Question

A portfolio contains three stocks (Stock A, Stock B, and Stock C). The overall value of the portfolio increased 20 percent during 2005--the value of Stock A increased by 15 percent, the value of Stock B increased by 22 percent, and the value of Stock C increased by 30 percent. If 40 percent of the total funds in the portfolio were in Stock A at the beginning of 2005, what was the percent of funds (weight) invested in stock B ?

Answer 1

This is pure math, I won't solve the problem for you but I'll give you a hint: you have to solve 2 equations with 2 unknowns and your goal is to find the weight of each stock (you already have the weight of stock A).

Answer 2

What are the two equations ?

Answer 3

Stock B=45%

Answer 4

let w1, w2 and w3 be the weights for stock A, B and C
obviously w1 + w2 + w3 = 1

In addition, w1 = 0.4, which is given in the question. In other words, w2 + w3 = 1 - w1 = 0.6

Further, w1 * 0.15 + w2 * 0.22 + w3 * 0.3 = 0.2
=> 0.4 * 0.15 + w2 * 0.22 + w3 * 0.3 = 0.2

So now you have two equations with two unknowns as follows:

w2 + w3 = 0.6
0.4 * 0.15 + w2 * 0.22 + w3 * 0.3 = 0.2

I assume you'll have no problem to solve that :)