Financial mathematics

[Kenibu]

Consider two risky assets with prices S1(0) = 100, S2(0) = 150
the price is:
S1(1), S2(1) =



(80, 250) with probability 2
8
(90, 150) with probability 4
8
(120, 200) with probability 2
8

(a) Compute mean and standard deviations (μ1, σ1) and (μ2, σ2) for the two
assets (10 marks)
(b) Compute the correlation coecient between the two assets (5 marks)
(c) Assuming :w1 ≥ −0.5 and w2 ≥ −0.5. On the (σ, μ)-plane, plot all the
portfolios attainable by investing in the risky assets. Highlight the two risky
assets on the plot. (10 marks)
(d) Assume we allow for borrowing and investment with the risk free rate
r = 3%. Compute the Sharp ratio with some arbitrary weights satisfying the
conditions set on the weights in (c). (5 marks)
(e) Following the assumptions in (d), maximise the Sharp ratio and on the
(σ, μ)-plane plot the ecient portfolios. (10 marks)
(f) Derive the Capial Market Line (CML) and plot this on the ecient (σ, μ)-
plane of part (d).

 

[HallsofIvy]

Unfortunately this is almost impossible to read!

What in the world does
"(80, 250) with probability 2
8"
mean?

My first thought was that you were trying to write the two "assets" together and mean that
"asset 1" has an initial price (the price at which you bought it) of 100 and then later could
go down to 80 with probability 2, down to 90 with probability 4, or up to 120 with probability 2
while "asset 2" had an initial price of 150 and could to up to 250 with probability 8, stay at 150 with probability 8, or go up to 200 with probability 8.

But then what do those "probabilities", 2, 4, 2, 8, 8, 8 mean? They are not "probabilities"! Probabilities have to be between 0 and 1 and add to 1.