Imagine we have two independent uniform distributions, A and B. A ranges between −2 and −1,...
Imagine we have two independent uniform distributions, A and B. A ranges between −2 and −1, and is zero everywhere else. B ranges between +1 and +2, and is zero everywhere else. What are the mean and standard deviation of a portfolio that consists of 50% A and 50% B? What are the mean and standard deviation
of a portfolio where the return is a 50/50 mixture distribution of A and B?
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Imagine we have two independent uniform distributions, A and B.
A ranges between −2 and −1,...
?1 and ?2 are independent random variable with uniform distributions between 0 and 1. Find ?(?1?2...
?1 and ?2 are independent random variable with uniform distributions between 0 and 1. Find ?(?1?2 < 1⁄4).
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2. Portfolio Choice Suppose we have assets A and B with the following distribution of returns:...
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An investor is considering two portfolios (Portfolio 1 and 2). Both possible portfolios consist of a...
An investor is considering two portfolios (Portfolio 1 and 2). Both possible portfolios consist of a 50% weight on Asset A: this asset has an expected return of 12% and a standard deviation of 18%. The other half of Portfolio 1 consists of Asset B: it has an expected return of 8% and a standard deviation of 10%. The other half of Portfolio 2 consists of Asset C: it has an expected return of 8% and a standard deviation of...
5. Suppose that annual precipitation is uniformly distributed, and ranges between 25 inches and 72 inches....
5. Suppose that annual precipitation is uniformly distributed, and ranges between 25 inches and 72 inches. (a) What is the probability that a year will have between 29 and 44 inches of precipitation? (2) (b) What is the 30th percentile of this distribution? (2) 6. Wheat yields per acre are normally distributed, with mean 46 bushels, and standard deviation 10 bushels. (a) What is the probability that next year’s yield is between 35 and 50 bushels? (2) (b) What is...
Stocks A and B each have an expected return of 15%, a standard deviation of 20%,...
Stocks A and B each have an expected return of 15%, a standard deviation of 20%, and a beta of 1.2. The returns on the two stocks have a correlation coefficient of -1.0. You have a portfolio that consists of 50% A and 50% B. Which of the following statements is CORRECT? The portfolio's standard deviation is zero (i.e., a riskless portfolio). The portfolio's beta is greater than 1.2. The portfolio's standard deviation is greater than 20%. The portfolio's expected...
A random variable follows the continuous uniform distribution between 20 and 50 a) Calculate the probabilities...
A random variable follows the continuous uniform distribution between 20 and 50 a) Calculate the probabilities below for the distribution. 1) P(x≤40) 2) P(x=39) b) What are the mean and standard deviation of this distribution?
1. Let's assume you live in a world where there are only 2 risky assets, asset A and asset B. The...
1. Let's assume you live in a world where there are only 2 risky assets, asset A and asset B. There is also a risk free asset. You have the following information about the assets: Asset A 10% 5% Asset B 20% 25% Risk free (F) 5% 09% Expected Return Standard Deviation Let's assume the correlation between the returns of asset A and B is +1. Make a portfolio Pl that invests 50% in A and 50% in B. Calculate...
1. The universe of available securities includes two risky stock funds, A and B, and T-blls....
1. The universe of available securities includes two risky stock funds, A and B, and T-blls. The data for the universe are as follows Expected Return Standard Deviation A 10% 20% В 30 60 T-bills The correlation coefficient between funds A and B is -0.2. a. Find the optimal risky portfolio, P, and its expected return and standard deviation. b. Find the slope of the CAL supported by T-bills and portfolio P c. How much will an investor with A...
Univariate Gaussians or normal distributions have a simple representation in that they can be completely described...
Univariate Gaussians or normal distributions have a simple representation in that they can be completely described by their mean and variance. These distributions are particularly useful because of the central limit theorem, which posits that when a large number of independent random variables are added, the distribution of their sum is approximated by a normal distribution. In other words, normal distributions can be applied to most problems Recall the probability density function of the Univariate Gaussian with mean and variance...
2. Portfolio Choice Suppose we have assets A and B with the following distribution of returns: Probability Return for A .01 Return for B -.14 .00 .03 TO .05 .07 14 .30 .09 .50 a. Compute the expected returns for assets A and B, rA and rg. b. Compute the variances of A and B, oả and oß. c. Compute the covariance of A and B, CAR- d. Use the formulas for portfolio returns and risk to write the expected...
1. Let's assume you live in a world where there are only 2 risky assets, asset A and asset B. There is also a risk free asset. You have the following information about the assets: Asset A 10% 5% Asset B 20% 25% Risk free (F) 5% 09% Expected Return Standard Deviation Let's assume the correlation between the returns of asset A and B is +1. Make a portfolio Pl that invests 50% in A and 50% in B. Calculate...
1. The universe of available securities includes two risky stock funds, A and B, and T-blls. The data for the universe are as follows Expected Return Standard Deviation A 10% 20% В 30 60 T-bills The correlation coefficient between funds A and B is -0.2. a. Find the optimal risky portfolio, P, and its expected return and standard deviation. b. Find the slope of the CAL supported by T-bills and portfolio P c. How much will an investor with A...
Univariate Gaussians or normal distributions have a simple representation in that they can be completely described by their mean and variance. These distributions are particularly useful because of the central limit theorem, which posits that when a large number of independent random variables are added, the distribution of their sum is approximated by a normal distribution. In other words, normal distributions can be applied to most problems Recall the probability density function of the Univariate Gaussian with mean and variance...
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