We consider a market with 1 riskfree asset and N risky assets. The following tables show theinvestment goal of three different investors:Investor AInvestor BInvestor CYou are given that● Expected return μp ≥ 0.2Standard deviation of return op ≤ 0.2● Expected return μp ≥ 0.15● Standard deviation of return op ≤ 0.12Expected return µp ≥ 0.1● Standard deviation of return op ≤ 0.15●Investment goals●Exactly 1 of the above investment goals is infeasible.The return rate of riskfree asset is rf = 0.05.Assuming that the tangency portfolio exists and is efficient(b) An investor is seeking for the minimum variance portfolio with expected return up =0.17. He chooses a portfolio consisting of these assets (riskfree and risky assets). It isfound that the expected return and standard deviation of return of this portfolio areMp = 0.17 and op = 0.2. Determine if it is the desired portfolio.

To determine if the portfolio chosen by the investor is the desired portfolio, we need to check if…

Answered: We consider a market with 1 riskfree…

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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1. ABC inc. stock is currently selling for $30, one year from today the stock price can either increase by 20% or decrease by 15%. The probability of an increase in the stock price is equal to 0.3. The one-year risk-free rate is 5% What is the value of a European put that expires in one year with an exercise price of $24. 2. Graphically, show the value and the profit and loss of the following butterfly position: Long in a call with an exercise price of $30, short in 2 calls with an exercise price of $45, and long in a call with an exercise price of 60. All calls are written on the same stock and have the same maturity. 3. "Early exercise of an American option on a stock that does not pay any dividend is not optimal regardless of whether the option is a Call or a Put". True, False, or Uncertain. Explain.
Suppose that the borrowing rate that your client faces is 9%. Assume that the equity market index has an expected return of 13% and standard deviation of 25%, that rf = 5%. Your fund manages a risky portfolio, with the following details: E(rp) = 11%, p = 15%. What is the largest percentage fee that a client currently lending (y 1)? (Negative values should be indicated by a minus sign. Do not round intermediate calculations. Round your answers to 1 decimal place.) y 1
Example 10: P and Q two securities, with expected returns of 15% and 24% respectively, and standard deviation of 35% and 52% respectively. Calculate the standard deviation of a portfolio weighted equally between the two securities if their correlation is -0.9.
1. In the credit card default data, we would like to predict the default status of a cus- tomer based on the monthly balance, the student indicator and the income. The input coding for class predictors is set as Deviation. Given the following output from logistic regression, what is the estimated probability of default for a student with a balance of $2500 and an income of $40000? Analysis of Haxinun Likelihood Estinates Standard Vald Error Chi-Square Pr > Chisq Paraneter default DF Estinate Intercept Yes -11.1924 0.4506 616.84 <.0001 balance Yes 0.00574 0.000232 611.89 <.0001 incone Yes 3.033E-6 8.203E-6 0.14 0.7115 student No Yes 0.3234 0.1181 7.49 0.0062
I need null hypothesis, alternative hypothsis, then X2, p-value
17. A risk manager would like to simulate the price of a stock using the discretized GBM, where St+At = St + µS{At+√Ã£$£€ where μ and o denote, respectively, the stock annual mean return and annual volatility. The data suggest that the weekly mean return on the stock is 0.5% and the weekly volatility is 4%. Assuming a weekly time step of At = 1/52 (in terms of annual units), what is the appropriate estimate of μ? (a) = 26.4% (b) û = 30.16% (c) û = 4.5% (d) û = 17.94% 18. Suppose that the price of an asset obeys geometric Brownian motion (GBM) with an annual drift μ = 0.01 and an annual volatility of o= 0.25. If today's price is $100, what is the probability that the price two years from now will drop below $80? Hint: Recall that under GBM, the future price at T, i.e. ST, given today's spot price, St, is with TT-t and €~ = (a) 21.51% (b) 35.48% (c) 51.1% (d) 30.47% ST= St x exp (μ x exp [(μ-27 ) XT + √F X 0 Xe] N (0, 1).
6. True or False? Assume the below life table was constructed from following individuals who were diagnosed with slow-progressing form of prostate cancer and decided not to receive treatment of any form. The calculated survival probability for year 3, if the Kaplan-Meir approach is used to calculate the survival probability, is approximately 0.7438. Time in years Number at risk Nt Number of deaths, Dt Number of censored Ct Survival Probability 0 20 1 1 20 3 2 17 1 3 16 2 1
21. in a regression model if the error distribution is normally distributed then A. None B. Residual plot will give a line with 45angles with the X-axis. C. Normal probability plot will give a line with slope 1. D. Normal probability plot will give a line with 15° angles with the X-axis.
3. Show your complete solution.
5. The average price of a new two story townhouse is P1,600,000, find the maximum and minimum prices of the townhouse that a contractor will build to include the middle 70% the market. Assume that the standard deviation of prices is P300,000 and the variable i normally distributed.
Suppose there are three fare classes in an airline fares p1 = $300, p2 = $200, and p3 = $100. You want to utilize the EMSR-b heuristic to calculate the protection level for classes 1 and 2 together. The demand distribution for class 1 is Normal with mean 50 and standard deviation 5. The demand distribution for class 2 is Normal with mean 75 and standard deviation 12. What is the price for the virtual class 1-2 under EMSR-b?
Asset A offers an expected rate of return of 10% with a standard deviation of 25%. Asset B offers an expected rate of return of 5% with a standard deviation of 30%. Assume that the risk-free interest rate is zero. Suppose Assets A and B are perfectly positively correlated. Draw a graph illustrates why a rational investor would or would not hold Asset B in one's portfolio. [Hint: Can provide verbal support to the graph, if necessary, in no more than two lines.]

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