Question

Suppose Avon and Nova stocks have volatilities of

50 %50%

and

23 %23%?,

?respectively, and they are perfectly negatively correlated. What portfolio of these two stocks has zero?risk?

The portfolio of these two stocks that has zero risk is

nothing?%

of Avon and

nothing?%

of Nova. ? (Round to two decimal? places.)

Answer 1

Here we are given two stocks Avon and Nova with their standard deviation 50% and 23%.We have to create a portfolio of A and B such that portfolio risk=standard deviation =0 or variance =0.(this is possible here only because correlation co-efficient is negative,-1).

Let w1 and w2 be the weights of Avon and Nova respectively. As w1+w2=1,we can take weights as w1 and (1-w1)

Variance   of the portfolio=w1²*variance A+(1-W1)²*variance B+2*w1*(1-W1)Correlation co- efficient*standard deviation of A*standard deviation of B

Variance          =W1²*50*50+(1-2w1+w1²)*23*23+2*w1(1-w1)*-1*50*23

When variance=0, W1²*2500+(1-2w1+w1²)*529-2300*w1(1-w1)=0

2500W1²+529-1058w1+529w1²-2300w1+2300w1² =0

5329w1²-3358w1+529=0

This is a quadratic equation.We can find its roots or values of w by using the formula,

-b +?(b2-4ac) /2a and -b-?b2-4ac/2a.(where b=-3358,a=5329& c=529)since b2-4ac=3358² -4*5329*529=11276164-11276164=0,w1 has only one value and it is –b/2a=- -3358/(2*5329)=0.315(31.50%)

W2=1-w1=0.685(68.50%)

Thus risk free portfolio consists of 31.50% of Avon and 68.50% of Nova