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 ($40,000$) and 1,500 shares of Woolworths ($60,000$). What is the portfolio weight of Woolworths?

$x_{\text{Woolworths}} = \frac{60,000}{100,000} = 0.6$

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: Calculate the portfolio variance for a two-asset portfolio with weights $z_1 = 0.5$, $z_2 = 0.5$, standard deviations $\sigma_1 = 0.051$, $\sigma_2 = 0.071$, and correlation $\rho_{12} = 0.46$.

$Var(R_p) = 0.5^2 \times 0.051^2 + 0.5^2 \times 0.071^2 + 2 \times 0.5 \times 0.5 \times 0.46 \times 0.051 \times 0.071$

Q: Using the Capital Asset Pricing Model (CAPM), what is the expected return of a stock with a risk-free rate of 5%, beta of 1.41, and market risk premium of 7%?

$E[R_i] = 5\% + 1.41 \times 7\% = 14.87\%$

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

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

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 ($40,000$) and 1,500 shares of Woolworths ($60,000$). What is the portfolio weight of Woolworths?

Accepted Answer

$x_{	ext{Woolworths}} = \frac{60,000}{100,000} = 0.6$

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 statement best describes the effect of diversification on portfolio risk?

Accepted Answer

Diversification reduces unsystematic (firm-specific) risk but cannot eliminate systematic (market) risk.

Question 5

If two assets have a correlation coefficient ($\rho$) of $+1$, what does this imply?

Accepted Answer

The assets are perfectly positively correlated and move exactly together.

Question 6

Calculate the portfolio variance for a two-asset portfolio with weights $z_1 = 0.5$, $z_2 = 0.5$, standard deviations $\sigma_1 = 0.051$, $\sigma_2 = 0.071$, and correlation $\rho_{12} = 0.46$.

Accepted Answer

$Var(R_p) = 0.5^2 	imes 0.051^2 + 0.5^2 	imes 0.071^2 + 2 	imes 0.5 	imes 0.5 	imes 0.46 	imes 0.051 	imes 0.071$

Question 7

Which formula is used to calculate the beta ($\beta_i$) of a stock?

Accepted Answer

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

Question 8

Using the Capital Asset Pricing Model (CAPM), what is the expected return of a stock with a risk-free rate of 5%, beta of 1.41, and market risk premium of 7%?

Accepted Answer

$E[R_i] = 5\% + 1.41 	imes 7\% = 14.87\%$

Question 9

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

Accepted Answer

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

Question 10

Which type of risk can be eliminated through diversification?

Accepted Answer

Unsystematic (firm-specific) risk

Question 11

If the correlation between two assets is zero, what is the implication for portfolio risk?

Accepted Answer

The assets are uncorrelated, and combining them can reduce portfolio risk through diversification.

Question 12

Which formula represents the expected portfolio return ($E[R_p]$) for $n$ assets?

Accepted Answer

$E[R_p] = \sum_{i=1}^{n} x_i E[R_i]$

Question 13

What does the efficient frontier represent in portfolio theory?

Accepted Answer

The set of optimal portfolios offering the highest expected return for a given level of risk.

Question 14

Which formula is used to calculate the correlation coefficient ($\rho_{ij}$) between two assets?

Accepted Answer

$ho_{ij} = \frac{Cov(R_i, R_j)}{SD(R_i) 	imes SD(R_j)}$

Question 15

If a portfolio contains assets with low or negative correlation, what is the expected impact on portfolio volatility?

Accepted Answer

Portfolio volatility is reduced due to diversification benefits.

Question 16

According to CAPM, which type of risk is priced in the market?

Accepted Answer

Systematic (market) risk

Question 17

Which formula best describes the relationship between expected return and systematic risk in CAPM?

Accepted Answer

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

Question 18

A portfolio has two assets: Asset 1 ($x_1 = 0.7$, $E[R_1] = 10\%$), Asset 2 ($x_2 = 0.3$, $E[R_2] = 20\%$). What is the expected portfolio return?

Accepted Answer

$E[R_p] = 0.7 	imes 10\% + 0.3 	imes 20\% = 13\%$

Question 19

Which statement is TRUE regarding the minimum variance portfolio (MVP)?

Accepted Answer

The MVP offers the lowest possible risk for a given set of assets.

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

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