Hello experts, PROBLEM SET You must support your answers with formulas or verbal
ID: 2780538 • Letter: H
Question
Hello experts,
PROBLEM SET You must support your answers with formulas or verbal explanations. Unsupported answers will result in no credit. As an active fund manager, you have obtained information on three individual stocks, the market index, and T-bills as follows: Total Asset Stock 1 Stock 2 Stock 3 Market Index T-bills Expected Return (% 20.0 16.0 6.0 10.0 4.0 Standard Deviation (% 80.00 60.00 50.00 40.00 0.00 Bcta 0.8 0.0 You decide to use the above information to form an optimal active portfolio, consisting of the three individual stocks. Determine the corresponding weights for the three stocks in the optimal active portfolio. Show your work. As an option trader on GM stock, you have collected the following information: (1) GM stock's current price is S $100 (2) GM's future prices follow a two-state path with u-1.1052 (in Up state) and d 0.9048 (in Down state) in each period. (3) The one-period riskfree holding period return is R-1.01. Consider two American options on GM stock (a Put and a Call), both have a strike price of $110 and 5 periods before expiration. (a) What is the value of the American Put today? Show your work. (b) What is the value of the American Call today? Show your work.Explanation / Answer
a) The expected rate of return on a portfolio is the weighted average of the expected returns of the individual portfolio:
Stock A= aA/s2(eA)= .20/.80=.25
Stock B= aB/s2(eB)= .16/.60=.27
Stock C= aC/s2(eC)= .06/.50=.12
Total = 0.25+0.27+0.12 = 0.64
Weight of Stock A= Stock A/ Total Stock
= 0.25/0.64 = 0.390
Weight of Stock B= Stock B/ Total Stock
= 0.27/0.64 = 0.421
Weight of Stock C= Stock C/ Total Stock
= 0.12/0.64 = 0.188
Total Weight of Optimal Portfolio = 0.390+0.421+0.188 = 0.999
b) Stock Price = $100
Strike Price = $ 110
Up state future price= 1.1052
Down State future Price = .9048
Value of Put Option= Max(Stock Price- Strike Price,0)
= (100-110,0)-0.9048
= 0-0.9048
= -0.9048
Value of Call Option = Max(Stock Price- Strike Price,0)
= (100-110,0)-1.1052
= 0-1.1052
= -1.1052
In both the cases, the value is negative as the stock price is less than the strike price.
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