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  3. consider two stocks with returns ?a and ?b with th

Consider two stocks with returns ?A and ?B with the following properties. ?A takes values -10...

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Basic Math

  1. Consider two stocks with returns ?A and ?Bwith the following properties. ?A takes values -10 and+20 with probabilities 1/2. ?B takes value -20 withprobability 1/3 and +50 with probability 2/3.????(?A,?B) = ? (some number between -1 and1). Answer the following questions

    1. (a) Express C??(?A,?B) as a function of?

    2. (b) Calculate the expected return of a portfolio that containsshare ? of stock ? and

      share 1 ? ? of stock ?. Your answer should be a function of?

    3. (c) Calculate the variance of the portfolio from part ? (Hint:returns are now potentially dependent)

    4. (d) What value of ?* minimizes the variance of the portfolio?Your answer should be a function of ?, denoted by ?*(?).

  2. (e) For what range of values for ? is your ?*(?) ? 1? What isthe solution to the above problem if ? is outside of that range?(Hint: draw a graph and nd ?* ? [0, 1] that minimizes variance)

  3. (f) Is ?*(?) increasing or decreading? (Hint: take thederivative with respect to ?)

  4. (g) Which ? would the investor prefer to have, positive ornegative? What is the intuition for that result?

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