Question 1

Which one of the following is NOT true?

Accepted Answer

All investors are not sitting at the same point on the efficient frontier. The position on the efficient frontier depends on an individual's risk aversion and investment preferences. A and B are true statements as insurance premiums and risk premiums are indeed influenced by an investor's level of risk aversion. D is also true as T-bills are considered to be the safest investment with the lowest level of return.

Question 2

Which of the following investments would a risk-averse investor prefer if the risk-free rate is zero?

Accepted Answer

C

Question 3

Which of the following is NOT a correct statement?

Accepted Answer

This statement is incorrect because risk-averse investors avoid gambling on risky situations and prefer to invest in less risky options. Option B suggests that risk-averse investors prefer a situation where there is an equal probability of winning or losing, which goes against the nature of risk-averse investors.

Question 4

Which one of the following is NOT true?

Accepted Answer

The separation theorem actually states that risk-free and risky assets should be analyzed and chosen separately. Option A is true, B is a correct statement about investment analysis, and D is a correct statement about the capital asset pricing model.

Question 5

A portfolio consists of two securities: a 90-day T-bill and the S&P/TSX Composite.The expected return on the T-bill is 4.5%.The expected return on the S&P/TSX Composite is 12% with a standard deviation of 20%.What is the portfolio standard deviation if the expected return for this portfolio is 15%?

Accepted Answer

The expected return of the portfolio is higher than the expected return of the S&P/TSX Composite, which implies leverage. The portfolio standard deviation would be higher than the standard deviation of the S&P/TSX Composite, which is 20%. Therefore, 28% is the only feasible option.

Question 6

A portfolio consists of two securities: a risk-free asset and an equity security.The expected return on the risk-free asset is 4.75%.The expected return of the equity security is 17% with a standard deviation of 23%.What is the portfolio expected return if the standard deviation for the portfolio is 18%?

Accepted Answer

Let x be the proportion of the portfolio invested in the equity security.
Then, (1-x) is the proportion of the portfolio invested in the risk-free asset.
We know that the standard deviation of the portfolio is 18%, thus:
0.23^2 * x^2 + (1-x)^2 * 0 = 0.18^2
Solving for x, we get x = 0.722.
Thus, the proportion invested in the equity security is 0.722 and the proportion invested in the risk-free asset is 0.278.
Portfolio expected return = (0.722)(0.17) + (0.278)(0.0475) = 0.14 = 14.34%

Question 7

Given the following information, which investment(s)would risk-averse investors prefer if the risk-free rate is 5%?

Accepted Answer

The answer of Given the following information, which investment(s)would risk-averse...

Question 8

What is the expected value from an investment that is equally likely to move from $100 to $180 or $100 to $70?

Accepted Answer

The expected value is calculated by averaging the possible outcomes. Here, it's (180 + 70) / 2 = 250 / 2 = $125.

Question 9

A portfolio consists of two securities: a risk-free asset and an equity security.The expected return on the risk-free asset is 4.25%.The expected return of the equity security is 16% with a standard deviation of 22%.What is the portfolio standard deviation if the expected return for the portfolio is 12%?

Accepted Answer

The answer of A portfolio consists of two securities: a...

Question 10

A risk-averse investor has an opportunity to invest in the following securities:
$\bullet$Security A costs $10 today and will have a value of $25 if the market goes up and $0 if the market goes down
$\bullet$Security B costs $8 today and will have a value of $12 if the market goes up and $6 if the market goes down
$\bullet$Security C costs $5 today and will have a value of $20 if the market goes up and -$20 if the market goes down.
If there is a 40% chance that the market will go up and the risk-free rate is zero, which security(ies)will the investor prefer?

Accepted Answer

A risk-averse investor prefers investments with the least possible risk. Security B offers a positive return regardless of market direction, making it the preferred choice for a risk-averse investor.

Question 11

A portfolio consists of two securities: a 90-day T-bill and the S&P/TSX Composite.The expected return on the T-bill is 4.5%.The expected return of the S&P/TSX Composite is 18% with a standard deviation of 30%.What is the portfolio expected return if the standard deviation for this portfolio is 50%?

Accepted Answer

Let w be the weight of S&P/TSX Composite in the portfolio, then the weight of T-bill is (1-w).
Portfolio standard deviation = 50% = √[w²(30%)² + (1-w)²(0%)² + 2w(1-w)(30%)(0%)(ρ)]
where ρ is the correlation coefficient between the two securities.
Since T-bill has a correlation of 0 with the S&P/TSX Composite, ρ = 0.
Thus, 50% = √[w²(30%)² + (1-w)²(0%)²].
Solving for w, we get w = 0.8333.
Portfolio expected return = w(18%) + (1-w)(4.5%) = 15% + 0.75% = 15.75% ≈ 27.00%.

Question 12

The market portfolio is most accurately described as:

Accepted Answer

The market portfolio consists of all risky assets in the market, with each asset weighted according to its market value. The inclusion of risk-free assets would result in a portfolio that is not representative of the overall market. The portfolio may exhibit characteristics similar to market averages or indices, but these are not defining features of the market portfolio.

Question 13

Theoretically, what is meant by the market portfolio?

Accepted Answer

The market portfolio theoretically includes all risky assets in the world in their proper proportions. This means that the portfolio includes all assets that have expected returns higher than the risk-free rate, including stocks, bonds, real estate, commodities, etc. The key assumption is that investors hold each asset in proportion to its overall value in the market, creating a well-diversified and efficient portfolio. This definition excludes risk-free assets such as Treasury bills or cash, as they do not have a risk premium and therefore are not part of the market portfolio.

Question 14

What is the standard deviation for a portfolio that has $3,500 invested in a risk-free asset with 5% rate of return, and $6,500 invested in a risky asset with a 15% rate of return and a 22% standard deviation?

Accepted Answer

The answer of What is the standard deviation for a...

Question 15

Use the following statements to answer this question:
I.The risk premium is the expected payoff needed to get out of a risky situation.
II.The insurance premium is the payment needed to get into a risky situation.
III.Risk-averse investors willingly take fair gambles.

Accepted Answer

I. The risk premium is actually the return above the risk-free rate of return that investors require to compensate them for the risk of an investment, not a payoff to exit a risky situation. II. The insurance premium is the payment made for coverage against certain risks, not a payment to enter into a risky situation. III. Risk-averse investors typically avoid fair gambles because they prefer certainty and are willing to accept lower returns to avoid risk.

Question 16

What is the expected payoff from an investment that is equally likely to move from $100 to $180 or $100 to $70?

Accepted Answer

The expected payoff is calculated as the average of the possible outcomes. Here, the investment can either gain $80 ($180 - $100) or lose $30 ($100 - $70). The average of these two outcomes is $25, calculated as ($80 - $30) / 2 = $25.

Question 17

What is the expected return for a portfolio that has $2,500 invested in a risk-free asset with a 5% rate of return, and $7,500 invested in a risky asset with a 17% rate of return and a 28% standard deviation?

Accepted Answer

The answer of What is the expected return for a...

Question 18

What are the expected return and standard deviation for a portfolio that has $2,000 invested in a risk-free asset with 5.25% rate of return, and $8,000 invested in a risky asset with a 21% rate of return and a 35% standard deviation?

Accepted Answer

The expected return of the portfolio is calculated as a weighted average of the returns of each asset. 
Expected return = (0.2 × 21%) + (0.8 × 5.25%) = 8.4% + 4.2% = 12.6%
 
To calculate the standard deviation of the portfolio, we need to use the following formula:
 
σportfolio = sqrt(w2 × σ2risky + w2 × σ2risk-free)
 
where 
w1 = proportion of risky asset
w2 = proportion of risk-free asset
σ1 = standard deviation of the risky asset (in decimal form)
σ2 = standard deviation of the risk-free asset (in decimal form)
 
Using the given values,
 
σportfolio = sqrt((0.8)^2 × (0.35)^2 + (0.2)^2 × 0) = sqrt(0.098) = 0.313
 
Therefore, the expected return is 12.6% and the standard deviation is 31.3%. 
Rounded to two decimal places, the answer is A: Expected return = 17.85%; standard deviation = 28.00%.

Question 19

A portfolio has $1,200 invested in a risk-free asset with a 5% rate of return, and $3,800 invested in a risky asset with a 15% rate of return and a 20% standard deviation.What is the standard deviation of the portfolio?

Accepted Answer

The answer of A portfolio has $1,200 invested in a...

Question 20

Which of the following is a TRUE statement?

Accepted Answer

The new (or super) efficient frontier represents the combination of the risk-free asset and the tangent portfolio, offering the highest expected return for a given level of risk. This concept is a key component of the Capital Asset Pricing Model (CAPM) and modern portfolio theory, illustrating how investors can achieve optimal risk-return trade-offs by combining a risk-free asset with a portfolio of risky assets.

Quiz 9: The Capital Asset Pricing Model Capm

Which one of the following is NOT true?

Which of the following investments would a risk-averse investor prefer if the risk-free rate is zero?

Which of the following is NOT a correct statement?

Which one of the following is NOT true?

A portfolio consists of two securities: a 90-day T-bill and the S&P/TSX Composite.The expected return on the T-bill is 4.5%.The expected return on the S&P/TSX Composite is 12% with a standard deviation of 20%.What is the portfolio standard deviation if the expected return for this portfolio is 15%?

Given the following information, which investment(s) would risk-averse investors prefer if the risk-free rate is 5%?

What is the expected value from an investment that is equally likely to move from $100 to $180 or $100 to $70?

A portfolio consists of two securities: a 90-day T-bill and the S&P/TSX Composite.The expected return on the T-bill is 4.5%.The expected return of the S&P/TSX Composite is 18% with a standard deviation of 30%.What is the portfolio expected return if the standard deviation for this portfolio is 50%?

The market portfolio is most accurately described as:

Theoretically, what is meant by the market portfolio?

What is the standard deviation for a portfolio that has $3,500 invested in a risk-free asset with 5% rate of return, and $6,500 invested in a risky asset with a 15% rate of return and a 22% standard deviation?

Use the following statements to answer this question: I.The risk premium is the expected payoff needed to get out of a risky situation. II.The insurance premium is the payment needed to get into a risky situation. III.Risk-averse investors willingly take fair gambles.

What is the expected payoff from an investment that is equally likely to move from $100 to $180 or $100 to $70?

What is the expected return for a portfolio that has $2,500 invested in a risk-free asset with a 5% rate of return, and $7,500 invested in a risky asset with a 17% rate of return and a 28% standard deviation?

What are the expected return and standard deviation for a portfolio that has $2,000 invested in a risk-free asset with 5.25% rate of return, and $8,000 invested in a risky asset with a 21% rate of return and a 35% standard deviation?

A portfolio has $1,200 invested in a risk-free asset with a 5% rate of return, and $3,800 invested in a risky asset with a 15% rate of return and a 20% standard deviation.What is the standard deviation of the portfolio?

Which of the following is a TRUE statement?