Question 1

You own two mutual funds. Fund A has an expected return of 12% and a beta of 0.8. Fund B has an expected return of 18% and a beta of 1.4. If your portfolio beta is the same as the market portfolio, what proportion of your portfolio is invested in fund A?

Accepted Answer

The portfolio beta should be equal to the market beta, which is typically considered to be 1.0. Since we know the betas and expected returns of both funds, we can set up the following equation:

Portfolio Beta = (Proportion in Fund A * Fund A Beta) + ((1 - Proportion in Fund A) * Fund B Beta)

1.0 = (Proportion in Fund A * 0.8) + ((1 - Proportion in Fund A) * 1.4)

Solving for Proportion in Fund A, we get:

Proportion in Fund A = (1.4 - 1.0)/(0.8 - 1.4) = 2/3

Therefore, 2/3 of the portfolio should be invested in Fund A.

Question 2

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?

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 3

A friend tells you about a fund that does just as well as the market in bull markets but cushions your fall in bear markets. That is, its returns fall by less than the market's in bear markets. Your friend is telling you that the fund's Beta is ________ in bull markets, but that the fund's Beta is ________ in bear markets.

Accepted Answer

Your friend is telling you that the fund's Beta is equal to one in bull markets (because it goes up by the same amount as the market), but that the fund's Beta is less than one in bear markets (because the fund's returns fall by less than the market's returns).

Question 4

Fishing supply company, Outside Tackle, has its returns graphed against the market returns for a 5 year period. The line that has the best fit for the data has the formula y = .1254 + 1.265x. What information can we derive from this?

Accepted Answer

The formula given (y = .1254 + 1.265x) represents the CAPM equation, where y is the expected return, .1254 is the risk-free rate, and 1.265 is the beta for Outside Tackle. Therefore, the correct answer is C - the beta for Outside Tackle is 1.265. The other answer choices are incorrect because we cannot determine the systematic risk of Outside Tackle from this equation, we do not know if the returns are better or worse than the market without additional information, and .1254 represents the risk-free rate, not the beta.

Question 5

Warren has a portfolio with three stocks as shown in the table. What is the beta of Warren's portfolio? $$\begin{array} { | c | c | c | c | } 
\hline \text { Stock } & \begin{array} { c } 
\text { Required } \
\text { Return }
\end{array} & \begin{array} { c } 
\text { Portfolio } \
\text { Weight }
\end{array} & \text { Beta } \
\hline \text { Raymond's } & 6.75 \% & 0.4 & 0.50 \
\hline \begin{array} { c } 
\text { Keller } \
\text { Industries }
\end{array} & 11.43 \% & 0.35 & 1.50 \
\hline \text { Huron Power } & 9.27 \% & 0.25 & 1.05 \
\hline
\end{array}$$

Accepted Answer

The beta of the portfolio is calculated as the weighted average of the betas of the individual stocks: (0.4 * 0.50) + (0.35 * 1.50) + (0.25 * 1.05) = 0.988.

Question 6

Last year the market's return was 7% and Hare Growth earned 9%. This year the market was up and yielded 17%. If Hare Growth's Beta is 1.75, then what is Hare's return this year?

Accepted Answer

Beta is the slope of the characteristic line. The slope is the rise over the run. In other words, the change in the y-axis variable (the stock) over the change in the x-axis variable (the market). Beta = 11ea7fdb_fc08_77de_a768_132308d96720_TB2902_11 Δk = Beta × Δk_M The market's return changed by +10% (from 7% to 17%) so: Δk = 1.75 × 10% = 17.50% Hare Growth's return this year is equal to its return last year plus the change in its return for this year: k = 9% + 17.50% = 26.5%

Question 7

What is the Beta for a security whose returns do not vary across states of nature (a risk-free security)?

Accepted Answer

The beta of a security measures the volatility of its returns compared to the overall market. A risk-free security, by definition, has a beta of 0 because its returns do not vary with changes in the market.

Question 8

The change of risk in a portfolio from the addition of one more share of a particular asset to the portfolio is called

Accepted Answer

The change of risk in a portfolio from the addition of one more share of a particular asset is called marginal risk. This is because it measures the incremental change in risk when a small additional amount of an asset is added to an already diversified portfolio. CAPM is a model that explains the relationship between systematic risk and expected returns. Market risk refers to the risk of the overall market, while diversifiable risk is the risk that can be eliminated through diversification.

Question 9

The table below gives the historic return over the past five months for the market portfolio and two assets: A and B. Which of the answers below best describes the historic beta for A and B? $$\begin{array} { | c | c | c | c | } 
\hline \text { Month } & \text { Market } & \text { Asset A } & \text { Asset B } \
\hline \mathbf { 1 } & 4 \% & 3 \% & 10 \% \
\hline \mathbf { 2 } & 2 \% & 1 \% & 5 \% \
\hline \mathbf { 3 } & 4 \% & 2 \% & 8 \% \
\hline \mathbf { 4 } & 9 \% & 7 \% & 12 \% \
\hline \mathbf { 5 } & 3 \% & 1 \% & 7 \% \
\hline
\end{array}$$

Accepted Answer

Asset A's returns are consistently less volatile than the market, indicating a beta less than 1. Asset B's returns are more volatile than the market, indicating a beta greater than 1.

Question 10

You own a stock portfolio invested 30% in a film company, 20% in a bank stock, 10% in a mining company, and 40% in an oil company. The betas of these four stocks are 1.4, 0.6, 1.5, and 1.8 respectively. What is the portfolio beta?

Accepted Answer

Take the weighted average of the individual betas to find the portfolio beta. β_p = w₁β₁ + . . . + w_nβ_n β_p = (0.30 × 1.4) + (0.20 × 0.6) + (0.10 × 1.5) + (0.40 × 1.8) β_p = 0.42 + 0.12 + 0.15 + 0.72 = 1.41

Question 11

Your friend tells you that the Prudent Mutual Fund gives you more downside protection than buying an exchange traded fund (ETF)that mimics the market portfolio. What is he telling you about the fund's Beta?

Accepted Answer

If the Prudent Mutual Fund gives more downside protection than an ETF that mimics the market portfolio, it means that the fund's Beta is less than 1. Beta is a measure of an asset's volatility in relation to the market, and a Beta of less than 1 indicates that the asset is less volatile than the market.

Question 12

The points that do not fall onto the characteristic line for a company don't do so because of

Accepted Answer

The characteristic line represents the relationship between a stock's return and the return of the overall market. Points that do not fall on the line are due to firm-specific risk, which is unique to the company and cannot be diversified away through broad market exposure. Market risk, non-diversifiable risk, total risk, and standard deviation of returns are all related to the overall market and are represented by the characteristic line.

Question 13

You hold the following portfolio, consisting of Assets A, B and C. What is the portfolio beta? $$\begin{array} { | c | c | c | c | } 
\hline \text { Asset } & \text { Return } & \text { Beta } & \begin{array} { c } 
\text { Portfolio } \
\text { Weight }
\end{array} \
\hline \text { A } & 10 \% & 0.75 & 0.20 \
\hline \text { B } & 12 \% & 1.00 & 0.40 \
\hline \text { C } & 14 \% & 1.25 & 0.40 \
\hline
\end{array}$$

Accepted Answer

The portfolio beta is calculated as the weighted sum of the individual asset betas: (0.20 * 0.75) + (0.40 * 1.00) + (0.40 * 1.25) = 0.15 + 0.40 + 0.50 = 1.05.

Question 14

You manage your own portfolio of about twenty stocks. One of which is Honda Motors. The returns on Honda tend to move up and down with the economy as a whole. You decide to sell Honda and replace it with the common stock of Repo-Man Inc., an asset recovery company. Repo-Man's shares tend to rise when the economy falls, and vice versa. Your portfolio's beta should:

Accepted Answer

Since Honda's returns move with the overall economy, it has a beta close to 1. By replacing Honda with Repo-Man, whose returns move in the opposite direction to the economy, the portfolio's beta should decrease. A lower beta means the portfolio is less sensitive to changes in the overall market, which may be desirable for some investors.

Question 15

Your portfolio had a beta of 1.233. The portfolio included two stocks. The first stock had a beta of 0.7 and the second had a beta of 1.1. What were the portfolio weights for each stock?

Accepted Answer

Let w be the portfolio weight of the first stock and (1 - w) the weight on the second: β_p = w₁β₁ + . . . + w_nβ_n 1.233 = w(0.7) + (1 - w)(1.1) 1.233 = 0.7w + 1.1 -1.1w 0.133 = -0.4w w = 11ea7fdb_fc08_c5ff_a768_7bfc79dc2170_TB2902_11 = -0.333 The weight of Stock 2 = (1 - (-0.333)) = 1.333

Question 16

The table below gives the historic return over the past five months for the market portfolio and two assets: A and B. Which of the answers below best describes the historic beta for A and B? $$\begin{array} { | c | c | c | c | } 
\hline \text { Month } & \text { Market } & \text { Asset A } & \text { Asset B } \
\hline \mathbf { 1 } & 3 \% & 5 \% & 4 \% \
\hline \mathbf { 2 } & - 5 \% & - 6 \% & 4 \% \
\hline \mathbf { 3 } & 1 \% & 4 \% & 4 \% \
\hline \mathbf { 4 } & - 10 \% & - 12 \% & 4 \% \
\hline \mathbf { 5 } & 6 \% & 10 \% & 4 \% \
\hline
\end{array}$$

Accepted Answer

The answer of The table below gives the historic return...

Question 17

In the Capital Asset Pricing Model (CAPM), beta measures

Accepted Answer

Beta is a measure of systematic risk, which is the risk that is inherent in the overall market and cannot be diversified away. Beta measures the historical relationship between the returns from an asset and the returns from the efficient portfolio. A beta of 1 indicates that the asset has the same systematic risk as the overall market, while a beta greater than 1 indicates higher systematic risk and a beta less than 1 indicates lower systematic risk.

Question 18

Peter Lynch has the following portfolio of investments: $$\begin{array} { | c | c | c | } 
\hline \text { Stock } & \text { Investment } & \text { Beta } \
\hline \text { A } & \$ 21 \text { million } & 0.945 \
\hline \text { B } & \$ 42 \text { million } & 1.47 \
\hline \text { C } & \$ 11 \text { million } & 2.10 \
\hline \text { D } & \$ 32 \text { million } & 1.26 \
\hline
\end{array}$$ What is the beta of Peter's portfolio?

Accepted Answer

The portfolio beta is calculated as a weighted average of the individual betas. The total investment is $106 million. The portfolio beta is: (21/106)*0.945 + (42/106)*1.47 + (11/106)*2.10 + (32/106)*1.26 = 1.366.

Question 19

You manage a portfolio in which you invest half of your money in T-Bills and the other half in a mutual fund that is indexed to match the market portfolio. What is the beta of this portfolio?

Accepted Answer

Take the weighted average of the individual betas. Remember the market has a beta of 1.0 and the risk free asset a beta of 0. β_p = w₁β₁ + . . . + w_nβ_n β_p = (0.50 × 1.0) + (0.50 × 0) β_p = 0.50 × 1.0 = 0.50 The beta for T-Bills (a risk-free asset) is 0, and the beta for the market (by definition) is 1. With half invested in each, that makes the beta of the portfolio 0.5.

Question 20

A friend tells you about a mutual fund that can protect you on the downside. In other words, in bear markets the return on the mutual fund does not fall as much as the market's return. The fund's Beta is:

Accepted Answer

A beta of less than one indicates that the mutual fund's returns are less volatile compared to the market's returns. In other words, the fund is less risky and can potentially protect the investor's downside during bear markets.

Quiz 6: Portfolio Theory

You own two mutual funds. Fund A has an expected return of 12% and a beta of 0.8. Fund B has an expected return of 18% and a beta of 1.4. If your portfolio beta is the same as the market portfolio, what proportion of your portfolio is invested in fund A?

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?