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

[Nicole Seaman]

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.

Answers here:

• In forum

 

[mkh]

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

 

[Nicole Seaman]

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]

Thanks for replying back.

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]

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)


Please advise if answers are not correct !

 

[Nicole Seaman]

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]

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 .

 

[AZamo1526]

Hello! Still do not understand why for the 2 question the answer is 10000, instead of 20000?
If we gain 1% extra profit for 2 mln. exposure, than I expected 20000 profit.
Where I am wrong?

 

[David Harper CFA FRM]

Hi @AZamo1526 Because only one leg of the long/short trade is mispriced which is the short on mis-priced B. Specifically, the arb trade is short B with $1.0 and use these $1.0 funds to buy $500K of each of A an C (keep in mind: this 50/50 is the only way to match the 0.9 beta such as to neutralize the beta). So the return on B is -10%*$1.0 million = -$100,000 and the return on A + C = 8%*$500K + 14%*$500K = $110,000; for net profit of -$100,000 +$110,000 and the 50/50 mix enabled us to achieve zero beta. Put another way, to get $20K profit, the long position (which is half of the $2.0 million) would need to mispriced; e.g. if ER(A) = +9% and ER(C) = +15%, then profit is +$20,000 because the entire $2.0 allocates to mispriced. Hope that's helpful!