 # Investment analysis finance

i am really confused on how to find the weight of the two asset portfolio
Question 1: Consider two assets with the following:
µ1 = 0.10, σ1 = 0.40
µ2 = 0.03; σ2 = 0
Calculate the weights of the portfolio, (w1, w2) such that the expected return,
µw = 16. Calculate the variance of this portfolio

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I trust that the target return is 16%, not 16 (= 1,600%).

If so, then,

w_1=\frac{16\%\ -\ 3\%}{10\%\ -\ 3\%}=1.8571
w_2=\frac{16\%\ -\ 10\%}{3\%\ -\ 10\%}=-0.8571

Without knowing the covariance of returns of asset 1 and asset 2, you cannot compute the variance of returns of the portfolio.

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Since Asset 2 is a risk-free asset, the variance of the portfolio would just depend on the weight and standard deviation of the risky asset (i.e. Asset 1). Based on the weights calculated by S2000:

\sigma^2_p = w^2_1 \sigma^2_1 + w^2_2 \sigma^2_2 + 2w_1 w_2 \rho_{1,2}\sigma_1 \sigma_2

\sigma^2_p = (1.8571)^2 (0.40)^2 + (-0.8571)^2 (0)^2 + 2(1.8571)(-0.8571)\rho_{1,2}(0.40)(0)

\sigma^2_p = (1.8571)^2 (0.40)^2 + 0 + 0

\sigma^2_p = 0.55181

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My error: I wasn’t looking at the variances to see that asset 2 is risk-free.

Good catch, fino!

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thank you for the help. Really Appreciated 1 Like

Another Help Please In this Question.
Consider a security with the stock prices
S(1) =80 with probability 1/8
=90 with probability 2/8
=100 with probability 3/8
=110 with probability 2/8
(a) What is the current price of the stock for which the expected return
would be 12%?
(b) What is the current price of the stock for which the standard deviation
would be 18%

What’s E(S(1))?

E(S(1)) is the expected price of first asset at time 1

I’m aware of that.

The question is: what’s its value?

Value is 97.5

i need step by step of this calculation so i need your help