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# P1.T1.611. Arbitrage pricing theory (APT) (Topic Review)

#### Nicole Seaman

##### Director of FRM Operations
Staff member
Subscriber
Questions:

611.1. Peter the portfolio manages observes the following three well-diversified portfolios (A, B and C) that exist in a single-factor economy:

If Peter seeks to conduct an arbitrage with a long/short portfolio with $2.0 million of gross exposure, what is the expected profit (assuming no transaction costs and no margin)? a. No profit, as an arbitrage is not possible b.$10,000
c. $25,000 d.$30,000

611.2. Assume security returns are generated by the single-index model: R(i) = α(i) + β(i)*R(M) + e(i); where R(i) is the excess return for security(i) and R(M) is the market's excess return. The risk free-rate is 2.0% and the volatility of the market index is 20.0%. Suppose that there are three securities, (A), (B) and (C), characterized by the following data:

Consider the following two statements:

I. Given their identical Treynor measures, there is no arbitrage opportunity among the three securities
II. Given their identical non-systematic risk, σ[e(i]], all three securities have an identical expected (ex ante) Sharpe ratio

Which of the above statements is (are) TRUE?

a. Both statements are true
b. I. is true (there is no arbitrage opportunity); but II. is false (their Sharpe ratios differ)
c. I. is false ((there is an arbitrage opportunity) , but II. is true (their Sharpe ratios are identical)
d. Both statements are false

611.3. According to Bodie, Kane, Marcus, each of the following statements is true about arbitrage pricing theory (APT) EXCEPT which is false? (Source: Zvi Bodie, Alex Kane, and Alan J. Marcus, Investments, 10th Edition (New York: McGraw-Hill, 2013))

a. Price relationships that satisfy the no-arbitrage condition are important because we do expect them to hold in real-world markets
b. In a well-diversified portfolio, the proportion held of any individual security is small enough that a reasonable change in that security's rate of return will have a negligible effect on the portfolio's rate of return
c. The arbitrage pricing theory (APT) model is inferior to the capital asset pricing model (CAPM) because APT cannot predict a security market line linking expected return to risk due to the reality that idiosyncratic risk is not diversified away in the APT
d. The arbitrage pricing theory (APT) does not require the restrictive assumptions of the capital asset pricing model (CAPM) and its unobservable market portfolio, but the price of this generality is that the APT does not guarantee this relationship for all securities at all times.

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#### mkh

##### New Member
Can we pl get the answers only, the explanation let it reside for premium participants..thanks.

#### Nicole Seaman

##### Director of FRM Operations
Staff member
Subscriber
Can we pl get the answers only, the explanation let it reside for premium participants..thanks.
Hello @[email protected]

Thank you for visiting the Bionic Turtle forum! The answers to the daily practice questions are only available to paid members who have purchased one of our study packages, as they are part of our practice question sets. You can view all of our study packages HERE on our website.

Thank you,

Nicole

#### mkh

##### New Member
Hello @[email protected]

Thank you for visiting the Bionic Turtle forum! The answers to the daily practice questions are only available to paid members who have purchased one of our study packages, as they are part of our practice question sets. You can view all of our study packages HERE on our website.

Thank you,

Nicole

#### desh

##### New Member
Questions:

611.1. Peter the portfolio manages observes the following three well-diversified portfolios (A, B and C) that exist in a single-factor economy:

If Peter seeks to conduct an arbitrage with a long/short portfolio with $2.0 million of gross exposure, what is the expected profit (assuming no transaction costs and no margin)? a. No profit, as an arbitrage is not possible b.$10,000
c. $25,000 d.$30,000

Ans: b $10,000/- ( Portfolio B is least efficient, so have long position of$1.0 million on portfolio A and C with weighted avg of 50% each, total return by long on A & C is 11% though return from portfolio B is 10%, going short for $1.0 million on Portfolio B , will earn 1% on$1 mn i.e. USD 10000/-

611.2. Assume security returns are generated by the single-index model: R(i) = α(i) + β(i)*R(M) + e(i); where R(i) is the excess return for security(i) and R(M) is the market's excess return. The risk free-rate is 2.0% and the volatility of the market index is 20.0%. Suppose that there are three securities, (A), (B) and (C), characterized by the following data:

Consider the following two statements:

I. Given their identical Treynor measures, there is no arbitrage opportunity among the three securities
II. Given their identical non-systematic risk, σ[e(i]], all three securities have an identical expected (ex ante) Sharpe ratio

Which of the above statements is (are) TRUE?

a. Both statements are true
b. I. is true (there is no arbitrage opportunity); but II. is false (their Sharpe ratios differ)
c. I. is false ((there is an arbitrage opportunity) , but II. is true (their Sharpe ratios are identical)
d. Both statements are false

611.3. According to Bodie, Kane, Marcus, each of the following statements is true about arbitrage pricing theory (APT) EXCEPT which is false?

a. Price relationships that satisfy the no-arbitrage condition are important because we do expect them to hold in real-world markets
b. In a well-diversified portfolio, the proportion held of any individual security is small enough that a reasonable change in that security's rate of return will have a negligible effect on the portfolio's rate of return
c. The arbitrage pricing theory (APT) model is inferior to the capital asset pricing model (CAPM) because APT cannot predict a security market line linking expected return to risk due to the reality that idiosyncratic risk is not diversified away in the APT
d. The arbitrage pricing theory (APT) does not require the restrictive assumptions of the capital asset pricing model (CAPM) and its unobservable market portfolio, but the price of this generality is that the APT does not guarantee this relationship for all securities at all times.

: CAPM IS A SPECIAL CASE OF APT WHERE THERE IS ONLY ONE PRICED RISK FACTOR (MARKET RISK)

#### Nicole Seaman

##### Director of FRM Operations
Staff member
Subscriber
Hello @desh

You can view all of the answers, along with their explanations by clicking on the forum link above. The answers to the daily practice questions are only available to paid members who have purchased one of our study packages, as they are part of our practice question sets.

Thank you,

Nicole

#### Elnur1

##### New Member
611.1 Need to find beta=tangens x=(E(r)-Rf)/Betta and then look Which of dont exists the same line find it and if it above buy it and sell the combination of others if it lower buy combination sell it .