Question

what is the expected return on a portfolio comprised of $9,750 of stock x and $4,520 of stock y if the economy enjoys a boom period?
state of economy | probability of state of economy | rate of return if state occurs
| stock x | stock y
boom |.25 |.108 |.156
normal |.65 |.087 |.097
recession |.10 |.024 | -.069
multiple choice
12.55%
12.32%
12.78%
11.93%
11.57%

Explanation:

Step1: Calculate total investment

First, find the total investment in the portfolio. The investment in Stock X is $9,750 and in Stock Y is $4,520. So total investment \( I = 9750 + 4520 = 14270 \).

Step2: Calculate weight of each stock

Weight of Stock X (\( w_X \)): \( w_X=\frac{9750}{14270}\approx0.6833 \)
Weight of Stock Y (\( w_Y \)): \( w_Y=\frac{4520}{14270}\approx0.3168 \)

Step3: Find returns in boom state

In boom state, return of Stock X (\( r_X \)) is 0.108 and return of Stock Y (\( r_Y \)) is 0.156.

Step4: Calculate portfolio return in boom

Portfolio return (\( r_p \)) in boom state is \( r_p = w_X \times r_X + w_Y \times r_Y \)
Substitute values: \( r_p = 0.6833\times0.108 + 0.3168\times0.156 \)
Calculate each term: \( 0.6833\times0.108\approx0.0738 \), \( 0.3168\times0.156\approx0.0494 \)
Sum: \( 0.0738 + 0.0494 = 0.1232 \) or 12.32%? Wait, wait, maybe I miscalculated weights. Wait, let's recalculate weights more accurately.

Wait, 9750 + 4520 = 14270.
\( w_X = 9750 / 14270 = 9750 ÷ 14270 ≈ 0.6833 \)
\( w_Y = 4520 / 14270 ≈ 0.3168 \)
\( r_X = 0.108 \), \( r_Y = 0.156 \)
\( r_p = 0.6833*0.108 + 0.3168*0.156 \)
0.68330.108: 0.68330.1=0.06833, 0.6833*0.008=0.0054664, total ≈0.0737964
0.31680.156: 0.31680.1=0.03168, 0.31680.05=0.01584, 0.31680.006=0.0019008; total=0.03168+0.01584=0.04752+0.0019008=0.0494208
Sum: 0.0737964 + 0.0494208 = 0.1232172 ≈12.32%

Answer:

12.32% (corresponding to the option 12.32%)