Question

1. Suppose we are offered to buy a portfolio made of six stocks from a set of twenty stocks seven of which are high risk (H). five are moderate risk (M) and eight are low risk (L a) How many such portfolios are available Hint: the risk category is irrelevant here. b) A portfolio is called balanced if it contains exactly two stocks of each risk category. How many balanced portfolios are available? Hint: use combinations.

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Answer #1

a) Number of stocks available = 20

Number of stocks to be chosen = 6

Number of portfolios available = 20C6

= 20!/(6! x (20-6)!)

= 38,760

b) Number of balanced portfolos = Number of ways in which 2 high risk stocks can be selected x Number of ways in which 2 moderate risk stocks can be selected c Number of ways in which 2 low risk stocks can be selected

= 7C2 x 5C2 x 8C2

= 21 x 10 x 28

= 5,880

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