Suppose that there are two assets that are available for investment and an investorhas the following expected utility:EU = E(R,)– 0.5Ao,where expected return and standard deviation are expressed in decimals. Forexample, if expected return is 25%, standard deviation is 15%, and risk aversion is5, expected utility is computed as:EU = 0.25 – 0.5×5x 0.15 = 0.1938Now, assume that there is no other instrument (such as the risk-free security)available. Then, derive the analytical expressions for the optimal portfolio weightsof the first and the second assets for this specific investor. (Hint: We are not talkingabout a numerical response here. Rather, you are asked to derive mathematicallyhow you would compute for the optimal portfolio.)

Answered: e that there are two assets that are…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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A regression function used to examine the factors affecting the chief executive officer salary in financial, manufacturing, utilities and transportation sector is given as below. Figures in parentheses are standard errors. Ln Y = 4.59 +0.257 log(X) + 0.158 D₁ +0.181D21 -0.283D31 se = (0.30) (0.032) (0.089) (0.085) (0.099) n = 209, R² = 0.357 Where Y = salary (in thousands) X₁ = annual sales D₁- D₂= D₂= (1, financial sector otherwise lo, manufacturing sector otherwise utililities sector otherwise Interpret the coefficient for D₂ Compute the approximate percentage difference in estimated salary between the utilities and transportation sector, holding annual sales fixed. Is the difference statistically significant at 1% level?
1.7. A study was conducted to analyse the effect of the size of the deposit level (X₂) and the likelihood that a returnable one-litre bottle will be returned. A return of a bottle recorded as Y = 1and no return Y = 0 was recorded. Use the following table to do a Pearson Chi-Square Goodness of Fit test in order to detect major departures from the logistic response function. That is that the logistic regression is a good fit for the data. ft = [1 + exp(2.077 -0.136X]-¹ Use x²(0.99, df) = 6.63 for a = 0.01, and determine the df-value. 2 10 300 80 ji | πι nj Yj Complete the following table: 1 2 3 j= X₁ 4 1 2 300 50 P₁ = Y/n Ojo not ret 3 15 300 126 E jo not ret n - Ej1 ret Oj1 ret Chi Square 22 300 150 = Ej1 ret = n* π Totals Totals Eo (Ojo - Ejo)² Ejo Totals E₁ (0₁₁ - Ej₁)² Ej₁
Calculate the estimate of σε What is the estimated resting heart rate for someone who is a smoker (Smoke=1) and exercises 1 hour a day (Exercise=1)?
4. When the Titanic sank in 1912, there were over 1,300 passengers aboard. A random sample of 50 passengers that were aboard is taken. The amount they paid for the voyage and whether or not they survived is recorded. A model is fit to predict the probability they survived when the ship sank is obtained. Survived Logistic Fit of Survived By Fare 1.00 0.75 0.50- 0.25- 50 4 Parameter Estimates 100 Term Intercept -1.404254 0.4353289 Fare 0.01246686 0.0097945 For log odds of Yes/No Fare Estimate Std Error ChiSquare 10.41 1.62 150 200 Prob>ChiSq 0.0013* 0.2031 No Yes a) Suppose someone paid a fare of 25 pounds. Predict the probability they survived. b) How much would someone pay to have at least a 65% chance of survival?
2.4
Two risky assets: A and B. The expected return for A is 10% and for B 30%. The variance for returns for A is 400(%2) and for B is 3600(%2). The covariance between A and B returns is -0.05. T-bills give a return of 5% with a standard deviation of 0%. The investor has a risk aversion index, A=5.0. Show all work. 1. calculate the correlation between A and B 2. calculate portfolio return / standard deviation for global mvp 3. optical risky portfolio, P (expected return and SD) 4. slope of CAL 5. how much will the investor invest (A=4) in T-bills, assets A and B?
Table 4 above is displaying odds ratios for each predictor estimated by a multivariablelogistic regression model with all 6 predictors included at the same time. Based onthis model, what is the minimum number of in-hospital deaths they should have intheir dataset? A) 30 B) 50 C) 60 D) 70
2. Suppose that in a certain chemical process the reaction time y (hour) is related to the temperature x (° F) in the chamber in which the reaction takes place according to the simple linear regression model with equation y= 5 - 0.01x and the standard deviation o=0.075. a. What is the expected reaction time when temperature is 250° F? b. Suppose that five observations are made independently on reaction time, each one for a temperature of 250° F. What is the probability that all five times are between 2.4 and 2.6 hours?
4. When the Titanic sank in 1912, there were over 1,300 passengers aboard. A random sample of 50 passengers that were aboard is taken. The amount they paid for the voyage and whether or not they survived is recorded. A model is fit to predict the probability they survived when the ship sank is obtained. Survived Logistic Fit of Survived By Fare 1.00 0.75 0.50- 0.25- 50 4 Parameter Estimates 100 Term Intercept -1.404254 0.4353289 Fare 0.01246686 0.0097945 For log odds of Yes/No Fare Estimate Std Error ChiSquare 10.41 1.62 150 200 Prob> ChiSq 0.0013 0.2031 No Yes a) Suppose someone paid a fare of 25 pounds. Predict the probability they survived. b) How much would someone pay to have at least a 65% chance of survival?
Suppose a point in a regression has a negative residual. This means: 1. The regression over-estimated this point 2. The regression under-estimated this point 3. The regression correctly estimated this point
A toll bridge charges $1.00 for passenger cars and $2.75 for other vehicles. Suppose that during daytime hours, 65% of all vehicles are passenger cars. If 20 vehicles cross the bridge during a particular daytime period, what is the resulting expected toll revenue? [Hint: Let X = the number of passenger cars; then the toll revenue h(X) is a linear function of X.]
(6) Find the mean , variance, autocorrelation function P for the following models: a. Y= 0.6Y+e,- 0.4e t-1 1 1 b.Y, = 2+e;-¿e,s*7 4

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