# How do you calculate the proportion of shares required to formulate a minimum risk portfolio?

An investor has decided to invest 1 million in the shares of two companies, company E and company B. the projections of returns from the shares of the two companies along with their probabilities is shown below. Required; Determine the proportion of each shares required to formulate a minimum risk portfolio.

``````probability  :  company E  :  Company B
0.20      :     12      :     16
0.25      :     14      :     10
0.25      :     -7      :     28
0.30      :     28      :     -2
``````

I used the approach of variance. From my insights i weighted the variances and got company E could weight 0.4241 and company B 0.5758. I am however not sure of the approach

• I’m voting to close this question because you should be doing your own homework. If you edit to say what you think the right answer is, someone might be willing to check your work. Nov 21, 2023 at 11:15
• Well this is not homework sir/madam. I am preparing for my Finance exam. I used the approach of variance. From my insights i weighted the variances and got company E could weight 0.4241 and company B 0.5758. I am however not sure of the approach Nov 21, 2023 at 11:20
• I'm sorry, but you used the term "minimum risk portfolio" right after saying that someone who is starting-out-investing was going to invest a substantial sum of money in only 2 stocks. Share investing carries inherent risks. Cash in the bank does not. So for a minimum risk strategy, (1) don't invest in shares, and (2) if you really must invest in shares then spread your investment across a range of stocks covering a range of industries. Nov 21, 2023 at 11:40
• Oh yes " minimum risk portfolio," in the context of the question. Nov 21, 2023 at 11:49
• Yeah, the question is somewhat self-negating . Whatever you calculate will still be bad advice. If I got this question, phrased this way, my answer would be "mu" Nov 21, 2023 at 20:36

Referring back to old notes this looks ok. `r` is the mean return, `x` & `y` are the proportions of E & B respectively, `s` is the risk

``````r = 0.20*(0.12 x + 0.16 y) +
0.25*(0.14 x + 0.10 y) +
0.25*(-0.07 x + 0.28 y) +
0.30*(0.28 x - 0.02 y)

s = (0.20*(0.12 x + 0.16 y - r)^2 +
0.25*(0.14 x + 0.10 y - r)^2 +
0.25*(-0.07 x + 0.28 y - r)^2 +
0.30*(0.28 x - 0.02 y - r)^2)^(1/2)

y = 1 - x
``````

Plotting `s` over a range of `x` from 0 to 1 the minimum risk is about 46.5% E and 53.5% B.