Question 1

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 the weighted average of the individual betas.

Question 2

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

Question 3

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 4

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?

A) 0.026
B) 0.085
C) 0.160
D) 0.190
E) 0.220

Accepted Answer

β_p = w₁β₁+ . . . + w_nβ_n Recall that the beta of the risk free asset is 0. β_p = 0.40 × 0.40 + 0.60 × 0 = 0.16

Question 5

Peter Lynch has the following portfolio of investments:

What is the beta of Peter's portfolio?
A) 1.000
B) 1.126
C) 1.366
D) 1.534
E) 1.877

Accepted Answer

First determine the weights of each stock in the portfolio: Total Investment = $21 + $42 + $11 + $32 Total Investment = $106 million. w₁ = 11ea7fdb_fc09_3b33_a768_2f3bf2eca068_TB2902_11 = 0.20 w₂ = 11ea7fdb_fc09_3b34_a768_57e7728ab987_TB2902_11 = 0.40 w₃ = 11ea7fdb_fc09_3b35_a768_2735829316b3_TB2902_11 = 0.10 w₁ = 11ea7fdb_fc09_3b36_a768_13fd74220c08_TB2902_11 = 0.30 Next take the weighted average of the individual betas to find the portfolio beta. β_p = w₁β₁ + . . . + w_nβ_n β_p = (0.20 × 0.945) + (0.40 × 1.47) + (0.10 × 2.10) + (0.30 × 1.26) β_p = 0.19 + 0.588 + 0.21 + 0.378 = 1.366

Question 6

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 7

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 8

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 9

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

The Market's Beta is Equal to 1.

Question 10

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:

What is the beta of the portfolio?
A) 1.50
B) 1.70
C) 2.50
D) 2.55
E) 2.70

Accepted Answer

Step 1 - Compute the weights of each asset in the portfolio. You issued $5,000 of T-Bills, so you are short T-Bills. Short positions are represented by negative portfolio weights. w_i = 11ea7fdb_fc09_d77e_a768_57ce0b7221c1_TB2902_11 11ea7fdb_fc09_d77f_a768_b19e418c6f0e_TB2902_11 = 11ea7fdb_fc09_d780_a768_6b553762c986_TB2902_11 = -0.50 11ea7fdb_fc09_fe91_a768_e93e6015ff9d_TB2902_11 = 11ea7fdb_fc09_fe92_a768_2716dff596e6_TB2902_11 = 1.50 Step 2 - Use the weights to compute the beta for the portfolio. β_p = w₁β₁ + . . . + w_nβ_n Recall that the beta of the risk free asset is 0 β_p = -0.50 × 0 + 1.50 × 1.70 = 2.55

Question 11

You own a portfolio that is equally invested in three assets: 1)the risk-free asset; 2)Stock 1; and 3)Stock 2.Stock 1 has a beta of 1.9 and the portfolio has the same risk as the market portfolio.
What is the beta of Stock 2 in the portfolio?
A) 1.0
B) 1.1
C) 1.2
D) 1.3
E) 1.4

Accepted Answer

The market has a beta of 1, so we know the total portfolio also has a beta of 1. The risk-free asset has a beta of 0. β_p = w₁β₁ + . . . + w_nβ_n 1.0 = (0.33 × 1.9) + (0.33 × β₂) + (0.33 × 0) 1.0 = 0.627 + (0.33 × β₂) 0.373 = (0.33 × β₂) Β₂ = 1.1

Question 12

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 13

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 market's beta is equal to 1.

Question 14

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

Let w be the weight of Stock X. β_p = w₁β₁ + . . . + w_nβ_n 0.825 = w(1.1) + (1 - w)0 0.825 = 1.1w w = 11ea7fdb_fc0a_73ca_a768_f58653142fa0_TB2902_11 = 0.75 Thus, the weight of the risk-free asset is 0.25. These weights yield the following portfolio expected return: E(k_p) = w₁ E(k₁) + w₂ E(k₂) + w_n E(k_n) E(k_p) = (0.75 × 0.12) + (0.25 × 0.05) = 0.1025 or 10.25% Yes, you can match her risk and return by investing 75% in asset X and the rest in the risk free asset.

Question 15

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 16

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 17

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

Since we want the portfolio to have a beta of 1.2, we equate this beta to the weighted average of the betas of our two securities, GE shares and T-Bills. Let w be the weight of GE. β_p = w₁β₁ + . . . + w_nβ_n 1.2 = w(1.4) + (1 - w)0 1.2 = 1.4w w = 11ea7fdb_fc0a_73c9_a768_c1ff661ed7d6_TB2902_11 = 0.857 or 0.86

Question 18

Warren has a portfolio with three stocks as shown in the table.What is the beta of Warren's portfolio?

A) 0.775
B) 0.988
C) 1.017
D) 1.340
E) 1.505

Accepted Answer

Take the weighted average of the individual betas to find the portfolio beta. β_p = w₁β₁+ . . . + w_nβ_n β_p = (0.40 × 0.50) + (0.35 × 1.50) + (0.25 × 1.05) β_p = 0.20 + 0.525 + 0.2625 = 0.9875 or 0.988

Question 19

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

β_p = w₁β₁ + . . . + w_nβ_n β_p = (0.50 × 0.80) + (0.50 × 1.3) β_p = 0.40 + 0.65 = 1.05

Question 20

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 beta of a portfolio is the weighted average of the individual betas.

Quiz 6: Portfolio Theory

The beta of a portfolio

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?

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?

Peter Lynch has the following portfolio of investments: What is the beta of Peter's portfolio?

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 beta coefficient of + 1 represents an asset that

You own a portfolio that is equally invested in three assets: 1) the risk-free asset; 2) Stock 1; and 3) Stock 2.Stock 1 has a beta of 1.9 and the portfolio has the same risk as the market portfolio. What is the beta of Stock 2 in the portfolio?

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.

The beta of the market

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?

Beta is the slope of the security market line.

Warren has a portfolio with three stocks as shown in the table.What is the beta of Warren's portfolio?

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?

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?