stock boom and stock bust are perfectly negatively correlated and their standard deviation are 24.495% and...
stock boom and stock bust are perfectly negatively correlated and their standard deviation are 24.495% and 9.798% respectively. what is the approximate weight of stock boom to form a portfolio that has no volatility?
a. 15%
b. 20%
c. 28%
d. 49%
e. it is not possible to form a risk-less portfolio with stocks boom and bust
Homework Answers
correlation between stocks , c = -1
Standard deviation of stock boom , S1 = 24.495% = 0.24495
Standard deviation of stock bust , S2 = 9.798% = 0.09798
let weight of stock boom in portfolio = w
weight of stock boom in portfolio = 1- w
volatility of portfolio = variance of portfolio, V = 0
V = (w*S1)2 + ((1-w)*S2)2 + 2*w*(1-w)*S1*S2*c
V = (w*24.495)2 + ((1-w)*9.798)2 + 2*w*(1-w)*24.495*9.798*-1
V =( 600.005025*w2) + ((1-w)2*96.000804) - (480.00402w*(1-w))
V = 600.005025*w2 + ((1+w2-2w)*96.000804) - 480.00402w + 480.00402w2
V = 600.005025*w2 + 96.000804 + 96.000804w2 - 192.001608w - 480.00402w + 480.00402w2
V = 1176.009849w2 - 672.005628w + 96.000804
V = 0
1176.009849w2 - 672.005628w + 96.000804 = 0
we will substitute the given options in the question for w in the above equation and confirm the answer
when we substitue, w = 28% = 0.28 in the above equation
1176.009849(0.28)2 - 672.005628*0.28 + 96.000804 = 0.038 or 0 ( after rounding off)
hence correct option is c) 28%
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