Portfolio Management (Part I)

Question 1

A measure of how the returns of two risky assets move in relation to each other is
the:
A. range.
B. c o v a r i a n c e .
C. s t a n d a r d deviation.

Answer 1

B

Question 2

asset classes with the greatest average returns also have the highest standard deviations of returns.

Answer 2

True

Question 3

Difference (and formulas) between Covariance and Correlation

Answer 3

Corr = ρ X,Y = Cov(X,Y) / σ X ⋅σ Y

Cov = Cov(X,Y) = [ (x i− xˉ)(y i− yˉ ) ] T-1

Stessa interpretazione, formula diversa. Unica differenza:
- Covariance esprime la correlazione in %, e non ha un range definito
- Correlation è un numero compreso tra -1 e +1, intervallo definito

Question 4

In a 5-year period, the annual returns on an investment are 5%, -3%, -4%, 2%, and
6%. The standard deviation of annual returns on this investment is closest to:
A. 4.0%
B. 4.5%
C. 20.7%

Answer 4

B

Question 5

Which of the following available portfolios most likely falls below the efficient frontier?

Portfolio ER St Dev
A. 7% 14% B. 9% 26% C. 12% 22%

Answer 5

B

Analizzala ad occhio:
a. per 1 unità di E(r) abbiamo 2 unità di rischio == 7:14 o se vuoi 1:2
b. per 1 unità di E(r) abbiamo 3 unità di rischio == 9:26 o se vuoi 1:3
c. per 1 unità di E(r) abbiamo 1.8 unità di rischio == 12:22 o se vuoi 1:1.8

Question 6

EXAMPLE: Calculating mean return, returns variance, returns covariance, and correlation. Given three years of percentage returns for Assets A and B in the following table, calculate the mean return and sample standard deviation for each asset, the sample covariance, and the correlation of returns.

Year Asset A Asset B
1 5% 7%
2 -2% -4%
3 12% 18%

Answer 6

• mean return for Asset A = (5% - 2% + 12%) / 3 = 5%
• mean return for Asset B = (7% - 4% + 18%) / 3 = 7%
• sample variance of returns for Asset A - (5-5)^2 + (-2-5)^2 + (12-5)^2 / 3-1 = 49
• sample standard deviation for Asset A = V49 = 7%
• sample variance of returns for Asset B - (7 - 7)2 + (-4 - 7)2 + (18 - 7)2 / 3 - 1 = 121
• sample standard deviation for Asset B = V121 = 11%
• sample covariance of returns for Assets A and B
  (5 - 5)(7 - 7) + (- 2- 5)(-4 - 7) + (12 - 5)(18 - 7) - 77
  3-1
• correlation of returns for Assets A and B = 7х 11 = 1

Question 7

expected return and standard deviation of a portfolio FORMULAS

Answer 7

E(Rp)=w1 E(R1 )+w2 E(R2)

σ p= w(1)^2 * σ (1) ^2+w (2) ^ 2 * σ(2) ^2 + 2*2w1w2ρ1,2σ1σ2
​

Question 8

Liquidity can be a major concern in emerging markets and for securities that trade infrequently, such as low-quality corporate bonds.
TRUE
FALSE

Answer 8

True

Question 9

Liquidity is most likely a concern for:
A. emerging market stocks.
B. high-quality corporate bonds.
C. U.S. Treasuries.

Answer 9

A

Question 10

portfolios that have the greatest expected
return for each level of risk (standard deviation) make up the e f fi c i e n t frontier.

Answer 10

True

Question 11

Sample Variance (variance) formula for an individual security

Answer 11

s^2 =( R - R_ ) ^2 /. T - 1

Question 12

small-capitalization stocks have greatest average returns and greatest risk in the past.
TRUE
FALSE

Answer 12

True

Question 13

The capital allocation line is a line from the risk-free return through the:
A. global maximum-return portfolio.
B. optimal risky portfolio.
C. global minimum-variance portfolio.

Answer 13

B

Question 14

the indifference curves of a more risk-averse investor will be more/less steep (ripida) than those of a less risk-averse investor,

Answer 14

More

Question 15

The variance of returns is 0.09 for Stock A and 0.04 for Stock B. The covariance between the returns of A and B is 0.006. The correlation of returns between A and
A. 0.10
B. 0.20.
C. 0.30.

Answer 15

A.

Question 16

What Covariance measures?

Answer 16

measures the extent to which two variables move together over time.

Question 17

What does an Indifference Curve tells us?

Answer 17

plots combinations of risk (standard deviation) and expected returns among which an investor is indifferent.

Question 18

What is the difference between Nominal and Real Value?

Answer 18

Real value keeps in mind inflation, nominad doesn’t.

Question 19

What is the difference between Variance and Standard deviation?

Answer 19

Variance (sigma^2) e Standard Deviation sono DIVERSI:

• Variance è il sigma al quadrato e misur la distanza tra i ritorni e la media
• Standard deviation è invece la radice quadrata della variance (e misura sempre
  la stessa distanza, ma nella stessa unità di misura - % per esempi0)

secondo me (Gandolfi) sono la stessa cosa, cambia solo l’unità di misura

Question 20

Which of the following asset classes has historically had the highest returns and STANDARD DEVIATION OF RETURN?
A. Small-cap stocks.
B. Large-cap stocks.
C. Long-term corporate bonds.

Answer 20

A.

Question 21

Which of the following statements about correlation is least accurate?
A. Diversification reduces risk when correlation is less than +1.
B. If the correlation coefficient is 0, a zero-variance portfolio can be constructed.
C. The lower the correlation coefficient, the greater the potential benefits from
diversification.

Answer 21

B.

Question 22

Which of the following statements about covariance and correlation is least accurate?
A. A zero covariance implies there is no linear relationship between the returns on 2 assets
B. If two assets have perfect negative correlation, the variance of returns for a portfolio that consists of these two assets will equal zero.
C. The covariance of a 2-stock portfolio is equal to the correlation coefficient times the standard deviation of one stock’s returns times the standard deviation of the other stock’s returns.

Answer 22

B.

c. is true because

Corr = ρ X,Y = Cov(X,Y) / σ X ⋅σ Y

Question 23

Which of the following statements about risk-averse investors is most accurate? A risk-averse investor:
A. seeks out the investment with minimum risk, while return is not a major consideration.
B. will take additional investment risk if sufficiently compensated for this risk.
C. avoids participating in global equity markets.

Answer 23

B.

Question 24

with P12 = 1, the portfolio standard deviation is simply a weighted average of the standard deviations of the individual asset returns.
TRUE
FALSE

Answer 24

True

Question 25

CAL – Capital Allocation Line

Answer 25

- Combina risk free asset e Optimal risky asset portfolio. - Ogni investitore può scegliere un punto sulla CAL in base alla sua tolleranza al rischio. -Quando la CAL è tangente alla frontiera efficiente, il portafoglio in quel punto si chiama portafoglio di mercato ottimale (M). Formula

Question 26

Efficient Frontier

Answer 26

È la combinazione di tutti i possibili portafogli aventi, per un detetrminato livello di Er, il minimo rischio (standard deviation) possibile. The efficient frontier coincides with the top portion of the minimum-variance frontier.

Question 27

CML – Capital Market Line

Answer 27

È un caso specifico della CAL: la retta che parte dal risk-free asset e tangente alla frontiera efficiente nel punto di mercato. * Valida solo per portafogli ben diversificati (rischio sistematico). * The capital market line (CML) plots return against total risk, which is measured by standard deviation of returns. * Mostra il miglior trade-off rischio-rendimento per gli investitori efficienti. E(R_p) =R_f + [[[ E(R{mkt}) - R_F} / {\sigma_{mkt} ]]] * sigma_{mkt} È lo Sharpe Ratio del mkt: SRmkt = {E(R_{mkt}) - R_F} / {\sigma_{mkt}} Quindi la possiamo riscrivere come: E(R_p) = R_f + SRmkt * sigma_{mkt}

Question 28

SML – Security Market Line - CAPM

Answer 28

Dove il CAPM È un modello teorico che descrive come il rendimento atteso di un'attività finanziaria è collegato al suo rischio sistematico (beta). La SML è la rappresentazione grafica del CAPM (Capital Asset Pricing Model). Mostra la relazione tra il rendimento atteso e il beta di un asset. - Valida sia per singoli asset che per portafogli. - Utilizza beta (rischio sistematico) invece della deviazione standard (o rischio totale). SML formula (che è uguale al CAPM): E(Ri) = Rf + Beta(i) *[(E(Rmkt) - Rf) Dove Beta si calcola: Beta(i) = {{COV_i,mkt} / {sigma_{mkt}^2} oppure: Beta(i) = {sigma_i} / {sigma_{mkt}

Question 29

Come si può chiamare la St. Dev?

Answer 29

Standard Deviation = sigma = Total risk (ovvero Tot risk = systmati (beta) + unsystematic risk)

Question 30

Systematic and unsystematic risk

Answer 30

When an investor diversifies across assets that are not perfectly correlated, the portfolio's risk is less than the weighted average of the risks of the individual securities in the portfolio. The risk that is eliminated by diversification is called The risk that remains cannot be diversified away and is called the systematic risk (also called nondiversifiable riskor market risk). total risk = systematic risk + unsystematic risk But it doesn’t means that you have to buy all the stocks in the market to diversify the portfolio.

Question 31

Unsystematic risk is compensated in equilibrium True False

Answer 31

False Unsystematic risk is not compensated in equilibrium because it can be eliminated for free through diversification. Systematic risk is measured by the contribution of a security to the risk of a well-diversified portfolio, and the expected equilibrium return (required return) on an individual security will depend only on its systematic risk.

Question 32

La pendenza della retta dipende dal Beta True False

Answer 32

False Quindi la pendenza della retta dipende dal E(Rm) e non dal Beta (chat). - Inclinazione = 45° = 1 unità di rendimento atteso per ogni unità di beta - Inclinazione > 45° = mercato premia molto il rischio sistematico - Inclinazione < 45° = mercato premia poco il rischio sistematico Questo NON implica che Il beta sia > 1 in quanto la pendenza è uguale a: Pendenza = E(Rm)−Rf

Question 33

To calculate whether a stock is over-under value, you compare:

Answer 33

Forecast Return: (End Year + Div) / Beginning Year Required Return: CAPM

Question 34

Se gli investitori possono sia prestare che prendere in prestito denaro al tasso privo di rischio (risk-free rate):

Answer 34

- Prestare → significa investire nel titolo privo di rischio, tipo Buoni del Tesoro. - Prendere a prestito → significa usare la leva finanziaria per investire ancora di più nei titoli rischiosi. Questo permette di costruire portafogli a destra del portafoglio di mercato (sulla CML) → cioè portafogli più rischiosi ma anche con rendimento atteso maggiore, usando la leva.

Question 35

Sharpe Ratio: what is it, formula and why is it important?

Answer 35

Sharpe Ratio, che ci permette di valutare la performance del portfolio in relazione al rischio utilizzato (unsystematic risk). The Sharpe ratio of a portfolio is its excess returns per unit of total portfolio risk. Higher Sharpe ratios indicate better risk-adjusted portfolio performance (banalmente il mio denominatore sta diminuendo). Sharpe Ratio: ER = Rportfolio - Rf / {\sigmaportfolio} In order to understand how my portfolio has performed compared to the market, is not enough saying “well, my active portfolio has generate an higher return compared to the benchmark”. However we should ask “well my portfolio has performed better than the market, but according to which risk? How much did I risk to get that result?” Ecco perche dobbiamo sempre analizzare le performance NON in termini assoluti, bensi relativei (al rischio a cui ci siamo esposti). Come dire  il benchmark ha fatto +100 e io ho fatto + 110, ma usando una leva x20. È diverso

Question 36

Sharpe Ratio is measured in terms of: A. Total Risk B. Unsystematic Risk C. Beta

Answer 36

A. Total Risk The Sharpe ratio is based on total risk (standard deviation of returns – infatti è espresso in termini di standard deviation = total risk) , rather than systematic risk (beta). For this reason, the Sharpe ratio can be used to evaluate the performance of concentrated portfolios (those affected by unsystematic risk) as well as well-diversified portfolios (those with only systematic, or beta, risk). Note that the value of the Sharpe ratio is only useful for comparison with the Sharpe ratio of another portfolio.

Question 37

Modigliani - Miller measures:

Answer 37

* Viene utilizzato per confrontare la performance di un portafoglio con quella del mercato, a parità di rischio TOTALE (σ). Ma com’è possibile che tra tutti i possibili portafogli esistenti, tu hai quello il cui rischio equivale a quello del mercato? Tra milioni di portafogli possibili…infatti non è plausibile! Ecco che affinché la definizione “confrontare la performance di un portafoglio con quella del mercato, a parità di rischio TOTALE (σ)” implica che dobbiamo artificialmente modificare il rischio del nostro portafoglio e renderlo uguale al punto di equilibrio (ovvero al rischio di mercato). Per fare ciò creeremo un altro portfolio clone, P*, in cui andremo ad aumentare o diminuire la quantità di rischio al fine di raggiungere il punto ottimale di equilibrio (ovvero eguagliare il rischio di mercato. Se il rischio del nostro portfolio è inferiore rispetto a quello di mercato, andremo ad aumentare il rischio (leverage) e ci sposteremo verso destra. Viceversa, se il rischio del nostro Portfolio è maggiore rispetto a quello di mercato, dovremo ridurre il rischio (deleverage) per raggiungere l’equilibrio, spostandoci quindi verso sinistra.

Question 38

Se σp < σm Se σp > σm

Answer 38

- Se σp < σm → si usa leva (si prende a prestito al tasso risk-free e si investe di più in P). - Se σp > σm → si deleverage (si combina P con il risk-free asset).

Question 39

Modigliani Miller formula:

Answer 39

M^2 = : [[[ R_f+ {{E(R)_{portfolio} - R_f} / {\sigma_{portfolio ]]] * sigma_{market} In pratica: si prende lo Sharpe Ratio e lo si moltiplica per il rischio del mercato, poi si aggiunge il tasso risk-free.

Question 40

Treynor measure and Jensen's alpha

Answer 40

Both of them are based on systematic risk (beta) rather than total risk. Treynor measure is a measure of slope and Jensen's alpha is a measure of percentage returns in excess of those from a portfolio that has the same risk (beta) but lies on the SML. Treynor = {Rp} - Rf / {betap} Jensen’s alpha misura quanto un portafoglio ha sovra- o sottoperformato rispetto al rendimento previsto dal modello CAPM, cioè rispetto a un portafoglio ipotetico con lo stesso rischio sistematico (β) ma che si trova esattamente sulla SML (Security Market Line). Quindi non è un confronto rispetto al mercato, bensì a quanto avrebbe dovuto performare il mio portafoglio secondo il CAPM. Infatti la formula è molto facile da ricordare: se è vero che ci dice quanto il tuo portafolgio ha sovra/sotto performato rispetto al CAPM, basta semplicemente togliere dalla performance del tuo portafoglio la performance del CAPM: alpha = R_p - [[ R_f + {beta_p} * R_{mkt - R_f]]]

Question 41

The line depicting the total risk and expected return of portfolio combinations of a risk-­ free asset and any risky asset is the: A security market line. B capital allocation line. C security characteristic line.

Answer 41

B.

Question 42

The portfolio of a risk-­ free asset and a risky asset has a better risk-­ return tradeoff than investing in only one asset type because the correlation between the risk-­ free asset and the risky asset is equal to: A −1.0. B 0.0. C 1.0.

Answer 42

B.

Question 43

With respect to capital market theory, an investor’s optimal portfolio is the combination of a risk-­ free asset and a risky asset with the highest: A expected return. B indifference curve. C capital allocation line slope.

Answer 43

B.

Question 44

Highly risk-­ averse investors will most likely invest the majority of their wealth in: A risky assets. B risk-­ free assets. C the optimal risky portfolio.

Answer 44

B.

Question 45

The capital market line (CML) is the graph of the risk and return of portfolio combinations consisting of the risk-­ free asset and: A any risky portfolio. B the market portfolio. C the leveraged portfolio.

Answer 45

B.

Question 46

Which of the following statements most accurately defines the market portfolio in capital market theory? The market portfolio consists of all: A risky assets. B tradable assets. C investable assets.

Answer 46

A. Anche perche in corrispondenza del market portfolio, abbiamo un Beta = 1 (quindi è un risky asset)

Question 47

With respect to capital market theory, the optimal risky portfolio: A is the market portfolio. B has the highest expected return. C has the lowest expected variance.

Answer 47

A.

Question 48

Relative to portfolios on the CML, any portfolio that plots above the CML is considered: A inferior. B inefficient. C unachievable.

Answer 48

C.

Question 49

A portfolio on the capital market line with returns greater than the returns on the market portfolio represents a(n): A lending portfolio. B borrowing portfolio. C unachievable portfolio.

Answer 49

B.

Question 50

With respect to the capital market line, a portfolio on the CML with returns less than the returns on the market portfolio represents a(n): A lending portfolio. B borrowing portfolio. C unachievable portfolio.

Answer 50

A.

Question 51

Which of the following types of risk is most likely avoided by forming a diversi- fied portfolio? A Total risk. B Systematic risk. C Nonsystematic risk.

Answer 51

C.

Question 52

Which of the following events is most likely an example of nonsystematic risk? A A decline in interest rates. B The resignation of chief executive officer. C An increase in the value of the US dollar.

Answer 52

B.

Question 53

With respect to the pricing of risk in capital market theory, which of the follow- ing statements is most accurate? A All risk is priced. B Systematic risk is priced. C Nonsystematic risk is priced.

Answer 53

B.

Question 54

The sum of an asset’s systematic variance and its nonsystematic variance of returns is equal to the asset’s: A beta. B total risk. C total variance.

Answer 54

C.

Question 55

With respect to return-­ generating models, the intercept term of the market model is the asset’s estimated: A beta. B alpha. C variance.

Answer 55

B.

Question 56

With respect to return-­ generating models, the slope term of the market model is an estimate of the asset’s: A total risk. B systematic risk. C nonsystematic risk.

Answer 56

B.

Question 57

With respect to return-­ generating models, which of the following statements is most accurate? Return-­ generating models are used to directly estimate the: A expected return of a security. B weights of securities in a portfolio. C parameters of the capital market line.

Answer 57

A.

Question 58

Security Annual. Return - St. Dev. - Correlation i,m Security 1 11 25 0.6 Security 2 11 20 0.7 Security 3 14 20 0.8 Market 10 15 1.0 Which security has the highest total risk? A Security 1. B Security 2. C Security 3.

Answer 58

A.

Question 59

Security Annual. Return - St. Dev. - Correlation i,m Security 1 11 25 0.6 Security 2 11 20 0.7 Security 3 14 20 0.8 Market 10 15 1.0 Which security has the highest beta measure? A Security 1. B Security 2. C Security 3.

Answer 59

C.

Question 60

Security Annual. Return - St. Dev. - Correlation i,m Security 1 11 25 0.6 Security 2 11 20 0.7 Security 3 14 20 0.8 Market 10 15 1.0 Which security has the least amount of market risk? A Security 1. B Security 2. C Security 3.

Answer 60

B. Era banalmente il Bet == Market risk, ricordati il Portfolio Efficiente che combina il rischio mercato (ovvero Beta = 1) e Er

Question 61

With respect to capital market theory, the average beta of all assets in the market is: A. less than 1.0. B. equal to 1.0. C. greater than 1.0.

Answer 61

B.

Question 62

The slope of the security characteristic line is an asset’s: A beta. B excess return. C risk premium.

Answer 62

A.

Question 63

The graph of the capital asset pricing model is the: A. capital market line. B. security market line. C. Security characteristic line.

Answer 63

B.

Question 64

With respect to capital market theory, correctly priced individual assets can be plotted on the: A. capital market line. B. security market line. C. capital allocation line.

Answer 64

B.

Question 65

With respect to the capital asset pricing model, the primary determinant of expected return of an individual asset is the: A. asset’s beta. B. market risk premium. C. asset’s standard deviation.

Answer 65

A.

Question 66

With respect to the capital asset pricing model, which of the following values of beta for an asset is most likely to have an expected return for the asset that is less than the risk-­ free rate? A −0.5 B 0.0 C 0.5

Answer 66

A. Il ragionamento fatto da me, che mi porta a dire (erroneamente che Beta = 0.0) fosse giusta, è sbagliato perche io assumevo il caso in cui Rm fosse negativo - e quindi inferiore al Rf - (scenario possibile). Qui la soluzione è piu semplice, perche si assume che questa possibilità di Rm negativo non esiste, ma che invece sia sempre positio, altrimento si uscirebbe dal modello e dalle aspettative del CAPM

Question 67

With respect to the capital asset pricing model, the market risk premium is: A less than the excess market return. B equal to the excess market return. C greater than the excess market return.

Answer 67

B.

Question 68

Security Standard Deviation (%) Beta Security 1 25 1.50 Security 2 15 1.40 Security 3 20 1.60 A 9.0%. B 12.0%. C 13.5%.

Answer 68

B. Risk premium = Rm-Rf Er = 3% + 1.5 * 6%

Question 69

Security Standard Deviation (%) Beta Security 1 25 1.50 Security 2 15 1.40 Security 3 20 1.60 With respect to the capital asset pricing model, if expected return for Security 2 is equal to 11.4% and the risk-­ free rate is 3%, the expected return for the market is closest to: A 8.4%. B 9.0%. C 10.3%.

Answer 69

B. 11.4% = 3% + 1.4 * (X - 3%) 0.114 = 0.03 + 1.4x - 0.042 0.126 = 1.4x x = 0.09

Question 70

Security Standard Deviation (%) Beta Security 1 25 1.50 Security 2 15 1.40 Security 3 20 1.60 With respect to the capital asset pricing model, if the expected market risk pre-mium is 6% the security with the highest expected return is: A Security 1. B Security 2. C Security 3.

Answer 70

C.

Question 71

Security Standard Deviation (%) Beta Security 1 25 1.50 Security 2 15 1.40 Security 3 20 1.60 With respect to the capital asset pricing model, a decline in the expected mar- ket return will have the greatest impact on the expected return of: A Security 1. B Security 2. C Security 3.

Answer 71

C.

Question 72

MANAGER Mean Annual Return (%) St. Dev Manager 1 14.38 10.53 Manager 2 9.25 6.35 Manager 3 13.10 8.23 Given a risk-­ free rate of return of 2.60%, which manager performed best based on the Sharpe ratio? A Manager 1 B Manager 2 C Manager 3

Answer 72

C.

Question 73

Which of the following performance measures is consistent with the CAPM? A M-squared. B Sharpe ratio. C Jensen’s alpha.

Answer 73

C.

Question 74

Which of the following performance measures does not require the measure to be compared to another value? A Sharpe ratio. B Treynor ratio. C Jensen’s alpha.

Answer 74

C. Perche Alpha di Jensen è data proprio da: α = Rp - CAPM Measures the abnormal return of a portfolio compared to what the CAPM α>0, the portfolio outperformed its CAPM-predicted return → positive alpha.

Question 75

Which of the following performance measures is most appropriate for an investor who is not fully diversified? A M-squared. B Treynor ratio. C Jensen’s alpha.

Answer 75

A. M-M because it is based on the Sharpe Ratio, which uses total risk (standard deviation) — not just systematic risk (beta). Viceversa, Treynor e Jensen sono entrambi basati sul Beta

Question 76

Analysts who have estimated returns of an asset to be greater than the expected returns generated by the capital asset pricing model should consider the asset to be: An overvalued. B undervalued. C properly valued.

Answer 76

B.

Question 77

With respect to capital market theory, which of the following statements best describes the effect of the homogeneity assumption? Because all investors have the same economic expectations of future cash flows for all assets, investors will invest in: A the same optimal risky portfolio. B the Standard and Poor’s 500 Index. C assets with the same amount of risk.

Answer 77

A.

Question 78

With respect to capital market theory, which of the following assumptions allows for the existence of the market portfolio? All investors: A are price takers. B have homogeneous expectations. C plan for the same, single holding period.

Answer 78

B.

Question 79

The intercept of the best fit line formed by plotting the excess returns of a manager’s portfolio on the excess returns of the market is best described as Jensen’s: A beta. B ratio. C alpha.

Answer 79

C.

Question 80

Portfolio managers who are maximizing risk-­ adjusted returns will seek to invest more in securities with: A lower values of Jensen’s alpha. B values of Jensen’s alpha equal to 0. C higher values of Jensen’s alpha

Answer 80

C.

Question 81

Portfolio managers, who are maximizing risk-­ adjusted returns, will seek to invest less in securities with: A lower values for nonsystematic variance. B values of nonsystematic variance equal to 0. C higher values for nonsystematic variance.

Answer 81

C.

Question 82

Synonym of Beta

Answer 82

Market Risk