Question 1

An investor invests 30% of his wealth in a risky asset with an expected rate of return of 0.15 and a variance of 0.04 and 70% in a T-bill that pays 6%.His portfolio's expected return and standard deviation are __________ and __________, respectively.

Accepted Answer

To calculate the portfolio's expected return, we use the following formula:

Expected portfolio return = (weight of risky asset x expected return of risky asset) + (weight of T-bill x expected return of T-bill)
= (0.3 x 0.15) + (0.7 x 0.06)
= 0.087 or 8.7%

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

Portfolio standard deviation = sqrt[(weight of risky asset)^2 x variance of risky asset + (weight of T-bill)^2 x variance of T-bill + 2 x weight of risky asset x weight of T-bill x covariance]

Since the covariance between the risky asset and T-bill is assumed to be zero, the formula simplifies to:

Portfolio standard deviation = sqrt[(weight of risky asset)^2 x variance of risky asset + (weight of T-bill)^2 x variance of T-bill]

= sqrt[(0.3)^2 x 0.04 + (0.7)^2 x 0]
= sqrt[0.0036]
= 0.06 or 6%

Question 2

You invest $100 in a risky asset with an expected rate of return of 0.12 and a standard deviation of 0.15 and a T-bill with a rate of return of 0.05. 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 0.09?

Accepted Answer

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

Question 3

An investor invests 70% of his wealth in a risky asset with an expected rate of return of 0.15 and a variance of 0.04 and 30% in a T-bill that pays 5%.His portfolio's expected return and standard deviation are __________ and __________, respectively.

Accepted Answer

The expected return of the portfolio is calculated as the weighted average of the returns of the individual assets, which is (0.70 * 0.15) + (0.30 * 0.05) = 0.105 + 0.015 = 0.12 or 12%. The standard deviation of the portfolio is calculated only for the risky asset, as T-bills are risk-free. The standard deviation is the square root of the variance, so for the risky asset, it's sqrt(0.04) = 0.2. However, since only 70% of the wealth is invested in the risky asset, the portfolio's standard deviation is 0.2 * 0.7 = 0.14.

Question 4

Based on their relative degrees of risk tolerance,

Accepted Answer

The answer of Based on their relative degrees of risk...

Question 5

You are considering investing $1,000 in a T-bill that pays 0.05 and a risky portfolio, P, constructed with two risky securities, X and Y.The weights of X and Y in P are 0.60 and 0.40, respectively.X has an expected rate of return of 0.14 and variance of 0.01, and Y has an expected rate of return of 0.10 and a variance of 0.0081. What would be the dollar value of your positions in X, Y, and the T-bills, respectively, if you decide to hold a portfolio that has an expected outcome of $1,120?

Accepted Answer

$568; $378; $54To achieve an expected outcome of $1,120 from an initial investment of $1,000, the portfolio must earn a 12% return ($120/$1,000). The expected return of the portfolio (E(Rp)) can be calculated using the weights and expected returns of X and Y: E(Rp) = 0.60*0.14 + 0.40*0.10 = 0.124 or 12.4%. To adjust the portfolio to achieve exactly a 12% return, some investment in the risk-free T-bill (which yields 5%) is necessary. The allocation in X and Y remains proportional to their weights in the risky portfolio P. Therefore, with $1,000 to invest and aiming for a 12% overall return, the investment in X is $1,000 * 0.60 = $600, and in Y is $1,000 * 0.40 = $400. However, to adjust the expected return from 12.4% to 12%, part of the investment is reallocated to T-bills. The exact reallocation isn't directly calculated in the question, but the choice given ($568 in X, $378 in Y, and $54 in T-bills) aligns with the need to slightly reduce the risky investment to achieve the desired return, considering the proportions of X and Y in the portfolio and the inclusion of a risk-free asset to fine-tune the expected return.

Question 6

The capital allocation line can be described as the

Accepted Answer

The capital allocation line is formed with a combination of the risky asset and the risk-free asset, allowing investors to create portfolios with varying levels of risk and expected returns. The line represents the efficient frontier of portfolios that maximize expected return for a given level of risk, and is therefore a key tool for investors in portfolio management.

Question 7

The Sharpe ratio is useful in

Accepted Answer

The Sharpe ratio is a measure of risk-adjusted return, meaning it helps investors understand how much return they are obtaining per unit of risk taken on. Therefore, the Sharpe ratio is useful in understanding how returns increase relative to risk increases.

Question 8

The first major step in asset allocation is

Accepted Answer

Assessing risk tolerance is the first major step in asset allocation because it helps determine the appropriate mix of assets based on an individual's risk tolerance and investment objectives. Without assessing risk tolerance, it is difficult to make informed decisions about allocating assets. Analyzing financial statements, estimating security betas, and identifying market anomalies are important steps in investment analysis, but they come after assessing risk tolerance and determining the appropriate asset mix.

Question 9

You invest $100 in a risky asset with an expected rate of return of 0.12 and a standard deviation of 0.15 and a T-bill with a rate of return of 0.05. 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 (CAL) is calculated as the difference between the expected return of the risky asset and the risk-free rate, divided by the standard deviation of the risky asset: (0.12 - 0.05) / 0.15 = 0.4667.

Question 10

An investor invests 30% of his wealth in a risky asset with an expected rate of return of 0.13 and a variance of 0.03 and 70% in a T-bill that pays 6%.His portfolio's expected return and standard deviation are __________ and __________, respectively.

Accepted Answer

E(r_P) = 0.3(13%) + 0.7(6%) = 8.1%; s_P = 0.3(0.03)^1/2 = 5.19%.

Question 11

You invest $100 in a risky asset with an expected rate of return of 0.12 and a standard deviation of 0.15 and a T-bill with a rate of return of 0.05. 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 0.06?

Accepted Answer

To achieve a portfolio with a specific standard deviation (in this case, 0.06) when combining a risk-free asset (with a standard deviation of 0) and a risky asset, we use the formula for the standard deviation of a portfolio. The standard deviation of the portfolio is proportional to the amount invested in the risky asset because the risk-free asset has a standard deviation of 0. To achieve a standard deviation of 0.06 when the risky asset has a standard deviation of 0.15, the proportion of the investment in the risky asset must be 0.06 / 0.15 = 0.4 or 40%. Therefore, 60% must be invested in the risk-free asset.

Question 12

You are considering investing $1,000 in a T-bill that pays 0.05 and a risky portfolio, P, constructed with two risky securities, X and Y.The weights of X and Y in P are 0.60 and 0.40, respectively.X has an expected rate of return of 0.14 and variance of 0.01, and Y has an expected rate of return of 0.10 and a variance of 0.0081. If you want to form a portfolio with an expected rate of return of 0.11, what percentages of your money must you invest in the T-bill and P, respectively?

Accepted Answer

Let x be the proportion of the portfolio invested in the risky portfolio P. Then (1-x) is the proportion invested in the T-bill. 
The expected rate of return of the portfolio is: 
0.11 = x(0.14) + (1-x)(0.05) 
Solving for x, we get: 
x=0.19 
So, we should invest 19% in the risky portfolio and 81% in the T-bill. Therefore, the answer is B.

Question 13

Which of the following statements regarding the capital allocation line (CAL) is false?

Accepted Answer

The CAL is not called the efficient frontier of risky assets in the absence of a risk-free asset, but rather the efficient frontier including a risk-free asset.

Question 14

You are considering investing $1,000 in a T-bill that pays 0.05 and a risky portfolio, P, constructed with two risky securities, X and Y.The weights of X and Y in P are 0.60 and 0.40, respectively.X has an expected rate of return of 0.14 and variance of 0.01, and Y has an expected rate of return of 0.10 and a variance of 0.0081. If you want to form a portfolio with an expected rate of return of 0.10, what percentages of your money must you invest in the T-bill, X, and Y, respectively, if you keep X and Y in the same proportions to each other as in portfolio P?

Accepted Answer

The answer of You are considering investing $1,000 in a...

Question 15

Steve is more risk-averse than Edie.On a graph that shows Steve and Edie's indifference curves, which of the following is true? Assume that the graph shows expected return on the vertical axis and standard deviation on the horizontal axis. I) Steve and Edie's indifference curves might intersect.
II. Steve's indifference curves will have flatter slopes than Edie's.
III. Steve's indifference curves will have steeper slopes than Edie's.
IV. Steve and Edie's indifference curves will not intersect.
V. Steve's indifference curves will be downward sloping, and Edie's will be upward sloping.

Accepted Answer

The answer of Steve is more risk-averse than Edie.On a...

Question 16

The change from a straight to a kinked capital allocation line is a result of

Accepted Answer

The change from a straight to a kinked capital allocation line occurs when there is a difference between the borrowing rate and the lending rate, specifically when the borrowing rate exceeds the lending rate. This creates a kink because the cost of borrowing to invest more in the risky asset is higher than the return on lending (investing in the risk-free asset), leading to a change in the slope of the capital allocation line beyond the point of tangency with the efficient frontier.

Question 17

You are considering investing $1,000 in a T-bill that pays 0.05 and a risky portfolio, P, constructed with two risky securities, X and Y.The weights of X and Y in P are 0.60 and 0.40, respectively.X has an expected rate of return of 0.14 and variance of 0.01, and Y has an expected rate of return of 0.10 and a variance of 0.0081. What would be the dollar values of your positions in X and Y, respectively, if you decide to hold 40% of your money in the risky portfolio and 60% in T-bills?

Accepted Answer

If you decide to hold 40% of your $1,000 investment in the risky portfolio, that amounts to $400. Within the risky portfolio, 60% of your funds would be allocated to X and 40% to Y. Therefore, $400 * 0.60 = $240 would be invested in X, and $400 * 0.40 = $160 would be invested in Y.

Question 18

You invest $100 in a risky asset with an expected rate of return of 0.12 and a standard deviation of 0.15 and a T-bill with a rate of return of 0.05. A portfolio that has an expected outcome of $115 is formed by

Accepted Answer

The expected outcome of $115 from an initial investment of $100 represents a 15% return. Option C, borrowing $43 at the risk-free rate and investing a total of $143 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 reach the desired outcome. This approach involves using leverage to amplify returns, assuming the risky asset performs as expected.

Question 19

Given the capital allocation line, an investor's optimal portfolio is the portfolio that

Accepted Answer

The optimal portfolio for an investor is the one that maximizes their expected utility, or their overall satisfaction from the investment. The capital allocation line represents the different combinations of risk and return available to an investor, and the optimal portfolio is the point on the line where the investor's utility is maximized. Therefore, the correct answer is D.

Question 20

An investor invests 40% of his wealth in a risky asset with an expected rate of return of 0.17 and a variance of 0.08 and 60% in a T-bill that pays 4.5%.His portfolio's expected return and standard deviation are __________ and __________, respectively.

Accepted Answer

To calculate the portfolio's expected return, we use the following formula:

Expected Return = (Weight of Asset 1 × Expected Return of Asset 1) + (Weight of Asset 2 × Expected Return of Asset 2)

= (0.40 × 0.17) + (0.60 × 0.045)

= 0.095

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

Standard Deviation = √[(Weight of Asset 1)^2 × Variance of Asset 1 + (Weight of Asset 2)^2 × Variance of Asset 2 + 2 × Weight of Asset 1 × Weight of Asset 2 × Covariance between Asset 1 and Asset 2]

Since T-bills have zero covariance with all other assets, the last term drops out of the equation, and we get:

Standard Deviation = √[(0.40)^2 × 0.08 + (0.60)^2 × 0]

= √(0.0128)

= 0.113

Therefore, the portfolio's expected return is 0.095 and its standard deviation is 0.113. The best answer is C.

Quiz 6: Capital Allocation to Risky Assets

An investor invests 30% of his wealth in a risky asset with an expected rate of return of 0.15 and a variance of 0.04 and 70% in a T-bill that pays 6%.His portfolio's expected return and standard deviation are and , respectively.

An investor invests 70% of his wealth in a risky asset with an expected rate of return of 0.15 and a variance of 0.04 and 30% in a T-bill that pays 5%.His portfolio's expected return and standard deviation are and , respectively.