pandas as pd

Input data from the question

data = { "Probability": [0.30, 0.40, 0.30], "PT A": [16, 13, 10], "PT B": [17, 13, 11] }

Convert data to a DataFrame

df = pd.DataFrame(data)

Calculate Expected Return for PT A and PT B

df["Weighted PT A"] = df["Probability"] * df["PT A"] df["Weighted PT B"] = df["Probability"] * df["PT B"] expected_return_a = df["Weighted PT A"].sum() expected_return_b = df["Weighted PT B"].sum()

Calculate Variance and Standard Deviation for PT A and PT B

df["Deviation PT A"] = df["PT A"] - expected_return_a df["Deviation PT B"] = df["PT B"] - expected_return_b df["Squared Deviation PT A"] = df["Deviation PT A"] ** 2 * df["Probability"] df["Squared Deviation PT B"] = df["Deviation PT B"] ** 2 * df["Probability"] variance_a = df["Squared Deviation PT A"].sum() variance_b = df["Squared Deviation PT B"].sum() std_dev_a = variance_a ** 0.5 std_dev_b = variance_b ** 0.5

Prepare results

results = { "Expected Return PT A": expected_return_a, "Expected Return PT B": expected_return_b, "Standard Deviation PT A": std_dev_a, "Standard Deviation PT B": std_dev_b }

resultsHere are the results for the calculations:

1. Expected Return:

   • PT A: 13.0%
   • PT B: 13.6%

2. Standard Deviation:

   • PT A: 2.32%
   • PT B: 2.37%

Let me know if you'd like further clarifications or additional calculations!

Here are 5 related questions to expand on the topic:

1. How does the standard deviation impact investment decisions?
2. What factors could influence the probabilities assigned in such calculations?
3. Can the variance be used alone without standard deviation for risk assessment?
4. What is the significance of having a higher expected return in PT B compared to PT A?
5. How can diversification reduce the overall portfolio risk?

Tip: Understanding both expected return and standard deviation is crucial, as higher returns often come with higher risks!