### Deduce formula for weights of stocks

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Q. 1) Consider portfolio P that is comprised from two stocks, A also B. Stock A has a standard deviation of return (A) of 25% while stock B has a standard deviation of return () of 40%. The correlation co-efficient between the two stocks () is 0.5.

a) Graph (sketch) the relation between weight of stock A also variance of portfolio P. Plot weight of stock A along horizontal axis.

b) Deduce formula for weights of stocks A also B at which variance of portfolio P is minimal. Hint: Consider the variance of portfolio P as a function of the weight of stock A, A, also minimize this function with respect to this weight. Find the values of weights.

2) Investors Robert also Linda have coefficients of risk aversions equal to 1 also 2, respectively. They trade risky portfolio P with other investors also can borrow at 2% also lend at 1% in T-bill market. In particular, Robert borrows 20% of his complete portfolio while Linda lends 20% of her complete portfolio. Find the expected return also the variance of return of portfolio P.

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