Question

An investor is concerned about the expected return and the risk associated with the investments. The investor wants to find out the optimal allocation of money in these two stocks. The investor's objective is to minimize the portfolio's risk while the portfolios expected return is at least 5%. Let s1 and s2 be the fraction of investments in stock 1 and stock 2, The investor wants to invest s1= 40% and s2= 60%. What is the investor's risk for this plan?

	Stock 1	Stock 2
	-1.62	-11.96
	3.12	-2.67
	1.34	16.31
	5.98	12.61
	7.96	8.56
	-3.3	13.22
	1.66	14.51
	3.24	-10.47
xBar	2.30	5.01
Variane	13.60	134.61
Cov	4.40

Answer 1

This is the most basic question of portfolio return and portfolio risk.

Given data:

Weights of each stock i.e. s1=40% or 0.40 and s2= 60% or 0.60

Return of each stock i.e. R1= 2.30 and R2 = 5.01.

Variance i.e. SD² V1= 13.60 and V2=134.61

Covariance i.e. relation between 2 stocks i.e. COV _AB = 4.40.

Return of the portfolio = s1*R1 + s2* R2 = 0.40*2.3+0.60* 5.01 = 3.926%.

Risk of the portfolio of 2 stocks = Sqrt of [s1²*V1 + s2²*V2 + 2*s1*s2*COV_AB]

= Sqrt[0.40*13.6 +0.60*134.61 + 2*0.40*0.60*4.40]

= 6.93 %

The investors risk for the plan is 6.93% with an expected return of 3.926% if he invests 40% in stock 1 and 60% in stock 2. It should be noted that the investors target was to achieve at least 5% return. Hence the portfolio should not be made in this way. It should also be noted that stock 2 is providing a return of 5.01% and stock 1 is providing less than 5%, hence the investor would have to invest almost all the money in stock 2 in order to achieve target of 5%. But it will also increase his risk as the risk of stock 2 is much higher than stock1.