Question

Ms. Maple is considering two securities, A and B, and the relevant information is given below:  

State of the economy	Probability	Return on A(%)	Return on B(%)
Bear	0.3	-2	0.5
Bull	0.7	16	0.5

Suppose Ms maple wants to have a portfolio, which pays 20% expected return. What are the weights of securities A and b in this new portfolio. What do these weights means?

Answer 1

For finding weight we need to first calculate expected return

so,

Expected return from Security A = (0.3 x -2%) + (0.7 x 16%) = 10.60%

Expected return from Security B = (0.3 x 5%) + (0.7 x 5%) = 5.00%

Portfolio return = (WA x ERA) + (WB x ERB)

Where,

WA = Weight of security A in portfolio

ERA = Expected Return of Security A

WB = Weight of security B in portfolio

ERB = Expected Return of Security B

We know that total weight is 1 so WA + WB = 1 so we can say WB = 1 - WA

0.20 = (WA x 0.106) + (WB x 0.05)

0.20 = 0.106WA + [ (1 - WA) x 0.05]

0.20 = 0.106WA + 0.05 - 0.05WA

0.15 = 0.056WA

WA = 2.67857 approx 2.6786 or say 267.86%

So, Weight of WB = 1 - WA = 1 - 2.6786 = -1.6786 or say -167.86%

Weight means that % of investement in that security of the total portfolio.

Here in this invester need to take portfolio position that means he require to buy Security A 267.86% of his total portflio value and short sell/sell the security B 167.86% of his total portfolio.

Calculation

Particular	Exp Return	Weight	W x EX. Ret.
Sec A	10.60%	2.6786	28.39%
Sec B	5.00%	-1.6786	-8.39%
Portfolio Return	20.00%