Question 1

A friend brags that she expects to earn a return of 10.25% on her portfolio with a beta of 0.825. Can you match her performance with Stock X (12% return and a beta of 1.1)and the risk free asset that earns a 5% return? With what portfolio weights?
A)Yes, 0.75 Stock X and 0.25 Risk Free Asset
B)Yes, 0.25 Stock X and 0.75 Risk Free Asset
C)Yes, 0.5 Stock X and 0.5 Risk Free Asset
D)No

Accepted Answer

To match a portfolio with a return of 10.25% and beta of 0.825, we need to use the Capital Asset Pricing Model (CAPM) equation:

Expected Return = Risk Free Rate + Beta * (Market Return - Risk Free Rate)

Solving for Market Return, we have:

Market Return = (Expected Return - Risk Free Rate) / Beta + Risk Free Rate
              = (10.25% - 5%) / 0.825 + 5%
              = 8.48%

To achieve this market return, we need to find the weights of Stock X and Risk Free Asset:

0.75 * 12% + 0.25 * 5% = 10.25%

0.75 * 1.1 + 0.25 * 0 = 0.825

Therefore, the portfolio weights are 0.75 for Stock X and 0.25 for the Risk Free Asset. Hence, the answer is A.

Question 2

The beta of a portfolio
A)does not change over time.
B)is irrelevant, only the betas of the individual assets are important.
C)is the weighted average of the betas of the individual assets in the portfolio.
D)is the sum of the betas of all assets in the portfolio.

Accepted Answer

The beta of a portfolio is calculated as the weighted average of the betas of the individual assets in the portfolio. This means that the beta of a portfolio takes into account the risk of each individual asset, as well as the relative size of each asset in the portfolio. Therefore, option C is the correct choice. Option A is incorrect because the beta of a portfolio can change over time if the composition of the portfolio changes. Option B is incorrect because the beta of a portfolio is an important measure of the risk of the overall portfolio, not just the individual assets. Option D is incorrect because the sum of the betas of all assets in a portfolio does not take into account the relative size of each asset, and is therefore not an accurate measure of the overall risk of the portfolio.

Question 3

The beta of the market
A)is 1.
B)is greater than 1.
C)cannot be determined.
D)is less than 1.

Accepted Answer

The beta of the market is always 1 by definition. Beta measures the volatility of an asset relative to the market, and since the market is the benchmark for beta calculations, its beta is set at 1.

Question 4

You are looking over your brother's portfolio. In his portfolio, he is holding one long position and one short position. Jimmy, your brother, bought 1,600 shares of Sunny Inc. each for $55. He sold 1,000 shares of Rainy Ltd. for $50 a share. Calculate the portfolio weight on the Rainy Ltd. position.
A)-1.32
B)-0.76
C)-0.50
D)0.24
E)0.30

Accepted Answer

The short position generates a positive cash flow, so your equity investment in the portfolio is the cost of buying Sunny less the proceeds from selling Rainy. Investment = Cost of buying Sunny - Proceeds from selling Rainy Investment = $88,000 - $50,000 Investment = $38,000 w_i = 11ea7fdb_fc0a_4cb6_a768_e9f675c9ef04_TB2902_11 The portfolio weight on the Sunny position is = 11ea7fdb_fc0a_4cb7_a768_23bcfe75668f_TB2902_11 = 2.32 The portfolio weight on the Rainy position is = 11ea7fdb_fc0a_4cb8_a768_d5e7ebd8ccf7_TB2902_11 = -1.32 The weight on Rainy is negative because it is a short position. Just to verify the weights: 2.32 + (-1.32) = 1.

Question 5

The ________ shows the possible risk/return combinations for a portfolio.
A)Portfolio Possibility Line
B)Portfolio Beta
C)Modern Portfolio Theory
D)Momentum Effect

Accepted Answer

The Portfolio Possibility Line (PPL) shows the possible risk/return combinations for a portfolio. It is also known as the Efficient Frontier, which represents the set of efficient portfolios that generate the maximum expected return for a given level of risk, or the minimum level of risk for a given expected return. Modern Portfolio Theory (C) is the framework for constructing an efficient portfolio, while Portfolio Beta (B) measures the systematic risk of a portfolio compared to the market. Momentum Effect (D) is a phenomenon where stocks that have performed well in the past tend to continue performing well in the future.

Question 6

Beta is the slope of the security market line.

Accepted Answer

The SML is the graph of the CAPM equation, E(k_i) = k_F + β_i[E(k_M) - k_F]. Remember that the graph of a straight line is y = b + mx, where m is the slope of the line. Therefore, the slope of the SML is the market risk premium: E(k_M) - k_F.

Question 7

An individual's portfolio consists of three separate assets. Asset 1 has a beta of 1.4, asset 2 has a beta of .84 and asset 3 has a beta of 1.05. The investor has invested $240 in asset 1, $500 in asset 2, and $260 in asset 3. Calculate the portfolio beta.
A)1.03
B)1.17
C)1.09
D)0.93
E)0.85

Accepted Answer

Step 1 - Calculate the portfolio weights. Total portfolio value = $240 + $500 + $260 = $1,000 w_i = 11ea7fdb_fc09_8957_a768_fb2d750a0803_TB2902_11 The weight of Asset 1 = 11ea7fdb_fc09_8958_a768_d1bf4a2bd8be_TB2902_11 = 0.24 The weight of Asset 2 = 11ea7fdb_fc09_8959_a768_373e20db3a4b_TB2902_11 = 0.50 The weight of Asset 3 = 11ea7fdb_fc09_895a_a768_2b2f7f638129_TB2902_11 = 0.26 Step 2 - Use the weights to compute the portfolio beta. β_p = w₁β₁ + . . . + w_nβ_n β_p = (0.24 × 1.4) + (0.50 × 0.84) + (0.26 × 1.05) β_p = 0.336 + 0.42 + 0.273 = 1.03

Question 8

Consider the two assets outlined in the table below. What is the beta of the two asset portfolio given that 40% is invested in X? $$\begin{array} { | c | c | c | } 
\hline \text { Asset } & \begin{array} { c } 
\text { Expected } \
\text { Return }
\end{array} & \text { Beta } \
\hline X & 12 \% & 0.40 \
\hline \text { Risk Free } & 5 \% & 0 \
\hline
\end{array}$$
A)0.026
B)0.085
C)0.160
D)0.190
E)0.220

Accepted Answer

The portfolio beta is calculated as the weighted sum of the betas of the individual assets. Here, 40% is invested in Asset X with a beta of 0.40, and 60% is invested in the risk-free asset with a beta of 0. Therefore, the portfolio beta = (0.40 * 0.40) + (0.60 * 0) = 0.16.

Question 9

You want to buy $20,000 worth of shares in Tootsie Roll Industries Inc. on margin, but you only have $10,000 of your own money to invest. The remaining $10,000 is borrowed by issuing T-Bills; assume the cost of borrowing is the risk-free rate. What is the portfolio weight for the risk free asset (T-Bills)?
A)-1.00
B)-0.50
C)1.00
D)0.50
E)2.00

Accepted Answer

w_i = 11ea7fdb_fc0a_9adb_a768_f7b532ac5f58_TB2902_11 You issued $10,000 of T-Bills, so you are short T-Bills. Short positions are represented by negative portfolio weights. w_i = 11ea7fdb_fc0a_9adc_a768_1bf50bdc497a_TB2902_11 = -1.0

Question 10

Your video-game addicted nephew tells you that the Nintendo Wii is much better than the Microsoft X-Box. To take advantage of this information, you decide to build a two asset portfolio by buying shares in Nintendo and selling shares short in Microsoft. For your long position you buy 1700 shares of Nintendo at a price of $40 per share. For the short position, you sell 1000 shares in Microsoft at a price of $35 per share. What is the portfolio weight for your short position in Microsoft?
A)-1.06
B)-0.94
C)0
D)0.34
E)0.50

Accepted Answer

The short position generates a positive cash flow, so your equity investment in the portfolio is the cost of buying Nintendo less the proceeds from selling Microsoft. Investment = Cost of buying Nintendo - Proceeds from selling Microsoft Investment = $68,000 - $35,000 Investment = $33,000 w_i = 11ea7fdb_fc0a_25a3_a768_0fa3e0070c6b_TB2902_11 The weight of Nintendo in the portfolio = 11ea7fdb_fc0a_25a4_a768_676ec983b466_TB2902_11 = 2.06 The portfolio weight on the Microsoft position = 11ea7fdb_fc0a_25a5_a768_45c066396177_TB2902_11 = -1.06 The weight on Microsoft is negative because it is a short position. Just to verify the weights: 2.06 + (-1.06) = 1.

Question 11

You live in an Eichler-built house in Cupertino California. You admire Apple so much that it is the only stock that you want in your portfolio. You have $100,000 of your own money to invest and you intend to buy more Apple on margin by borrowing an additional $40,000. Your broker will lend to you at the risk free rate, 5%, and has guaranteed the lending rate for the duration of your investment. Apple's expected return is 12% and the expected return on the market is 8%. Apple's beta is 1.25. What beta do you expect from your portfolio?
A)1.25
B)1.45
C)1.55
D)1.65
E)1.75

Accepted Answer

Your investment is $100,000. The portfolio weight on the Apple position is: w_i = 11ea7fdb_fc0a_e8fe_a768_311adba0f837_TB2902_11 = 11ea7fdb_fc0a_e8ff_a768_b97bae919009_TB2902_11 = 1,4 The margin loan is risk free (guaranteed by the broker) so it is equivalent to a short position in the risk free asset. Thus, its beta is zero. β_p = w₁β₁ + . . . + w_nβ_n β_p = (w)1.25 + (1 - w)0 β_p = 1.4 × 1.25 = 1.75

Question 12

Your friend, Dobson, manages the Formula Growth mutual fund. Dobson expects to earn 11% on his portfolio with a beta of 1.2. You only invest in shares of General Electric and T-Bills. You like GE because it was started in 1890 by Thomas Edison, the great American inventor, and it has a diversified portfolio of products including jet engines and MRI diagnostic imaging machines. The expected return of GE is 13% and its beta is 1.40. The expected return on T-Bills is 2%. If you construct your portfolio so that its risk is equal to the risk of Formula Growth, then what portfolio weight do you need on the shares of GE?
A)0.85
B)0.86
C)0.87
D)0.88
E)0.89

Accepted Answer

To compensate for the risk of Formula Growth, we need a portfolio with the same beta as Formula Growth's beta of 1.2. We can achieve this by combining GE and T-Bills in different proportions.

Let x be the weight of GE in the portfolio, then the weight of T-Bills would be (1 - x). The beta of the portfolio is:

(beta of GE) × x + (beta of T-Bills) × (1 - x) = 1.2

Solving for x, we get:

1.4x + 0.02(1 - x) = 1.2

0.4x = 0.118

x = 0.295

Therefore, the weight of GE in the portfolio should be 0.295 or 29.5%.

Question 13

If Acme Dynamite stock has a beta of .8 and a standard deviation of 15% and Splat Paintball stock has a beta of 1.3 and a standard deviation of 9%, what is the beta of a portfolio comprised of equal weights of both securities?
A)24%
B)12%
C)18%
D)1.05
E)2.10

Accepted Answer

To find the beta of a portfolio, we use the formula:

Portfolio beta = (Weight of Stock 1 x Beta of Stock 1) + (Weight of Stock 2 x Beta of Stock 2)

In this case, both securities have equal weights, so the formula simplifies to:

Portfolio beta = (0.5 x 0.8) + (0.5 x 1.3) = 1.05

Therefore, the beta of the portfolio is 1.05.

Question 14

You want to buy $20,000 worth of shares in Tootsie Roll Industries Inc. on margin, but you only have $10,000 of your own money to invest. The remaining $10,000 is borrowed by issuing T-Bills; assume the cost of borrowing is the risk-free rate. What is the portfolio weight for Tootsie Roll?
A)0.25
B)0.50
C)1.00
D)1.50
E)2.00

Accepted Answer

w_i = 11ea7fdb_fc09_b06b_a768_4b52b7368d5e_TB2902_11 w_i = 11ea7fdb_fc09_b06c_a768_6300a8b28229_TB2902_11 = 2.0

Question 15

Tom wishes to calculate the riskiness of his portfolio, which is comprised of equal amounts of two stocks. Which of the following measures would you recommend?
A)Weighted average betas of the two securities
B)A weighted average of the correlation between the two securities
C)Weighted average standard deviations
D)The slope of the security market line
E)A weighted average of the coefficients of variation

Accepted Answer

The weighted average betas of the two securities would give Tom a measure of the riskiness of his portfolio. Beta measures the systematic risk of a security or portfolio in relation to the market. A portfolio with a higher beta would be riskier than a portfolio with a lower beta. Therefore, calculating the weighted average of the two securities' betas would give Tom an idea of how much systematic risk his portfolio has.

Question 16

A friend tips you off on a hot stock: Sure Thing Mines Ltd. You only have $10,000 to invest but you want to invest more. Assume that you can borrow an additional $5,000 by short-selling the risk free asset (issuing T-Bills). You purchase $15,000 worth of shares in Sure Thing Mines Ltd. The expected returns and standard deviations of the two assets are outlined in the table below:
$$\begin{array} { | c | c | c | } 
\hline \text { Asset } & \begin{array} { c } 
\text { Expected } \
\text { Return }
\end{array} & \text { Beta } \
\hline \text { T-Bills } & 5.5 \% & 0 \
\hline \begin{array} { c } 
\text { Sure Thing } \
\text { Mines }
\end{array} & 15 \% & 1.70 \
\hline
\end{array}$$ What is the beta of the portfolio?
A)1.50
B)1.70
C)2.50
D)2.55
E)2.70

Accepted Answer

The beta of the portfolio is calculated as a weighted average of the betas of the individual assets. Since you are investing $15,000 in Sure Thing Mines with a beta of 1.70 and short-selling $5,000 in T-Bills with a beta of 0, the portfolio beta is: (15,000/10,000) * 1.70 + (−5,000/10,000) * 0 = 2.55.

Question 17

When buying on margin, the amount of money provided by the investor is called:
A)Collateral
B)Margin
C)Capital
D)Order
E)Cash

Accepted Answer

When buying on margin, the amount of money provided by the investor is called margin. Collateral refers to assets that are pledged as security for a loan, capital refers to the total amount of funds invested in a business, order refers to the request to buy or sell a security, and cash is the actual money held in an account.

Question 18

You want to buy $20,000 worth of shares in Tootsie Roll Industries Inc. on margin, but you only have $10,000 of your own money to invest. The remaining $10,000 is borrowed by issuing T-Bills; assume the cost of borrowing is the risk-free rate. The weight of Tootsie Roll Industries in your portfolio is 2.0. The weight of T-Bills in your portfolio is -1.0. Assume that the expected return on Tootsie Roll is 12% and the expected return on the risk free asset (T-Bills)is 5%. What is the return on your portfolio?
A)17%
B)18%
C)19%
D)20%
E)21%

Accepted Answer

E(k_p) = w₁E(k₁) + w₂E(k₂) + w_nE(k_n) E(k_p) = 2.0(.12) + -1.0(.05) = .19

Question 19

A beta coefficient of + 1 represents an asset that
A)is unaffected by market movement.
B)is less responsive than the market portfolio.
C)has the same response as the market portfolio.
D)is more responsive than the market portfolio.

Accepted Answer

A beta coefficient of +1 represents an asset that has the same response as the market portfolio. This means that it will move in the same direction as the overall market and with the same magnitude.

Question 20

You want to buy $20,000 worth of shares in Tootsie Roll Industries Inc. on margin, but you only have $10,000 of your own money to invest. The remaining $10,000 is borrowed by issuing T-Bills; assume the cost of borrowing is the risk-free rate. The weight of Tootsie Roll Industries in your portfolio is 2.0. The weight of T-Bills in your portfolio is -1.0. Assume that Tootsie Roll has a beta of 0.75. What is the beta of the portfolio?
A)0.75
B)1.25
C)1.50
D)1.75
E)2.00

Accepted Answer

β_p = w₁β₁ + . . . + w_nβ_n Recall that the beta of the risk free asset is 0 β_p = 2.0 × 0.75 = 1.50

Quiz 6: Portfolio Theory

A friend brags that she expects to earn a return of 10.25% on her portfolio with a beta of 0.825. Can you match her performance with Stock X (12% return and a beta of 1.1) and the risk free asset that earns a 5% return? With what portfolio weights?

The beta of a portfolio

The beta of the market

You are looking over your brother's portfolio. In his portfolio, he is holding one long position and one short position. Jimmy, your brother, bought 1,600 shares of Sunny Inc. each for $55. He sold 1,000 shares of Rainy Ltd. for $50 a share. Calculate the portfolio weight on the Rainy Ltd. position.

The ________ shows the possible risk/return combinations for a portfolio.

Beta is the slope of the security market line.

An individual's portfolio consists of three separate assets. Asset 1 has a beta of 1.4, asset 2 has a beta of .84 and asset 3 has a beta of 1.05. The investor has invested $240 in asset 1, $500 in asset 2, and $260 in asset 3. Calculate the portfolio beta.

If Acme Dynamite stock has a beta of .8 and a standard deviation of 15% and Splat Paintball stock has a beta of 1.3 and a standard deviation of 9%, what is the beta of a portfolio comprised of equal weights of both securities?

You want to buy $20,000 worth of shares in Tootsie Roll Industries Inc. on margin, but you only have $10,000 of your own money to invest. The remaining $10,000 is borrowed by issuing T-Bills; assume the cost of borrowing is the risk-free rate. What is the portfolio weight for Tootsie Roll?

Tom wishes to calculate the riskiness of his portfolio, which is comprised of equal amounts of two stocks. Which of the following measures would you recommend?

When buying on margin, the amount of money provided by the investor is called:

A beta coefficient of + 1 represents an asset that