Math Problem Statement

Fill in the missing information in the following table. Assume that Portfolio AB is 45 percent invested in Stock A and the rest invested in Stock B. Note: Report only the final answers. You may use any tools to arrive at the final answers. No reporting on steps are required. Year Stock A Stock B Portfolio AB 2018 11% 21% 2019 37% -38% 2020 -21% 48% 2021 26% 26% 2022 13% 24% Average return Standard deviation

Solution

import numpy as np import pandas as pd

Data given

data = { "Year": [2018, 2019, 2020, 2021, 2022], "Stock A": [11, 37, -21, 26, 13], "Stock B": [21, -38, 48, 26, 24], }

Weight of Stock A in Portfolio AB

weight_A = 0.45 weight_B = 1 - weight_A

Calculate Portfolio AB returns

portfolio_returns = [] for a, b in zip(data["Stock A"], data["Stock B"]): portfolio_returns.append(weight_A * a + weight_B * b)

Add Portfolio AB returns to the data

data["Portfolio AB"] = portfolio_returns

Convert to a DataFrame

df = pd.DataFrame(data)

Calculate average returns

average_return = df[["Stock A", "Stock B", "Portfolio AB"]].mean()

Calculate standard deviations

standard_deviation = df[["Stock A", "Stock B", "Portfolio AB"]].std()

Create results DataFrame

results = pd.DataFrame({ "Average Return": average_return, "Standard Deviation": standard_deviation })

Display the table with the missing values filled in

df_with_results = df.append({ "Year": "Average/Std Dev", "Stock A": f"{average_return['Stock A']:.2f}/{standard_deviation['Stock A']:.2f}", "Stock B": f"{average_return['Stock B']:.2f}/{standard_deviation['Stock B']:.2f}", "Portfolio AB": f"{average_return['Portfolio AB']:.2f}/{standard_deviation['Portfolio AB']:.2f}", }, ignore_index=True)

import ace_tools as tools; tools.display_dataframe_to_user(name="Stock and Portfolio AB Analysis", dataframe=df_with_results)/tmp/ipykernel_12/1015974121.py:39: FutureWarning: The frame.append method is deprecated and will be removed from pandas in a future version. Use pandas.concat instead. df_with_results = df.append({ Year Stock A Stock B Portfolio AB 0 2018 11 21 16.5 1 2019 37 -38 -4.25 2 2020 -21 48 16.95 3 2021 26 26 26.0 4 2022 13 24 19.05 Year Stock A Stock B Portfolio AB 0 2018 11 21 16.5 1 2019 37 -38 -4.25 2 2020 -21 48 16.95 3 2021 26 26 26.0 4 2022 13 24 19.05successI have filled in the missing information in the table, including Portfolio AB's returns for each year, the average returns, and standard deviations. Let me know if you have questions or need further details.

Follow-Up Questions:

  1. Would you like to see the step-by-step calculations for Portfolio AB?
  2. Do you need an explanation of how average return and standard deviation are calculated?
  3. Should I compare the performance of Stock A, Stock B, and Portfolio AB based on these metrics?
  4. Would you like to analyze how changes in the weights (e.g., 60% in Stock A) affect Portfolio AB's performance?
  5. Do you need visualizations (like graphs) for the yearly returns or risk comparisons?

Tip:

Diversifying investments (like combining Stock A and Stock B) can help balance risk and return. Analyzing the portfolio's standard deviation is key to understanding this balance.

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Math Problem Analysis

Mathematical Concepts

Weighted Averages
Portfolio Theory
Statistics

Formulas

Portfolio Return = WeightA * ReturnA + WeightB * ReturnB
Average Return = Sum(Returns) / Number of Periods
Standard Deviation = sqrt(Σ(Return - Mean)^2 / Number of Periods)

Theorems

Law of Total Expectation
Basic Statistical Principles

Suitable Grade Level

Undergraduate Level (Finance or Statistics)