Let y be a random variable representing annual return for Vanguard Balanced Index (60% stock and 40% bond). For the past several years, we have the following data. x: 26 0 26 32 23 29 32 −23 −15 −24 y: 9 −10 20 23 23 17 17 −8 −10 −7 a. Use the...
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Answer the question for a normal random variable x with mean u and standard deviation o specified below. (Round your answer to four decimal places.) μ = 1.3 and σ = 0.16. Find P(1.00<x< 1.10). P(1.00<x< 1.10) = Answer the question for a normal random variable x with mean u and standard deviation o specified below. (Round your answer to four decimal places.) μ = 1.3 and σ = 0.16. Find P(x >1.35). P(x > 1.35) =
Do bonds reduce the overall risk of an investment portfolio? Let x be a random variable representing annual percent return for the Vanguard Total Shock Index (all Stocks). Let y be a random variable representing annual return for the Vanguard Balanced Index (60% stock and 40% bond). For the past several years, assume the following data. Compare Question 7 Not yet answered Points out of 4.00 P Flag question Do bonds reduce the overall risk of an investment portfolio? Let...
x You estimate that a passive portfolio, that is, one invested in a risky portfolio that mimics the S&P 500 stock index, yields an expected rate of return of 13% with a standard deviation of 25%. You manage an active portfolio with expected return 18% and standard deviation 28%. The risk-free rate is 8%. Your client's degree of risk aversion is A 3.5 a. If he chose to invest in the passive portfolio, what proportion, y, would he select? (Do...
Assume that you manage a risky portfolio with an expected rate of return of 17% and a standard deviation of 36%. The T-bill rate is 6%. Your risky portfolio includes the following investments in the given proportions: Stock A 27 % Stock B 35 % Stock C 38 % Suppose that your client decides to invest in your portfolio a proportion y of the total investment budget so that the overall portfolio will have an expected rate...
Assume the random variable x is normally distributed with mean u 84 and standard deviation o 5. Find the indicated probability. P(x< 81) P(x <81)(Round to four decimal places as needed.)
Q1. [4 marks Find the expectation and standard deviation of the uniform random variable X that takes values 2, 4, 6, 8, .,98. Hint: consider the random variable Y X/2. Q1. [4 marks Find the expectation and standard deviation of the uniform random variable X that takes values 2, 4, 6, 8, .,98. Hint: consider the random variable Y X/2.
Do bonds reduce the overall risk of an investment portfolio? Let x be a random variable representing annual percent return for the Vanguard Total Stock Index (all Stocks). Let y be a random variable representing annual return for the Vanguard Balanced Index (60% stock and 40% bond). For the past several years, assume the following data. Compute the coefficient of variation for each fund. Round your answers to the nearest tenth. x: 13 0 38 23 35 25 26 -13...