Modern Portfolio Theory

Question 1

Sharpe Ratio Limitations

Answer 1

• assumes returns follow a normal distribution, not true in reality (lots of price shocks)
• all volatility is penalised, even upside
• can be manipulated to boost the apparent risk-adjusted returns

Question 2

Markovitz’s Diversification

Answer 2

• Combining securities with less-than-perfect positive correlation, p<1
• Reduce the risk of the portfolio without sacrificing the portfolio’s expected return
• Relation between correlation and risk level

Question 3

Expected Return of a Portfolio

Answer 3

E(r_p) = w₁E(r₁) + w₂E(r₂)

Question 4

Variance of a portfolio’s return

Answer 4

σ²_p = w₁²σ₁² + w₂²σ₂² + w₃²σ₃² + 2w₁w₂σ₁₂ + 2w₁w₃σ₁₃ + 2w₂w₃σ₂₃

Question 5

Assumptions of MPT

Answer 5

• All investors have the same one-period time horizon
• All investors are risk-averse, and their goal is to maximise their expected utility
• All investors can borrow or lend at the risk free rate
• All investors choose portfolio following mean-variance model
• no tx costs
• no income taxes

Question 6

Expected utility

Answer 6

Function of expected returns and variance
* E[u(R)] = f(E(R), σ²(R))

Question 7

Global Minimum Variance Portfolio

Answer 7

Furthest left point on efficient frontier

Question 8

Sharpe Ratio

Answer 8

E(r_p) - r_f / σ_p

Question 9

CAPM

Answer 9

E(R) = r_f + 𝛽_i(E(R_m - r_f)

Question 10

CAPM Assumptions

Answer 10

• All investors have the same one-period time horizon
• All investors are risk-averse, and their goal is to maximise their expected utility
• All investors can borrow or lend at the risk free rate
• All investors choose portfolio following mean-variance model
• no tx costs
• no income taxes
• All investors have identical expectations about E(R), std dev and p for all securities
• All investors are price-takers

Question 11

Beta

Answer 11

𝛽_i = Cov_i,M / σ²_M

Question 12

Portfolio Beta

Answer 12

𝛽_p = w₁𝛽₁ + w₂𝛽₂ + … + w_n𝛽_n

Question 13

Security Market Line

Answer 13

graph of the CAPM
* Represents the relationship between an asset’s risk, measured by beta, and its expected return

Question 14

Jensen’s Alpha

Answer 14

measures the risk-adjusted excess return earned by a security or portfolio over a given period
* α = (R_i - r_f) - 𝛽_i(R_M - r_f)

Question 15

Fama-French Three-Factor Model

Answer 15

small stocks (and value stocks) outperform big stocks (and growth stocks)
* r_i = r_f + (E(r_m) - r_f)𝛽_m + (SMB)𝛽_smb + (HML)𝛽_hml + e_i

Question 16

Criticisms of Fama-French Three-Factor Model

Answer 16

• some argue that the size and value factors are a result of data mining
• ignores momentum factor

Question 17

Carhart Four-Factor Model

Answer 17

Considered momentum factor
* r_i - r_f = α_i + (E(r_m) - r_f)𝛽_m + (SMB)𝛽_smb + (HML)𝛽_hml + (UMD)𝛽_umd + e_i

Question 18

Fama-French Five-Factor Model

Answer 18

Added profitability and investment factors on the previous model (Robust minus Weak, Conservative minus Aggressive)
* r_i - r_f = α_i + (E(r_m) - r_f)𝛽_m + (SMB)𝛽_smb + (HML)𝛽_hml + (RMW)𝛽_rmw + (CMA)𝛽_cma + e_i

Question 19

Treynor Ratio

Answer 19

reward-to-volatility ratio
* TR_p = E(r_p) - r_f / 𝛽_p

Question 20

market portfolio

Answer 20

fully diversified portfolio of all risky assets

Question 21

Capital Market Line

Answer 21

Special case of CAL.
* represents all possible combinations of risk-free assets and the market portfolio

Question 22

Prospect Theory

Answer 22

individuals are more sensitive to potential losses than to equivalent potential gains

Question 23

SMB

Answer 23

Small minus Big
* represents the difference in returns due to the small firm effect, small stocks have greater returns that big stocks

Question 24

HML

Answer 24

High minus Low
* High B/M vs Low B/M, represents the difference in returns between value (High B/E) and growth (Low B/E) stocks

Question 25

UMD

Answer 25

Up minus Down * represents momentum, strong performance tends to continue, weak performance tends to continue

Question 26

RMW

Answer 26

Robust minus Weak * represents the difference in returns between stocks with robust profitability vs stocks with weak profitability

Question 27

CMA

Answer 27

Conservative minus Aggressive * represents the difference in returns between stocks with conservative investment vs stocks with aggressive investment

Question 28

How is the efficient frontier calculated?

Answer 28

By changing weights of risky assets to minimise the variance for a given return, or maximise the return for a given variance

Question 29

Explain how two firms can have the same expected return but one has a significantly higher standard deviation

Answer 29

* standard deviation = total risk = systematic + unsystematic risk * CAPM only rewards for bearing systematic risk * As diversifiable risk can be eliminated through efficient asset allocation, the presence of this risk is purely down to the manager's asset choice and, in an efficient market, would not be compensated

Question 30

Weak form efficiency

Answer 30

prices reflect all historical market information

Question 31

Semi-strong form efficiency

Answer 31

Prices reflect all publicly available information

Question 32

Strong form efficiency

Answer 32

Prices reflect all information including public and private

Question 33

Frame dependance

Answer 33

If an investment problem is presented in two different ways (with identical results), investors often make inconsistent choices

Question 34

House money effect

Answer 34

More likely to take big risks with money already gained (house money)

Question 35

CAL

Answer 35

represents all possible portfolio combinations of risk-free assets and risky assets

Question 36

Criticisms of Fama French 5 Factor

Answer 36

- profitability and investment factors are less robust - ignores momentum

Question 37

Information Ratio

Answer 37

- measures a managers ability to generate excess returns relative to a benchmark, adjusted for the additional risk taken

Question 38

Modigliani and Modigliani Ratio

Answer 38

- measures risk-adjusted performance - A portfolio manager who has taken the same risk as its benchmark should generate returns similar to the benchmark - adjusts a portfolio's risk to match the risk of a chosen benchmark and calculates the hypothetical return the portfolio would achieve at that risk level

Question 39

Sortino Ratio

Answer 39

- performance metric that evaluates a portfolio's return relative to its downside risk - focusing only on negative volatility (returns below a target or minimum threshold) - modification of Sharpe, better as it only penalises downside risk; especially when investors are primarily concerned with avoiding losses

Question 40

The Equity Premium Puzzle

Answer 40

- a financial anomaly referring to the observation that historical returns on stocks have significantly exceeded returns on risk-free assets by a margin that is much larger than can be explained by standard economic theories, e.g. CAPM suggests that the premium should be much smaller - According to models of rational risk aversion, the observed equity premium implies an unrealistically high level of risk aversion among investors

Question 41

CAPM Limitations

Answer 41

- assumes returns are normally distributed - reliance on the market portfolio, which is unobservable in reality - assumes investors can borrow and lend at the risk free rate

Question 42

Myopic Loss Aversion

Answer 42

- the tendency of people to focus on short-term losses rather than long-term gains

Question 43

Behavioural Finance Assumptions

Answer 43

- people are normal - people's portfolio wants extend beyond high expected returns and low risk, such as for social responsibility and social status - differences in expected returns are determined by more than differences in risk, such as by levels of social responsibility and social status