Question

You have a portfolio of three stocks: Stock A, Stock B, and Stock C.  The expected return of Stock A is 8%, the expected return of Stock B is 10%, and the expected return of Stock C is 12%.  The expected return of the portfolios is 10.5%. If the weight of asset B is three times the weight of asset A, what are the weights for the three assets?

Answer 1

• The expected return of the portfolio is the weighted average of the returns of all the securities held in the portfolio.
• Total of weights of assets held in the portfolio is always 1. (i.e. 100%)

• Let the weight of stock A be ‘p’

• Then, the weight of stock B = 3p (three times the weight of asset A)

• And, weight of stock C = 1 - p – 3p = 1 – 4p (i.e. remaining weight)

• Security	Expected return (%)	Weight
  Stock A	8	p
  Stock B	10	3p
  Stock C	12	1 – 4p
  Total		1

• Given, the expected return of the portfolio = 10.5% (this is the weighted average of the returns of Stocks A, B and C)

• 

• Security	Weight		Expected return (%)	Weighted return (%)
  	i		ii	i × ii
  Stock A	p	0.15	8	1.2
  Stock B	3p = 3 × 0.15	0.45	10	4.5
  Stock C	1 – 4p = 1 – 4 × 0.15	0.40	12	4.8
  		1.00		10.5