1 2026 (792539) - DUE 19 April 2026; 100% Correct
solutions and explanations.
QUESTION 1
1.1 Calculate the expected return of the
market portfolio (6 marks)
We use the expected value formula:
E(Rm)=∑Pi×RiE(R_m) = \sum P_i \times R_iE(Rm)=∑Pi×Ri
Where:
PiP_iPi = probability
RiR_iRi = market return
Step 1: Multiply each return by its probability
Probability Market Return P×RP \times RP×R
0.1 10% 0.1 × 10% = 1.0%
0.2 12% 0.2 × 12% = 2.4%
0.4 13% 0.4 × 13% = 5.2%
0.2 16% 0.2 × 16% = 3.2%
0.1 17% 0.1 × 17% = 1.7%
𝑺𝒕𝒆𝒑 𝟐: 𝑨𝒅𝒅 𝒕𝒉𝒆 𝒘𝒆𝒊𝒈𝒉𝒕𝒆𝒅 𝒓𝒆𝒕𝒖𝒓𝒏𝒔
𝐸(𝑅𝑚) = 1.0 + 2.4 + 5.2 + 3.2 + 1.7𝐸(𝑅_𝑚) = 1.0 + 2.4 + 5.2 + 3.2 + 1.7𝐸(𝑅𝑚)
= 1.0 + 2.4 + 5.2 + 3.2 + 1.7 𝐸(𝑅𝑚) = 13.5%𝐸(𝑅_𝑚) = 13.5\%𝐸(𝑅𝑚)
= 13.5%
𝑨𝒏𝒔𝒘𝒆𝒓 𝟏. 𝟏
𝐸(𝑅𝑚) = 13.5%\𝑏𝑜𝑥𝑒𝑑{𝐸(𝑅_𝑚) = 13.5\%}𝐸(𝑅𝑚) = 𝟏𝟑. 𝟓%