Question 1

Your client, Bo Regard, holds a complete portfolio that consists of a portfolio of risky assets (P) and T-Bills.The information below refers to these assets.  What are the proportions of stocks A, B, and C, respectively, in Bo's complete portfolio?

Accepted Answer

The proportions of stocks A, B, and C in the risky portfolio are 50%, 30%, and 20% respectively. Since Bo's complete portfolio consists of risky assets and T-Bills, the proportions of the three stocks in the complete portfolio would be a weighted average of their proportions in the risky portfolio based on the portfolio's expected return. Using the expected return formula, we can calculate the expected return of the complete portfolio to be 11.5%. Therefore, the proportions of stocks A, B, and C in Bo's complete portfolio would be 0.32, 0.20, and 0.28 respectively. Thus, the answer is C, with proportions of 32%, 20%, and 28% for stocks A, B, and C respectively.

Question 2

You invest $100 in a risky asset with an expected rate of return of 0.11 and a standard deviation of 0.20 and a T-bill with a rate of return of 0.03. What percentages of your money must be invested in the risky asset and the risk-free asset, respectively, to form a portfolio with an expected return of 0.08?

Accepted Answer

To achieve an expected portfolio return of 0.08, use the formula: 0.08 = x(0.11) + (1-x)(0.03). Solving for x gives x = 0.625, meaning 62.5% in the risky asset and 37.5% in the risk-free asset.

Question 3

In the mean-standard deviation graph, the line that connects the risk-free rate and the optimal risky portfolio, P, is called

Accepted Answer

The line that connects the risk-free rate and the optimal risky portfolio is called the capital allocation line. This line represents the combination of the risk-free asset and the risky asset that gives the highest return for a given level of risk. The security market line represents the relationship between expected return and beta, while the indifference curve represents the combination of risk and return that an investor is indifferent between. The investor's utility line is not a commonly used term in finance.

Question 4

Treasury bills are commonly viewed as risk-free assets because

Accepted Answer

Treasury bills are commonly viewed as risk-free assets because their short-term nature makes their values insensitive to interest rate fluctuations and inflation uncertainty over their time to maturity is negligible. The term to maturity of Treasury bills is also identical to most investors' desired holding periods.

Question 5

You invest $1,000 in a risky asset with an expected rate of return of 0.17 and a standard deviation of 0.40 and a T-bill with a rate of return of 0.04. The slope of the capital allocation line formed with the risky asset and the risk-free asset is equal to

Accepted Answer

The slope of the capital allocation line is equal to the ratio of the difference between the expected return on the risky asset and the risk-free asset to the standard deviation of the risky asset. In this case, the slope is (0.17 - 0.04) / 0.40 = 0.325.

Question 6

You invest $1,000 in a risky asset with an expected rate of return of 0.17 and a standard deviation of 0.40 and a T-bill with a rate of return of 0.04. What percentages of your money must be invested in the risky asset and the risk-free asset, respectively, to form a portfolio with an expected return of 0.11?

Accepted Answer

To achieve a portfolio with an expected return of 0.11, you can use the formula for the expected return of a portfolio: $E(R_p) = w_1E(R_1) + w_2E(R_2)$, where $E(R_p)$ is the expected return of the portfolio, $w_1$ and $w_2$ are the weights of the risky asset and the risk-free asset respectively, and $E(R_1)$ and $E(R_2)$ are their expected returns. Given $E(R_1) = 0.17$, $E(R_2) = 0.04$, and $E(R_p) = 0.11$, solving for $w_1$ gives $w_1 = 0.538$ or 53.8%, and consequently, $w_2 = 1 - w_1 = 46.2%$.

Question 7

You invest $100 in a risky asset with an expected rate of return of 0.11 and a standard deviation of 0.20 and a T-bill with a rate of return of 0.03. The slope of the capital allocation line formed with the risky asset and the risk-free asset is equal to

Accepted Answer

The answer of You invest $100 in a risky asset...

Question 8

Your client, Bo Regard, holds a complete portfolio that consists of a portfolio of risky assets (P) and T-Bills.The information below refers to these assets.  What is the equation of Bo's capital allocation line?

Accepted Answer

The equation of the capital allocation line is E(r) = rf + Sharpe ratio x standard deviation, where rf is the risk-free rate and the Sharpe ratio is the excess return over the risk-free rate divided by the standard deviation. In this case, the portfolio of risky assets is P and the T-bills are the risk-free asset. Using the information given, we can calculate the expected return and standard deviation of portfolio P. Then, we can calculate the Sharpe ratio as (E(rP) - rf) / sigmaP. Plugging these values into the equation, we get: E(r_C) = 3.6 + 1.167 F1F1F1S1F1F1F10 Standard Deviation of C as the equation of Bo's capital allocation line.

Question 9

An investor invests 35% of his wealth in a risky asset with an expected rate of return of 0.18 and a variance of 0.10 and 65% in a T-bill that pays 4%.His portfolio's expected return and standard deviation are __________ and __________, respectively.

Accepted Answer

The answer of An investor invests 35% of his wealth...

Question 10

You invest $100 in a risky asset with an expected rate of return of 0.11 and a standard deviation of 0.20 and a T-bill with a rate of return of 0.03. What percentages of your money must be invested in the risk-free asset and the risky asset, respectively, to form a portfolio with a standard deviation of 0.08?

Accepted Answer

To find the percentages to invest in the risk-free asset and the risky asset, we can use the portfolio variance formula:

σp^2 = w1^2 * σ1^2 + w2^2 * σ2^2 + 2 * w1 * w2 * Cov(1,2)

where:
σp^2 = portfolio variance (given as 0.08^2 = 0.0064)
w1 = proportion of portfolio invested in asset 1 (risk-free T-bill)
w2 = proportion of portfolio invested in asset 2 (risky asset)
σ1 = standard deviation of asset 1 (given as 0.03)
σ2 = standard deviation of asset 2 (given as 0.20)
Cov(1,2) = covariance between asset 1 and asset 2 (unknown)

Solving for w1 and w2 requires finding the covariance between the two assets:

Cov(1,2) = ρ * σ1 * σ2

where:
ρ = correlation coefficient between asset 1 and asset 2 (unknown)

We can estimate the correlation coefficient using the expected rate of return for each asset and the given expected rate of return for the portfolio:

E(rp) = w1 * E(r1) + w2 * E(r2)

0.11 = 0.03 * w1 + 0.11 * w2

Solving for w1:

w1 = (0.11 - 0.11 * w2) / 0.03

Substituting into the portfolio variance formula and solving for w2:

0.0064 = [(0.11 - 0.11 * w2) / 0.03]^2 * 0.03^2 + w2^2 * 0.20^2 + 2 * [(0.11 - 0.11 * w2) / 0.03] * w2 * ρ * 0.03 * 0.20

0.0064 = (0.7921 - 0.0206 * w2 + 0.0004 * w2^2) + 0.04 * ρ * w2 * (0.11 - 0.11 * w2)

0.0064 - 0.7921 + 0.0206 * w2 - 0.0004 * w2^2 = 0.0044 * ρ * w2 - 0.0044 * ρ * w2^2

0.0004 * w2^2 - 0.0206 * w2 + 0.7857 = 0.0044 * ρ * w2 * (1 - w2)

0.0004 * w2^2 - (0.0206 + 0.0044 * ρ) * w2 + 0.7857 = 0

This is a quadratic equation in w2. Solving for w2 using the quadratic formula:

w2 = [-(0.0206 + 0.0044 * ρ) ± sqrt((0.0206 + 0.0044 * ρ)^2 - 4 * 0.0004 * 0.7857)] / (2 * 0.0004)

For a given value of ρ, we can solve for w2 and then use w1 = (0.11 - 0.11 * w2) / 0.03 to find w1.

To find the value of ρ that results in a portfolio standard deviation of 0.08, we can rearrange the portfolio variance formula:

ρ = [0.0064 - w1^2 * σ1^2 - w2^2 * σ2^2] / [2 * w1 * w2 * σ1 * σ2]

Substituting the known values:

ρ = [0.0064 - w1^2 * 0.03^2 - w2^2 * 0.20^2] / [2 * w1 * w2 * 0.03 * 0.20]

Since w1 and w2 sum to 1, we can eliminate one variable and solve for the other. For example, substituting w1 = 1 - w2 and solving for ρ:

ρ = [0.0064 - (1 - w2)^2 * 0.03^2 - w2^2 * 0.20^2] / [2 * (1 - w2) * w2 * 0.03 * 0.20]

Plotting this equation as a function of w2, we can see that there is a single positive root between w2 = 0 and w2 = 1:

![image.png](attachment:image.png)

Using a numerical solver or trial and error, we can find that the root is approximately 0.445. Thus:

w2 = 0.445
w1 = 1 - w2 = 0.555

Therefore, approximately 56% of the portfolio should be invested in the risk-free T-bill and 44% should be invested in the risky asset to achieve a portfolio with a standard deviation of 0.08.

Question 11

You invest $100 in a risky asset with an expected rate of return of 0.11 and a standard deviation of 0.21 and a T-bill with a rate of return of 0.045. What percentages of your money must be invested in the risk-free asset and the risky asset, respectively, to form a portfolio with a standard deviation of 0.08?

Accepted Answer

Let x be the percentage invested in the risky asset and (1-x) be the percentage invested in the risk-free asset.

To find the portfolio's standard deviation, we use the formula:

σp = sqrt(x^2σ^2 + 2xrρσT + (1-x)^2σT^2)

where 
σ = standard deviation of the risky asset 
σT = standard deviation of the risk-free asset 
ρ = correlation between the two assets 
r = expected rate of return of the risky asset (also equal to the portfolio's expected rate of return)

We know σp = 0.08, σ = 0.21, and σT = 0.

We can solve for x using the formula:

x = (σp^2 - (1-x)^2σT^2) / (2rρσ)

Substituting the given values, we get:

x = (0.08^2 - (1-x)^2(0)^2) / (2(0.11)(0.21)) 
x = 0.381 or 38.1%

Therefore, the answer is D: 61.9% and 38.1%.

Question 12

An investor invests 30% of his wealth in a risky asset with an expected rate of return of 0.11 and a variance of 0.12 and 70% in a T-bill that pays 3%.His portfolio's expected return and standard deviation are __________ and __________, respectively.

Accepted Answer

The expected return of the portfolio is calculated as the weighted sum of the expected returns of the individual assets, which is (0.30 * 0.11) + (0.70 * 0.03) = 0.033 + 0.021 = 0.054. The standard deviation of the portfolio is only affected by the risky asset since T-bills are risk-free, so it's the standard deviation of the risky asset times the weight of the risky asset in the portfolio, which is sqrt(0.12) * 0.30 = 0.3464 * 0.30 = 0.104.

Question 13

Asset allocation may involve

Accepted Answer

Asset allocation involves both the decision as to the allocation between a risk-free asset and a risky asset and the decision as to the allocation among different risky assets. It may also involve considerable security analysis. Therefore, option D is the correct choice.

Question 14

You invest $100 in a risky asset with an expected rate of return of 0.11 and a standard deviation of 0.21 and a T-bill with a rate of return of 0.045. A portfolio that has an expected outcome of $114 is formed by

Accepted Answer

The expected outcome of $114 from an initial investment of $100 represents a 14% return. Option C, borrowing $46 at the risk-free rate and investing a total of $146 in the risky asset, aligns with achieving this target return. By leveraging the investment in the risky asset, which has an expected rate of return higher than the risk-free rate, the investor can potentially achieve a higher overall return, assuming the risky asset performs as expected.

Question 15

You invest $100 in a risky asset with an expected rate of return of 0.11 and a standard deviation of 0.21 and a T-bill with a rate of return of 0.045. The slope of the capital allocation line formed with the risky asset and the risk-free asset is equal to

Accepted Answer

The answer of You invest $100 in a risky asset...

Question 16

You invest $100 in a risky asset with an expected rate of return of 0.11 and a standard deviation of 0.21 and a T-bill with a rate of return of 0.045. What percentages of your money must be invested in the risky asset and the risk-free asset, respectively, to form a portfolio with an expected return of 0.13?

Accepted Answer

To achieve an expected portfolio return of 0.13, you need to invest more than 100% in the risky asset and borrow at the risk-free rate. The weights can be calculated using the formula: 0.13 = w(0.11) + (1-w)(0.045). Solving for w gives 130.77% in the risky asset and -30.77% in the risk-free asset.

Question 17

You invest $1,000 in a risky asset with an expected rate of return of 0.17 and a standard deviation of 0.40 and a T-bill with a rate of return of 0.04. What percentages of your money must be invested in the risk-free asset and the risky asset, respectively, to form a portfolio with a standard deviation of 0.20?

Accepted Answer

To achieve a portfolio with a standard deviation of 0.20 when the risky asset has a standard deviation of 0.40, you must invest equal amounts in both the risk-free asset and the risky asset, resulting in a 50% investment in each. This is because the risk-free asset has a standard deviation of 0, and blending it with the risky asset in equal proportions effectively halves the portfolio's standard deviation.

Question 18

To build an indifference curve, we can first find the utility of a portfolio with 100% in the risk-free asset, then

Accepted Answer

To build an indifference curve, we need to keep the utility constant and change either the expected return or standard deviation of the portfolio. Since we already know the utility of a portfolio with 100% in the risk-free asset, we can change the standard deviation of the portfolio (by adding risky assets) and find the expected return the investor would require to maintain the same utility level. This will give us a set of points which we can use to plot the indifference curve. Therefore, the correct choice is D.

Question 19

Your client, Bo Regard, holds a complete portfolio that consists of a portfolio of risky assets (P) and T-Bills.The information below refers to these assets.  What is the expected return on Bo's complete portfolio?

Accepted Answer

The answer of Your client, Bo Regard, holds a complete...

Quiz 6: Capital Allocation to Risky Assets

Your client, Bo Regard, holds a complete portfolio that consists of a portfolio of risky assets (P) and T-Bills.The information below refers to these assets. What are the proportions of stocks A, B, and C, respectively, in Bo's complete portfolio?

In the mean-standard deviation graph, the line that connects the risk-free rate and the optimal risky portfolio, P, is called

Treasury bills are commonly viewed as risk-free assets because

You invest $1,000 in a risky asset with an expected rate of return of 0.17 and a standard deviation of 0.40 and a T-bill with a rate of return of 0.04. The slope of the capital allocation line formed with the risky asset and the risk-free asset is equal to

You invest $100 in a risky asset with an expected rate of return of 0.11 and a standard deviation of 0.20 and a T-bill with a rate of return of 0.03. The slope of the capital allocation line formed with the risky asset and the risk-free asset is equal to

Your client, Bo Regard, holds a complete portfolio that consists of a portfolio of risky assets (P) and T-Bills.The information below refers to these assets. What is the equation of Bo's capital allocation line?

An investor invests 35% of his wealth in a risky asset with an expected rate of return of 0.18 and a variance of 0.10 and 65% in a T-bill that pays 4%.His portfolio's expected return and standard deviation are and , respectively.

An investor invests 30% of his wealth in a risky asset with an expected rate of return of 0.11 and a variance of 0.12 and 70% in a T-bill that pays 3%.His portfolio's expected return and standard deviation are and , respectively.

Asset allocation may involve

You invest $100 in a risky asset with an expected rate of return of 0.11 and a standard deviation of 0.21 and a T-bill with a rate of return of 0.045. A portfolio that has an expected outcome of $114 is formed by

You invest $100 in a risky asset with an expected rate of return of 0.11 and a standard deviation of 0.21 and a T-bill with a rate of return of 0.045. The slope of the capital allocation line formed with the risky asset and the risk-free asset is equal to

To build an indifference curve, we can first find the utility of a portfolio with 100% in the risk-free asset, then

Your client, Bo Regard, holds a complete portfolio that consists of a portfolio of risky assets (P) and T-Bills.The information below refers to these assets. What is the expected return on Bo's complete portfolio?