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CFA L1 > Portfolio Management (Part One) > Flashcards

Portfolio Management (Part One) Flashcards

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1
Q

Real Return

A

= Nominal Return Less Inflation

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2
Q

Why is evaluating investments using expected return and variance of returns a simplif ication?

A

Because returns do not follow a normal distribution; distributions are negatively skewed, with greater kurtosis (fatter tails) than a normal distribution. The negative skew ref lects a tendency towards large downside deviations, while the positive excess kurtosis re flects frequent extreme deviations on both the upside and
downside. These non-normal characteristics of skewness (≠ 0) and kurtosis (≠ 3) should be taken into account when analyzing investments.

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3
Q

How does liquidity impact evaluation of investments?

A

Liquidity can affect the price and, therefore, the expected return of a security. Liquidity can be a major concern in emerging markets and for securities that trade infrequently, such as low-quality corporate bonds.

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4
Q

Who is a risk-averse investor?

A

A risk-averse investor is simply one that dislikes risk (i.e., prefers less risk to more risk). Given two investments that have equal expected returns, a risk-averse investor will choose the one with less risk (standard deviation, σ). Financial models assume all investors are risk averse.

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5
Q

Who is a risk-seeking investor?

A

A risk-seeking (risk-loving) investor would actually prefer more risk to less and, given equal expected returns, would prefer the more risky investment.

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6
Q

Who is a risk-neutral investor?

A

A risk- neutral investor would have no preference regarding risk and would therefore be indifferent between any two investments with equal expected returns.

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7
Q

What are an investor’s utility functions?

A

Investors’ utility functions represent their preferences regarding the tradeoff between risk and return (i.e., their degrees of risk aversion)

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8
Q

What is an indifference curve?

A

An indifference curve is a tool from economics that, in this application, plots combinations of risk (standard deviation) and expected returns among which an investor is indifferent.
In constructing indifference curves for portfolios based on only their expected return and standard deviation of returns, we are assuming that these are the only portfolio characteristics that investors care about.

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9
Q

Expected Risk for a 2 Asset Portfolio where one asset is risk free

A

Wa*SDa
where, a is the risk bearing asset

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10
Q

An Indifference curve for a risk averse investor will be (flatter/steeper)

A

Steeper - as they will require a greater increase in expected return per unit increase in risk reflecting a higher risk aversion coefficient

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11
Q

The capital allocation line is a line from the risk-free return through the:

A

optimal risky portfolio

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12
Q

Expected Return for a 2 Asset Portfolio

A

E(Rp) = WaE(Ra) + WbE(Rb)

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13
Q

Sample Variance

A

S^2 = [Sum of (Rt - R_)]^2 / T-1

Rt = Return for period t
R_ = Mean of Sample
T = Total periods

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14
Q

Expected Risk for a 2 Asset Portfolio

A

SDp = Root of Wa^2SDa^2 + Wb^2SDb^2 + 2WaWbCorrel(A,B)SDa*SDb

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15
Q

Capital Allocation Line

A

The line representing thes possible combinations of risk-free assets and the optimal risky asset portfolio is referred to as the capital allocation line.

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16
Q

Two-fund separation theorem

A

Combining a risky portfolio with a risk-free asset is the process that supports the two-fund separation theorem, which states that all investors’ optimal portfolios will be made up of some combination of the optimal portfolio of risky assets and the risk-free asset.

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17
Q

Combination of Capital Allocation Line + Indifference Curve

A

Gives the Optimal Portfolio that maximises investors expected utility

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18
Q

Population Variance

A

SD^2 = [Sum of (Rt - Mu)]^2 / T

Rt = Return for period t
Mu = Mean of Population
T = Total periods

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19
Q

Covariance for Returns of Two Assets (Features)

A
  • extent to which two variables move together over time
  • does not indicate strength, only direction
  • Cov = 0 - no LINEAR relation (may have non-linear relation)
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20
Q

Covariance for Returns of Two Assets (Formula)

A

Cov1,2 = Sum of [(Rt,1 - R_1)(Rt,2 - R_2)] / n-1

Rt,1 = return on Asset 1 in period t
Rt,2 = return on Asset 2 in period t
R_1 = mean return on asset 1
R_2 = mean return on asset 2
n = number of periods

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21
Q

Correlation

A
  • magnitude of covariance
  • standardised measure

P1,2 = Cov1,2 / SD1*SD2

P1,2 = Correlation Coefficient
-1 <= P1,2 <= 1
-1 = perfectly negatively correlated
1 = perfectly positively correlated
0 = no LINEAR relationship

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22
Q

Portfolio Variance

A

Varp = Wa^2SDa^2 + Wb^2SDb^2 + 2WaWb*Cov(a,b)

= Wa^2SDa^2 + Wb^2SDb^2 + 2WaWbCorrel(a,b)SDa*SDb

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23
Q

Zero-Variance Portfolio

A

A zero-variance portfolio can only be constructed if the correlation coeff icient between assets is -1

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24
Q

Can you get diversification benefits if correlation is less than 1?

A

Yes

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25
Q

Lower the correlation, (lower/greater) the expected benefit of diversification

A

greater - one stock hedges the other

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26
Q

If Correl (1,2) = 1, then Standard Deviation of Portfolio is…

A

weighted average of Std devs

SDp = Root of Varp = Root of W1^2SD1^2 + W2^2SD2^2 + 2W1W2SD1SD21 = Root of (W1SD1 + W2*SD2)^2

= W1SD1 + W2SD2

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27
Q

Portfolio Risk decreases as correlation….

A

decreases, thus, diversification benefit

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28
Q

minimum variance frontier

A

For each level of expected portfolio return, we can vary the portfolio weights on the individual assets to determine the portfolio that has the least risk. These portfolios that have the lowest standard deviation of all portfolios with a given expected return are known as minimum-variance portfolios. Together they make up the minimum-variance frontier.

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29
Q

Efficient Frontier

A

Those portfolios that have the greatest expected return for each level of risk (standard deviation) make up the ef ficient frontier. The ef ficient frontier coincides with the top portion of the minimum-variance frontier. A risk-averse investor would only choose portfolios that are on the eff icient frontier because all available portfolios that are not on the eff icient frontier have lower expected returns than an eff icient portfolio with the same risk.

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30
Q

Global minimum variance portfolio

A

The portfolio on the ef icient frontier that has the least risk is the global minimum-variance portfolio.

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31
Q

Homogenous expectations

A
  • simplifying assumption underlying modern portfolio theory and capital asset pricing model
  • investors have homogeneous expectations (i.e., they all have the same estimates of risk, return, and correlations with other risky assets for all risky assets). Under this assumption, all investors face the same eff icient frontier of risky portfolios and will all have the same optimal risky portfolio and CAL.
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32
Q

Optimal CAL

A
  • tangent to Efficient Frontier
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33
Q

Market Portfolio

A

Depending on their preferences for risk and return (their indifference curves), investors may choose different portfolio weights for the risk-free asset and the risky (tangency) portfolio. Every investor, however, will use the same risky portfolio. When this is the case, that portfolio must be the market portfolio of all risky assets because all investors that hold any risky assets hold the same portfolio of risky assets.

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34
Q

Capital Market Line

A

Under the assumption of homogeneous expectations, the optimal CAL for all investors is termed the capital market line (CML). Along this line, expected portfolio return, E(RP), is a linear function of portfolio risk, σP. The equation of this line is as follows:

E(Rp) = Rf + {[(E(Rm) - Rf)]/SDm}*SDp

y intercept = Rf
slope = (E(Rm) - Rf)]/SDm

An investor who choose no risk ie SDp=0 will earn only Rf

35
Q

Market Risk Premium

A

The difference between the expected
return on the market and the risk-free rate is termed the market risk premium.

We can rewrite CML equation as:

E(Rp) = Rf + [(E(Rm) - Rf)]*(SDp/SDm)

36
Q

Passive Investment Strategy

A

Investors who believe market prices are informationally eff icient often follow a passive investment strategy (i.e., invest in an index of risky assets that serves as a proxy for the market portfolio and allocate a portion of their investable assets to a risk-free asset, such as short-term government securities)

37
Q

Active Portfolio Management

A

In practice, many investors and portfolio managers believe their estimates of security values are correct and market prices are incorrect. Such investors will not use the weights of the market portfolio but will invest more than the market weights in securities that they believe are undervalued and less than the market weights in securities which they believe are overvalued. This is referred to as active portfolio management.

38
Q

Systematic Risk

A

Because the market portfolio contains all risky assets, it must be a well-diversif ied portfolio. All the risk that can be diversi fied away has been. The risk that remains cannot be diversi fied away and is called the systematic risk (also called nondiversi fiable risk or market risk).

39
Q

Unsystematic risk

A

When an investor diversi ies 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 diversi fication is called unsystematic risk (also called unique, diversi fiable, or f irm-speci fic risk).

40
Q

Total Risk

A

= Systematic Risk + unsystematic risk

41
Q

Equilibrium Security Returns depend on a stock’s or a portfolio’s

A

systematic risk (not total risk as measured by standard deviation) as diversifaction is free. The reasoning is that investors will not be compensated for bearing risk that can be eliminated at no cost.

Implication: The riskiest stock, with risk measured as standard deviation of returns, does not necessarily have the greatest expected return.

Lower systematic risk –> Lower equilibrium rate of return (CMT)

Eliminate unsystematic risk by diversification

42
Q

Return generating models

A

Used to estimate the expected returns on risky securities based on specif ic factors.
For each security, we must estimate the sensitivity of its returns to each speci fic factor. Factors that explain security returns can be classi fied as macroeconomic, fundamental, and statistical factors.

43
Q

Multifactor models

A

Most commonly use macroeconomic factors such as GDP growth, inf lation, or consumer conf idence, along with fundamental factors such as earnings, earnings growth, firm size, and research expenditures.

Statistical factors often have no basis in finance theory

E(Ri) - Rf = Bi1 x E(Factor 1) + Bi2 x E(Factor 2) ….

44
Q

Factor sensitivity

A

AKA Factor Loading

Multifactor model states that the expected excess return (above the risk-free rate) for Asset i is the sum of each factor sensitivity or factor loading (the βs) for Asset i multiplied by the expected value of that factor for the period.
The f irst factor is often the expected excess return on the market, E(Rm − Rf).

45
Q

Fama & French Multifactor Model

A

They estimated the sensitivity of security returns to three factors: f irm size, firm book value to market value ratio, and the return on the market portfolio minus the risk-free rate (excess return on the market portfolio).

46
Q

Carhart Multifactor model

A

Carhart suggests a fourth factor to the F&F Model -
measures price momentum using prior period returns.

47
Q

Single Index Model

A

E(Ri) - Rf = Bi x [E(Rm) - Rf]

only excess market returns as a factor

48
Q

Market Model

A

A simplif ied form of a single-index model is the market model, which is used to estimate a security’s (or portfolio’s) beta and to estimate a security’s abnormal return (return above its expected return) based on the actual market return.

Ri = Alphai + Bi*Rm + ei

Ri = Returns of Asset i
Alphai = intercept
Bi = slope coefficient
Rm = Market returns
ei = abnormal returns of asset i

Alphai, Bi = historical data

49
Q

Beta in Market Model

A

The sensitivity of an asset’s return to the return on the market index in the context of the market model is referred to as its beta. Beta is a standardized measure of the covariance of the asset’s return with the market return.

Bi = covar(i,m)/Varm

50
Q

Security Characteristic line

A

In practice, we estimate asset betas by regressing returns on the asset on those of the market index. we represent the excess returns on Asset i as the dependent variable and the excess returns on the market index as the independent variable. The least squares regression line is the line that minimizes the sum of the squared distances of the points plotted from the line (this is what is meant by the line of best it). The slope of this line is our estimate of beta. This regression line is referred to as the asset’s security characteristic line.

51
Q

What is the risk measure associated with the capital market line (CML)?

A

Total risk

52
Q

A portfolio to the right of the market portfolio on the CML is a

A

Borrowing Portfolio

53
Q

A return generating model is least likely to be based on a security’s exposure to:

A

Statistical factors

54
Q

When you increase the number of stocks in a portfolio, unsystematic risk will…

A

decrease at a decreasing rate

55
Q

Security Market Line

A

Given that the only relevant (priced) risk for an individual Asset i is measured by the covariance between the asset’s returns and the returns on the market, Covi,mkt, we can plot the relationship between risk and return for individual assets using Covi,mkt as our measure of systematic risk. The resulting line, plotted in is one version of what is referred to as the security market line (SML).

56
Q

Equation of SML

A

E(Ri) = Rf + Cov(i,mkt)/Var(mkt) x [E(Rmkt) - Rf)

Bi = Cov(i,mkt)/Var(mkt)

This is also CAPM

57
Q

Capital Asset Pricing Model

A

This relation between beta (systematic risk) and expected return is known as the capital asset pricing model (CAPM).

B = Cov(i,mkt)/var(mkt)

Beta measures the relation between a security’s excess returns and the excess returns to the market portfolio.

CAPM:
E(Ri) = Rf + Bi[E(rmkt) - Rf] - same as SML

The CAPM holds that, in equilibrium, the expected return on risky asset E(Ri) is the risk-free rate (Rf) plus a beta-adjusted market risk premium, βi[E(Rmkt) − Rf]. Beta measures systematic (market or covariance) risk.

58
Q

SML - Beta

A

standardised measure of systematic risk

B = Cov(i,mkt)/var(mkt)

59
Q

If Ba > 1, E(Ra) >/< E(Rmkt)

A

E(Ra) > E(Rmkt)

60
Q

Assumptions of CAPM

A
  • Risk Aversion: Greater Risk –> Greater Returns
  • Utility Maximising Investors
  • Frictionless Markets: No taxes, not costs or impediments to trading
  • One-period horizon: all investors have the same one-period time horizon
  • Homogenous expectations: all investors have same expectations: expected returns, std dev, correl
  • Divisible assets: all investments are infinitely divisible
  • Competitive Markets: Investors take the market price as given and no investor can in fluence prices with their trades.
61
Q

Any stock not on the SML is…

A

mispriced

Forecasted Return > Required Return (E(R)) = undervalued

Forecasted Return < Required Return (E(R)) = overvalued

Forecasted Return = Required Return (E(R)) = properly valued

62
Q

Performance Evaluation

A

Performance evaluation of an active manager’s portfolio choices refers to the analysis of the risk and return of the portfolio.

63
Q

Attribution Analysis

A

An analysis of the sources of returns differences between active portfolio returns and those of a passive benchmark portfolio, is part of performance evaluation.

Success in active portfolio management cannot be determined simply by comparing portfolio returns to benchmark portfolio returns; the risk taken to achieve returns must also be considered. A portfolio with greater risk than the benchmark portfolio (especially beta risk) is expected to produce higher returns over time than the benchmark portfolio.

64
Q

Sharpe Ratio

A

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.
= E[Rportfolio] - Rf / SDEVportfolio

Also the Slope for CAL for that portfolio and can be compared to the slope of the CML which is the Sharpe ration for the portfolios that lie on the CML

65
Q

Ex-Ante / Ex-Post

A

Ex-Ante: before the fact ie using expected values

Ex-Post: after the fact ie. using actual values ie sample mean returns and sample Standard Deviation

66
Q

Use of Sharpe Ratio

A

The Sharpe ratio is based on total risk (standard deviation of returns), 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-diversi fied portfolios (those with only systematic, or beta, risk).

The value of the Sharpe ratio is only useful for comparison with the Sharpe ratio of another portfolio.

67
Q

M-sqaured (M^2)

A

Alternative to Sharpe Ratio
Expressed in %
Given a Portfolio P, we can calculate the return on a Portfolio P* that is leveraged (when σM > σP), or deleveraged (when σM < σP), so that P* has the same risk
(standard deviation of returns) as the market portfolio.

The return on P* is

= Rf + SDEVm/SDEVp (Rp - Rf)

and we refer to that as the M2 measure for Portfolio P.

68
Q

M^22 Alpha

A

The extra return on the Portfolio P* above the return on the market portfolio, (P* - RM), is referred to as M2 alpha.

P* - RM

69
Q

If M^2 > Rm, M^2 Alpha (</>/=) 0

A

If M^2 > Rm, M^2 Alpha > 0

70
Q

Measures of portfolio performance based on systematic risk

A

Treynor measure and Jensen’s alpha

Treynor - slope (like SR)
Jensons - % measure of excess returns (like M2)

71
Q

Treynor Measure

A

= (Rp - Rf) / Bp

excess returns per unit
of systematic risk

Slope of risk/beta graph of portfolio p

72
Q

Jensons Alpha

A

Ap = Rp - [Rf + Bp(Rm - Rf)]

is the percentage portfolio return above that of a portfolio (or security) with the same beta as the portfolio that lies on the SML

73
Q

How to decide if risk adjustment should be based on standard deviation of returns or portfolio beta?

A

Standard Deviation = using SR/M^2 = when the portfolio bears both systematic & unsystematic risk, single manager

Beta = using Treynore & Jensons = well diversified ie. no unsystematic risk, multiple managers

74
Q

Note of Caution

A

Estimating the values needed to apply these theoretical models and performance measures is often diff icult and is done with error.

The expected return on the market, and thus the market risk premium, may not be equal to its average historical value.

Estimating security and portfolio betas is done with error as well.

75
Q

According to the CAPM, a rational investor would be least likely to choose as his optimal
portfolio:

A

global minimum variance portfolio

76
Q

Stock 1 has a standard deviation of 10. Stock 2 also has a standard deviation of 10. If the
correlation coefficient between these stocks is –1, what is the covariance between these two
stocks?

A

-100

77
Q

Which of the following statements best describes an investment that is not on the efficient
frontier?
A) There is a portfolio that has a lower return for the same risk.
B) The portfolio has a very high return.
C) There is a portfolio that has a lower risk for the same return.

A

C

The efficient frontier outlines the set of portfolios that gives investors the highest return
for a given level of risk or the lowest risk for a given level of return. Therefore, if a portfolio
is not on the efficient frontier, there must be a portfolio that has lower risk for the same
return. Equivalently, there must be a portfolio that produces a higher return for the same
risk.

78
Q

A line that represents the possible portfolios that combine a risky asset and a risk free asset
is most accurately described as a:

A

CAL

79
Q

A line that represents the possible combinations of the market portfolio with the risk-free asset.

A

CML

80
Q

Portfolios on the capital market line:

A

are perfectly positively correlated with each other.

81
Q

James Franklin, CFA, has high risk tolerance and seeks high returns. Based on capital market
theory, Franklin would most appropriately hold:

A

the market portfolio as his only risky asset.

82
Q

In the context of the CML, the market portfolio includes:

A

all existing risky assets

The market portfolio has to contain all the stocks, bonds, and risky assets in existence.
Because this portfolio has all risky assets in it, it represents the ultimate or completely
diversified portfolio.

83
Q

Which of the following pooled investment shares is least likely to trade at a price different
from its NAV?

A

Open Ended

84
Q

Investment Constraints & Objectives

A

Risk tolerance and return requirements make up the investment objectives. Investment
constraints include liquidity needs, time horizon, tax concerns, legal and regulatory
factors, and unique circumstances.

CFA L1 (16 decks)

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