4. Passive Risk & Return

Question 1

What is passive return?

Answer 1

Return of a market index (e.g. S&P500, NZX50, etc.)

Question 2

Why is portfolio risk lower than the weighted average risks of assets included in the portfolio?

Answer 2

Diversification

Question 3

Harry Markowitz is credited with…

Answer 3

developing the first modern portfolio theory (MPT)

Question 4

Harry Markowitz model is the…

Answer 4

theoretical framework for the analysis of risk-return choices, with these choices made based on the concept of efficient portfolios

Question 5

What is an efficient portfolio?

Answer 5

Portfolio’s expected return has the smallest variance for that particular level of expected return OR
a portfolio with the largest expected return for a specified amount of portfolio variance

Question 6

Efficient Frontier

Answer 6

Set of optimal portfolios that offer the highest expected return for a given level of risk (no rational investor would choose to hold a portfolio not located on the efficient frontier)

Question 7

Unsystematic risk

Answer 7

Can be reduced through diversification

Question 8

Systematic risk

Answer 8

Risk inherent to the whole market

Question 9

Three ingredients of optimisation

Answer 9

Objective function, choice variables and constraints

Question 10

Return of portfolio

Answer 10

h (weights) vector transposed x R (return) vector

Question 11

Expected return

Answer 11

h (weights) vector transposed x E(R) vector –> E(R) vector = h vector transposed x average return vector

Question 12

Variance

Answer 12

= h vector transposed x VCV x h vector

Question 13

Beta of a portfolio relative to benchmark

Answer 13

Bp,b = h vector transposed x VCV x hb vector/hb vector transposed x VCV x hb vector

Question 14

Beta of a portfolio that’s not fully invested

Answer 14

delta x beta of a portfolio relative to benchmark where delta = proportion of portfolio invested in risky portfolio

Question 15

Beta for individual stock, i, relative to a portfolio thats not fully invested

Answer 15

1/delta x beta of portfolio relative to benchmark

Question 16

covariance

Answer 16

hp vector transposed x VCV x hb vector

Question 17

Local extrema problem in numerical optimisation

Answer 17

Need to try different starting points to ensure that we are achieving the actual solution and not just local extrema.

Question 18

Numerical vs. Analytical Optimisation

Answer 18

Numerical - software (complicated/more constraints)
Analytical - pencil and paper (faster and more accurate)

Question 19

Why do practitioners care about MPT?

Answer 19

• Introduced the notation of unsystematic risk
• Passive MPT portfolios can be used in active portfolio management

Question 20

Main consideration of Markowitz frontier

Answer 20

Considers expected risk and return of individual assets and their interrelationship as measured by correlation of VCV.

Question 20

CAPM is simplified

Answer 20

Markowitz MPT

Question 21

Tangent of the Tobin Frontier is

Answer 21

most optimal

Question 22

Tangency portfolio is

Answer 22

market portfolio

Question 23

SML depicts the relationship between

Answer 23

Systematic risk and return (beta and return)

Question 24

CML depicts the relationship between

Answer 24

total risk and return

Question 25

Systematic risk is measured with

Answer 25

beta

Question 26

CAPM relates the returns on…

Answer 26

individual assets or entire portfolios to the return on the market as a whole

Question 27

Investors are compensated for

Answer 27

systematic risk but not unsystematic (firm specific risk)

Question 28

Unlike other points on Tobin frontier, the tangency portfolio is

Answer 28

fully invested (weights in risky assets = 1), the tangency portfolio is the optimal portfolio of risky assets (a.k.a market portfolio) and holds the highest sharpe ratio compared with any portfolio on the efficient frontier.

Question 29

CAPM says that

Answer 29

the return on asset is the riskless rate plus a risk premium –> remember that investors are compensated only for systematic risk

Question 30

Beta in CAPM =

Answer 30

Covar/var

Question 31

What does CAPM say about alpha?

Answer 31

CAPM says that alpha in the long run has an expected value of zero, meaning that the returns investors get are due to to their exposure to the “systematic risk”

Question 32

Ex Ante Meaning

Answer 32

If we plot the CAPM-derived expected return on stocks/portfolios against the betas of those stocks/portfolios, we find that they lie on a straight line with intercept equal to the risk-free rate and slope equal to the expected excess return on the market (SML)

Question 33

Ex Post Meaning

Answer 33

“after the facts” - if we plot actual return against their betas, then we might find a scatter diagram

Question 34

Can we test CAPM?

Answer 34

Roll (1977) - CAPM is untestable, the only economic prediction of CAPM is that the market portfolio is mean-variance efficient.

Question 35

CAPM’s market portfolio cannot…

Answer 35

be observed - market portfolio includes all assets in the universe therefore, we use stock indexes as proxies for the return of a market portfolio

Question 36

We can’t say what the true reason is for discrepancies between actual returns and returns forecasted by CAPM it could be…

Answer 36

the proxy for the market is not correct or CAPM is not valid for the chosen security

Question 37

The linear return/beta relationship can be found in any sample irrespective of

Answer 37

how returns are determined in the market, we only need to identify an index that is ex-post efficient “after the facts”

Question 38

All existing CAPM tests only tell us

Answer 38

whether the market proxy used by researches is efficient or not, nothing about the efficiency of market portfolio itself –>market proxies only contain information about the subsets that are equities, not the whole market –> testing only a fraction of the market

Question 39

A true market portfolio should include

Answer 39

all assets in the universe!