Q: Which formula correctly calculates the portfolio weight $x_i$ for asset $i$?

$x_i = \frac{\text{Value of investment in asset } i}{\text{Total portfolio value}}$

Q: A portfolio consists of 8,000 shares of Qantas ($5 each) and 1,500 shares of Woolworths ($40 each). What is the portfolio weight of Woolworths?

$x_{\text{Woolworths}} = \frac{1,500 \times 40}{8,000 \times 5 + 1,500 \times 40} = 0.6$

Q: Given expected returns of 18% for Stock A and 25% for Stock B, with portfolio weights of 0.3 and 0.7 respectively, what is the expected portfolio return?

$E[R_p] = 0.3 \times 18\% + 0.7 \times 25\% = 23.9\%$

Q: Which formula is used to calculate the covariance between two assets $i$ and $j$?

$\text{Cov}(R_i, R_j) = E[(R_i - E[R_i])(R_j - E[R_j])]$

Question 1

Which formula correctly calculates the portfolio weight $x_i$ for asset $i$?

Accepted Answer

$x_i = \frac{	ext{Value of investment in asset } i}{	ext{Total portfolio value}}$

Question 2

A portfolio consists of 8,000 shares of Qantas ($5 each) and 1,500 shares of Woolworths ($40 each). What is the portfolio weight of Woolworths?

Accepted Answer

$x_{	ext{Woolworths}} = \frac{1,500 	imes 40}{8,000 	imes 5 + 1,500 	imes 40} = 0.6$

Question 3

Given expected returns of 18% for Stock A and 25% for Stock B, with portfolio weights of 0.3 and 0.7 respectively, what is the expected portfolio return?

Accepted Answer

$E[R_p] = 0.3 	imes 18\% + 0.7 	imes 25\% = 23.9\%$

Question 4

Which of the following best describes systematic risk?

Accepted Answer

It affects all firms and cannot be eliminated through diversification.

Question 5

If two assets have a correlation coefficient $\rho = 1$, what does this imply?

Accepted Answer

The assets are perfectly positively correlated and move together.

Question 6

Which formula is used to calculate the covariance between two assets $i$ and $j$?

Accepted Answer

$	ext{Cov}(R_i, R_j) = E[(R_i - E[R_i])(R_j - E[R_j])]$

Question 7

A portfolio is made up of 50% Woodside (SD=0.051), 50% Tex Oil (SD=0.071), and their correlation is 0.46. What is the portfolio standard deviation?

Accepted Answer

$SD(R_p) = \sqrt{0.5^2(0.051^2) + 0.5^2(0.071^2) + 2(0.5)(0.5)(0.46)(0.051)(0.071)} = 0.051 = 5.1\%$

Question 8

According to the Capital Asset Pricing Model (CAPM), which formula gives the expected return of asset $i$?

Accepted Answer

$E[R_i] = r_f + \beta_i(E[R_M] - r_f)$

Question 9

If the risk-free rate is 5%, the expected market return is 12%, and a stock's beta is 1.41, what is the expected return according to CAPM?

Accepted Answer

$E[R_i] = 5\% + 1.41(12\% - 5\%) = 14.87\%$

Question 10

What does a portfolio beta ($\beta_p$) of 1.338 indicate about the portfolio's risk relative to the market?

Accepted Answer

The portfolio is 33.8% more volatile than the market.

Question 11

Which statement about diversification is correct?

Accepted Answer

Diversification reduces unsystematic (firm-specific) risk but not systematic risk.

Question 12

If two assets have a correlation coefficient $\rho = -1$, what is the effect on portfolio risk?

Accepted Answer

Portfolio risk can be minimized to zero if weights are chosen appropriately.

Question 13

Which formula is used to calculate the beta ($\beta_i$) of asset $i$?

Accepted Answer

$\beta_i = \frac{	ext{Cov}(R_i, R_M)}{	ext{Var}(R_M)}$

Question 14

A portfolio consists of 40% 3M (beta=0.69) and 60% HPQ (beta=1.77). What is the portfolio beta?

Accepted Answer

$\beta_p = 0.4 	imes 0.69 + 0.6 	imes 1.77 = 1.338$

Question 15

Which of the following is true about the efficient frontier?

Accepted Answer

It represents the set of portfolios offering the highest expected return for a given level of risk.

Question 16

What is the effect of increasing the number of assets ($n$) in a portfolio on unsystematic risk?

Accepted Answer

Unsystematic risk approaches zero as $n$ increases.

Question 17

Which formula correctly calculates the variance of a two-asset portfolio?

Accepted Answer

$	ext{Var}(R_p) = x_1^2 \sigma_1^2 + x_2^2 \sigma_2^2 + 2x_1x_2ho_{12}\sigma_1\sigma_2$

Question 18

Which statement about the relationship between correlation and diversification benefit is correct?

Accepted Answer

Lower correlation between assets leads to greater diversification benefit.

Question 19

If the correlation between two assets is zero, what does this imply about their returns?

Accepted Answer

Their returns are uncorrelated and move independently.

Systematic Risk and the Equity Risk Premium: Portfolio Theory & CAPM

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