The problem presents a series of questions related to portfolio construction and risk assessment. We are asked to calculate the beta of a portfolio P constructed from Amazon, Meta, and T-bills. We also need to calculate the non-systematic risk and the variance of the portfolio P. Finally, we are asked to compute the beta of another portfolio J, comprising portfolio P, the market, and T-bills. Crucially, risk measures (beta, systematic, and unsystematic risk) for Amazon, Meta, and the Market are needed but are missing from the given information. Without these values, the specific requested calculations cannot be performed.

1. Problem Description

The problem presents a series of questions related to portfolio construction and risk assessment. We are asked to calculate the beta of a portfolio P constructed from Amazon, Meta, and T-bills. We also need to calculate the non-systematic risk and the variance of the portfolio P. Finally, we are asked to compute the beta of another portfolio J, comprising portfolio P, the market, and T-bills. Crucially, risk measures (beta, systematic, and unsystematic risk) for Amazon, Meta, and the Market are needed but are missing from the given information. Without these values, the specific requested calculations cannot be performed.

2. Solution Steps

Since the problem lacks key information like the beta of individual assets (Amazon, Meta, Market), the systematic and unsystematic risks for Amazon and Meta, and relevant return and risk measures required to find portfolio variance, I will outline the formulas and steps that would be followed IF the required information was available.

Step 7: Computing the beta of the portfolio P.

Formula: $\beta_p = w_1\beta_1 + w_2\beta_2 + w_3\beta_3$

where:

$\beta_p$ = Portfolio beta

$w_i$ = Weight of asset i in the portfolio

$\beta_i$ = Beta of asset i

In this case:

$w_1$ = 0.35 (Amazon)

$w_2$ = 0.40 (Meta)

$w_3$ = 0.25 (T-bill)

$\beta_1$ = Beta of Amazon (Required, but not given)

$\beta_2$ = Beta of Meta (Required, but not given)

$\beta_3$ = Beta of T-bill = 0 (T-bills are considered risk-free)

Portfolio Beta = $(0.35 * \beta_{Amazon}) + (0.40 * \beta_{Meta}) + (0.25 * 0)$

Portfolio Beta = $0.35\beta_{Amazon} + 0.40\beta_{Meta}$

Step 8: Computing the non-systematic risk of the portfolio P.

Portfolio Non-Systematic Risk = $\sqrt{w_1^2 * \sigma_{\epsilon_1}^2 + w_2^2 * \sigma_{\epsilon_2}^2 + w_3^2 * \sigma_{\epsilon_3}^2}$

Where:

$w_i$ are the weights of the assets in the portfolio

$\sigma_{\epsilon_i}$ are the unsystematic risk (standard deviation of idiosyncratic error term) of the individual assets.

The unsystematic risk of a T-Bill is considered to be zero. The unsystematic risk for Amazon and Meta is needed. Without these values, this cannot be computed.

Step 9: Computing the variance of portfolio P returns.

Variance requires expected returns, standard deviations, and correlations for each asset. Since the expected returns, standard deviations and correlation figures are not given, this calculation cannot be performed.

Step 10: Computing the beta of the portfolio J.

Portfolio J consists of 45% in P, 35% in the market, and 20% in T-bill.

$\beta_J = (0.45 * \beta_P) + (0.35 * \beta_{Market}) + (0.20 * \beta_{T-bill})$

We have $\beta_P$ from Step 7 (which depends on betas of Amazon and Meta), $\beta_{Market} = 1$, and $\beta_{T-bill} = 0$.

$\beta_J = (0.45 * \beta_P) + (0.35 * 1) + (0.20 * 0)$

$\beta_J = 0.45\beta_P + 0.35$

If we had values for betas of Amazon and Meta, we can derive the value of $\beta_J$.

3. Final Answer

Since the problem lacks key information, I can only provide the formulas. Without betas of Amazon, Meta and other required information, I cannot provide numerical answers to the questions. The following are the answers as formulas based on the missing information:

5. Systematic Risk for Meta: Beta of Meta * Market Risk Premium (Information for Beta of Meta and Market Risk Premium is missing)

6. Unsystematic Risk for Amazon: Standard Deviation of the error term in the market model for Amazon (Information missing)

7. Beta of the Portfolio: $0.35\beta_{Amazon} + 0.40\beta_{Meta}$ (Betas of Amazon and Meta missing)

8. Non-Systematic Risk of the Portfolio: $\sqrt{0.35^2 * \sigma_{\epsilon_{Amazon}}^2 + 0.40^2 * \sigma_{\epsilon_{Meta}}^2}$ (Unsystematic Risk of Amazon and Meta missing)

9. Variance of Portfolio P returns: Cannot be computed due to missing expected return data, standard deviation and correlation data of each asset in Portfolio P.

1

0. Beta of the portfolio J: $0.45\beta_P + 0.35$ which is equivalent to $0.45(0.35\beta_{Amazon} + 0.40\beta_{Meta}) + 0.35$ (Betas of Amazon and Meta missing).