Question

you invest $1000 in a stock that has a 15% chance of a 1% return, a 60% chance of a 5% return and a 25% chance of a 7% return. what is your expected return after one year? 4.3% 4.5% 4.9% 5.3%

Explanation:

Step1: Recall Expected Value Formula

The expected return \( E(R) \) is calculated as the sum of each return \( r_i \) multiplied by its corresponding probability \( p_i \), i.e., \( E(R)=\sum_{i} r_i \times p_i \).

Step2: Identify Returns and Probabilities

• Return 1: \( r_1 = 1\% = 0.01 \), Probability \( p_1 = 15\% = 0.15 \)
• Return 2: \( r_2 = 5\% = 0.05 \), Probability \( p_2 = 60\% = 0.60 \)
• Return 3: \( r_3 = 7\% = 0.07 \), Probability \( p_3 = 25\% = 0.25 \)

Step3: Calculate Each Term

• First term: \( 0.01 \times 0.15 = 0.0015 \)
• Second term: \( 0.05 \times 0.60 = 0.03 \)
• Third term: \( 0.07 \times 0.25 = 0.0175 \)

Step4: Sum the Terms

Add the three terms together: \( 0.0015 + 0.03 + 0.0175 = 0.049 \), which is \( 4.9\% \).

Answer:

4.9%