1

In order to maximize diversification benefits, an investor should add a security with a correlation to the existing portfolio closest to:

     0.0.

B.   -1.0.

C.    1.0.

B

Choice B is correct. The maximum diversification benefits can be achieved by adding a security with a correlation of -1.0 (perfectly negatively correlated).

Choice A is not the best answer in that although diversification benefits occur any time an investor adds a security with correlation to the portfolio less than 1, adding uncorrelated (zero correlation) assets does not achieve the maximum diversification benefits.

Choice C is incorrect in that adding perfectly positively correlated assets have no diversification effect.  Nevertheless, instead of adding (longing) assets, shorting positively correlated assets provides diversification benefits.

2

An analyst gathers the following data about the returns for two stocks.

The covariance between returns on stocks A and B is 0.12%.  The correlation between the returns of Stock A and Stock B is closest to:

            0.16.

B.            0.22.

C.            0.33.

b

Choice B is correct.  The correlation is calculated according to the following equations:

.

Note: there are two formulas similar to the above:

Beta coefficient: 

, M  denoted as the market portfolio.

Coefficient of determination:   

3

When constructing unleveraged portfolios consisting of only risky assets, investors should only consider the set of portfolios that:

   reside on the efficient frontier.

B.   are minimum variance portfolios.

C.   reside on the capital market line.

a

Choice A is correct. The efficient frontier represents the set of portfolios of risky assets having the maximum return at any level of risk. This set of portfolios dominate any other portfolios or risky assets and individual risky assets.

Choice B is incorrect.  The minimum variance portfolios represent portfolio of risky assets having the minimum risk at any level of return.  Since the minimum variance set is concave in the framework of return and standard deviation, there are two minimum variance portfolios given at any level of risk (standard deviation). 

Choice C is incorrect in that portfolios reside on the capital market line must have position (either long or short) on the risk-free asset. 

4

A stock has a beta of 0.92 and an estimated return of 11%. The risk-free rate is 3%, and the expected return on the market is 12%. According to the CAPM, this stock:

   is overvalued.

B.   is undervalued.

C.   is properly valued.

a

According to the CAPM the required return of the stock is E(R) = 3% + 0.92(12% - 3%) = 11.28%. Because the expected return of 11% is less than the required return of 11.28%, the security is overvalued.  The stock value is the discounted value of future dividends.  When the discount rate is lower than it should be (11% < 11.28%), the current price is overvalued.

Note that the required return by the investor is the cost of capital to the firm.  Investors require premium to compensate risk of investment.  Thus, the required return is equal to the risk-free return plus risk premium.  According to the CAPM, the risk premium is Beta×Market Risk Premium.

5

The relevant measure of risk for the capital market line (CML) and security market line (SML) rely on which of the following for their measure of risk:

   Standard deviation for CML and covariance for SML.

B.   Covariance for CML and SML.

C.   Covariance for CML and standard deviation for SML.

a

Choice A is correct. The beta in the SML equation is derived from the covariance between portfolio’s returns and market returns divided by the variance of the market portfolio.  The capital market line (CML) shows the relationship between the required returns on efficient portfolios (rather than individual securities) and their total risk measured as standard deviation.

Choice B is incorrect in that CML is in the framework between expected return and standard deviation. 

Choice C is incorrect.  It should be stated that "Standard deviation for CML and covariance for SML."

6

Which of the following least accurate regarding the capital market line (CML)?

   The Sharpe ratio of any portfolios lies on the CML has the same Sharpe ratio of the market portfolio.

B.   All portfolios lie on the CML are as efficient as those lie on the efficient frontier.

C.   The CML contains the set of all efficient portfolios, but all portfolios and all stocks lie on the security market line in an efficient market that is in equilibrium.

b

Choice "B" is incorrect. Portfolios lie on the CML are a combination of the market portfolio and the risk-free asset with different allocation.  Since the CML is above the efficient frontier in mean-standard deviation framework, the CML portfolios dominate those on the efficient frontier. 

Choice A is correct in that the slope of CML is the Sharpe ratio of the market portfolio.  All points in a line have the same slope.  Thus, all portfolios lies on the CML have the same Sharpe ratios.

Choice C is correct because only efficient portfolios lie on the capital market line. However, all portfolios and all stocks lie on the security market line in an efficient market that is in equilibrium. This is because the capital market line is the relationship between expected return and total portfolio risk, while the security market line is the relationship between expected return and the systematic component of risk (which is what the market compensates the investor for taking).

7

The goal of diversification under the traditional portfolio  theory is to minimize:

   Systematic risk.

B.   Unsystematic risk.

C.   Beta.

b

Choice B is correct. Unsystematic risk is unique to a particular security and can be diversified in a portfolio through adding additional uncorrelated assets.

Choice A is incorrect in that systematic risk is the only risk remaining in a fully diversified portfolio (such as the market portfolio).

Choice C is incorrect in that minimizing beta at the extreme

would only result in an investor receiving the risk-free rate and would only apply to an investor wishing the risk-free rate (which could be achieved more efficiently by investing in the risk-free asset).

8

There are two statements about portfolio management  process:

Statement 1:  The investment policy statement is an initial step of the portfolio management process.  The investment process should be changed according to the change of market trends. 

Statement 2: The primary purpose of the monitoring process in portfolio management is to measure the performance of a client's portfolio relative to the performance of the stock market benchmark over a comparable period of time.

   Only statement 1 is accurate.

B.   Only statement 2 is accurate.

C.   Both statements are inaccurate.

c

Statement 1  is incorrect in that the investment policy statement is an integral part of the portfolio management process.  The investment policy statement guides the entire investment process. 

Statement 2 is not consistent with the portfolio management process. The primary purpose of the monitoring process is to determine whether or not the portfolio manager is staying within the constraints imposed by the investment policy and whether or not the expected return on the portfolio is likely to be maximized within those constraints based on new capital market expectations and current needs and circumstances of the investor. This is much more complex than simply attempting to beat the stock market's overall performance.

9

An analyst gathered the following information about a portfolio comprised of two assets, X and Y: 

         Asset                Expected               Expected

      Weight (%)         Return           Standard Deviation

X        75%                  1%                           5%

Y        25%                  7%                           4%   

If the correlation of returns for the two assets equals 0.75, and the risk-free interest rate 1 percent, then the Sharpe ratio of this portfolio is closest to: 

   0.95

B.   0.67

C.   0.33

c

Choice is correct in that portfolio expected return is

=(0.75 × 1%) + (0.25 × 7%) = 2.5%, and

portfolio expected standard deviation of two assets is calculated by:

=

=  [(0.752 × 0.052) + (0.252 × 0.042) + (2 × 0.75 × 0.25 × 0.75 × 0.05 × 0.04)]^0.5 = 4.55%;

The Sharpe ratio = (2.5% - 1%)/4.55% = 0.33.

Note that Sharpe ratio can be interpreted as "risk-adjusted excess return" or "portfolio’s risk-premium per unit of risk (standardized risk-premium).

10

Which of the following constraints would most likely appear in the unique needs and preferences section of a trust’s investment policy statement (IPS) ? The portfolio is: 

   subject to the prudent-man standard.

B.   prohibited from investing in tobacco companies.

C.   prohibited from holding less than 5% in cash instruments.

b

Choice is correct in that in developing IPS, unique needs and preferences include the prohibition of certain investments. The investment constraints of liquidity, tax concerns, and legal and regulatory factors adequately address the portfolio’s other constraints. 

Choice A is incorrect, because prudent-man standard is a judiciary responsibility of portfolio managers not the unique needs of investors. This fiduciary is required to invest trust assets as a "prudent man" would invest his own property with the following factors in mind: (1) the needs of beneficiaries; (2)

the need to preserve the estate (or corpus of the trust); and (3)

the amount and regularity of income.

Choice C is incorrect in that the prohibition from holding less than 5% in cash instruments is related to investor risk aversion not the uniqueness of asset allocation requirement.

11

A stock has a beta of 1.2 and an estimated return of 11%. The risk-free rate is 3%, and the expected return on the market is 12%. According to the CAPM, this stock:

   is overvalued.

B.   is undervalued.

C.   is properly valued.

a

Acording to CAPM, = 3% + 1.2(12% - 3%) = 13.8%. Because the expected return of 11% is less than the required return of 13.8%, the security is overvalued.  Note that the stock value is a discounted value of future cash flows.  The discounted rate is the required return by the investor.  It is also the cost of capital to the firm.  Lower the discounted rate (required return or cost of capital), higher the stock value.

12

The type of return objective least likely to be used in an investment policy statement is a(n):

   total return objective.

B.   benchmark return objective.

C.   absolute return objective.

b

Choice B is incorrect because although a return object can be related to a benchmark return such as 1.5% above S&P 500 index, it is not termed a benchmark return objective.

Choice A is correct.  The total return including reinvested  or recapitalized return could be a return objective in the IPS. .

Choice C is correct. Return objectives in an investment policy statement can take the form of an absolute objective, such as 8%. 

13

In a case where a client's capacity to bear risk is significantly less than the client's expressed willingness to bear risk, the most appropriate action for a financial advisor is to:

   counsel the client and attempt to change his attitude towards risk.

B.   base the assessment of risk tolerance in the IPS on client's ability to bear risk.

C.   attempt to educate the client about investment risk and correct any misconceptions.

b

In a situation where the clients expressed willingness to bear investment risk is significantly greater than the client’s ability to bear investment risk, the advisor's assessment of the client's risk tolerance in the IPS should relate the clients ability to bear investment risk.

Choice A is incorrect.  Financial advisor should not attempt to change the client’s attitude toward risk.

Choice C is incorrect.  It depends, if clients risk behavior involves "emotional bias" such as loss aversion or overconfidence, financial advisor should adopt the bias instead of providing education about investment.

14

Which of the following pairs least likely refer to the same type of risk?

   Total risk and the variance of returns.

B.   Residual variance and firm-specific risk.

   Undiversifiable risk and unsystematic risk.

c

Unsystematic risk is diversifiable risk.  Investors are able to eliminate unsystematic risk by forming diversified portfolios. 

Choice A is correct; variance is a measure of total risk.

Choice B is correct in that the residual variance under the market model is a measure of idiosyncratic (or firm-specific) risk.

15

Which of the following statements about risk is least  accurate:

    The capital market line plots expected return against market risk.

B.    The efficient frontier plots expected return against total risk.

C.    The security market line plots expected return against systematic risk.

a

The capital market line plots expected return against standard deviation of returns.  The standard deviation of return is a measure of total risk not the market risk.

Choice B is accurate.  The efficient frontier represents efficient portfolios of risky assets. The efficient frontier plots expected return against total risk.

Choice C is accurate.  The security market line (CAPM) represents the equilibrium of risk-adjusted required return for individual assets.  It plots expected return against systematic risk, which is measured by the beta coefficient (β).

16

Which of the following possible portfolios cannot lie on the efficient frontier?

                   Expected     Standard

Portfolio     Return        Deviation

1                 5%              16%

2                 5%              18%

3                 7%              16%

4                 9%              20%

   Portfolio 2 only.

B.   Portfolios 1 and 2.

C.   Portfolios 2 and 4.

b

Neither portfolio 1 nor portfolio 2 lies on the efficient frontiers.  Efficient frontier contains a set of efficient portfolios.  Portfolios are efficient in that no portfolio in the set dominates each other.  Portfolio 2 is dominated by portfolio 1 in that the standard deviation of portfolio 1 is lower than that of portfolio 2.  However, portfolio 1 is dominated by the portfolio 3.  It is because although both portfolios 1 and 3 have the same standard deviations, portfolio 3 has a higher expected return. 

Choice A is incorrect because it ignores that portfolio 1 is also a dominated portfolio.

Choice C is incorrect that portfolio 4 is an efficient portfolio in this set.  There is no portfolio dominates portfolio 4.  So, portfolio could lie on the efficient frontier.

17

Unimark Inc. stock pays $1 dividend annually and currently trades at $25. Based on the CAPM and assuming an expected return on the market of 13% and a risk-free rate of 5%, the expected price for Unimark one year from now is $28. The beta of Unimark shares is closest to:

      0.88

B.      1.38

C.      1.68

b

Unimark's expected return for the coming year is [(28+1) / 25] - 1 = 16%.  According to CAPM,

 or.

 Its risk premium relative to the risk-free rate is 16% - 5.0% = 11%. The market risk premium is 13% - 5% = 8%. Therefore, the beta of Unimark must be 11% / 8% = 1.38.  Note that the divided must be included in calculation.

18

A portfolio manager is constructing a new equity portfolio consisting of a large number of randomly chosen domestic stocks. As the number of stocks in the portfolio increases, what happens to the expected levels of systematic and unsystematic risk?

            Systematic risk       Unsystematic risk

   Increases                    Remains the same

B.   Decreases                   Increases

C.   Remains the same      Decreases

c

As randomly selected securities are added to a portfolio, the diversifiable (unsystematic) risk decreases, and the expected level of non-diversifiable (systematic) risk remains the same.

Note that the above is adding randomly long positions (buying securities).  If there is long-short position, meaning buying and shorting securities at the same time, the systematic risk may decrease.  It is because the long and short positions have a negative correlation.  The negative correlation among assets' positions will reduce even eliminate systematic risk.

19

Using historical index returns for an equities market over a 10-year period, an analyst has calculated the average annual return as 8.46% and the holding period return as 130%. The compound annual index return over the period is closest to:

A. 8.32%.

B. 8.58%.

C. 8.69%.

c

Note that the total holding period return is a compounded value of annual return over the entire period of years such that

; 2.3 = (1+AR)¹⁰ ;

Solve for AR, and AR = 8.69%

20

Jeff Bishop, CFA, is meeting with one of his portfolio management clients, Paul Wu to discuss Paul's investment constraints. Jeffl has established that:

·  Wu plans to retire from his job as a bond salesman in 15 years, after which this portfolio will be his primary source of income.

·  Wu may not have sufficient cash available that he will need this portfolio to generate cash outflows until he retires.

·  Wu, as a registered securities representative, is required to have Jeff send a copy of his account statements to the compliance officer at Paul’s employer.

·  Jeff owns low cost stocks from his company when he joined the firm 15 years ago.

To complete his assessment of Pope's investment constraints, Samuel still needs to inquire about Pope's:

A. tax concerns.

B. liquidity needs.

C. unique needs and preferences.

c

There are five categories of investment constraints: Time, Tax, Liquidity, Legal, and Unique (TTLLU).

The four matters listed are related to

(1)   Wu's time horizon (years to retirement).

(2)   liquidity needs (available cash).

(3)   legal and regulatory factors (required copies of account statements to Pope's compliance officer).

(4)   tax situation (Jeff owns low cost stocks and will have to pay high capital gain tax when he sells the stocks.).  

However, none of these constrains address Wu's unique needs and preferences.

21

When a risk-free asset is combined with a portfolio of risky assets, which of the following is most correct?

   The standard deviation of the return for the newly created portfolio is the standard deviation of the returns of the risky asset portfolio multiplied by its portfolio weight.

B.    The expected return for the newly created portfolio and correlation coefficient between the two assets are positive.

C.    The variance of the resulting portfolio is a weighted average of the returns variances of the risk-free asset and of the portfolio of risky assets.

a

The correlation between a risky asset and a risk-free asset is zero.  Thus, the answer B is incorrect.  Since the correlation between these assets is zero, the covariance is also zero.  Note that the variance (or standard deviation of the risk-free asset is equal to zero).  Then, the standard deviation of the portfolio is .

Answer C is incorrect in that the portfolio variance is weight-square times the variance of the risky asset. 

22

If stock A’s beat is 1.2 and stock B’s beta is 0.9.  Both stocks have the same standard deviation of returns of 30%.  The standard deviation of the returns on the market portfolio is 14%, the correlation between stock A and stock B is closest to:

A. 88%

B. 94%.

C. 97%

b

From the single index (market) model, the correlation between returns on stock A and stock B is calculated by

 = (1.2)(0.9)(.28)²  =0.08467.  

Since statistically, , 

the correlation coefficient is 0.08467÷(0.3×0.3) = 0.94.

23

Betty Cole is an aggressive investor.  She has $100,000 capital but is borrowing additional $50,000 to invest in S&P500 index fund.  Although the current risk-free rate is only 1%, her borrowing rate is 2%.  The current expected return and standard deviation of S&P 500 index are 10% and 20%, respectively.  What is the expected Sharpe ratio of Cole’s portfolio?

A. 0.45

B. 0.31

C. 0.12

c

This is a question that borrowing and lending rates are different (which is quite realistic).  Cole’s portfolio is a leveraged portfolio with a leverage ratio (λ) of 1.5.  Consider that Shape Ratio of a leveraged portfolio can be calculated from the following equation:

= (9%÷20%) - (0.5/1.5) ×(2% ─1%) = 0.12

24

Millennium Investments (MI), an investment advisory firm, relies on mean-variance analysis to advise its clients. One of MI's clients requests an analysis of four risky mutual funds (Fund W, Fund X, Fund Y, and Fund Z). MI calculates the average variance of returns across all assets within each mutual fund, the average covariance of returns across all pairs of assets within each mutual fund, and each mutual fund's total variance of returns. The results of MI's calculations are reported as follows:

Of the four mutual funds listed in the Exhibit, which is most likely to include the largest number of assets?

     Fund W.

B.      Fund X.

C.      Fund Z.

A

Fund W and Fund X have the same average asset variance and covariance.  However, Fund X has higher total variance that indicates Fund X is less diversified than Fund W.  Fund W has more securities in the portfolio.  As comparing Fund W to Fund Z, the average covariance of assets in Fund Z has much lower than in Fund W.  Nevertheless, Fund Z has the same total variance as Fund W.  This also indicates that Fund W is more diversified than Fund Z.  Thus, Fund W is most likely to include the largest number of assets.

25

A portfolio manager made the following statements:

Statement 1: "All portfolios lying on the minimum variance frontier are desirable portfolios."

Statement 2: "Because I am highly risk-averse, I expect that my investment portfolio on the capital allocation line will have risk and return equal to that of the global minimum variance portfolio."

Are Statements 1 and 2 made by the manager correct?

     Statement 1 is incorrect.

B.      Statement 2 is incorrect.

C.      Both statements are incorrect.

C

Statement 1 is incorrect in that not all minimum variance portfolios are efficient.  Only those lying on the Efficient Frontier ( the upper part of the minimum variance frontier) are efficient (or mean-variance desirable) portfolios.

Statement 2 is also incorrect because the capital allocation lines could be different from (below) the capital market line.  That is, low sharp ratio and inefficient choice.  In addition, if you are highly risk averse, according to the theory of two-fund separation, you should invest most of your capital in risk-free assets (e.g. Treasury securities).