4. Passive Risk & Return Flashcards by Lucy Murray

What is passive return?

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

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

Diversification

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Harry Markowitz is credited with…

developing the first modern portfolio theory (MPT)

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Harry Markowitz model is the…

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

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What is an efficient portfolio?

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

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Efficient Frontier

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)

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Unsystematic risk

Can be reduced through diversification

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Systematic risk

Risk inherent to the whole market

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Three ingredients of optimisation

Objective function, choice variables and constraints

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Return of portfolio

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

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Expected return

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

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Variance

= h vector transposed x VCV x h vector

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Beta of a portfolio relative to benchmark

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

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Beta of a portfolio that’s not fully invested

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

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

1/delta x beta of portfolio relative to benchmark

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covariance

hp vector transposed x VCV x hb vector

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Local extrema problem in numerical optimisation

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

Numerical vs. Analytical Optimisation

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

Why do practitioners care about MPT?

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

Main consideration of Markowitz frontier

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

CAPM is simplified

Markowitz MPT

Tangent of the Tobin Frontier is

most optimal

Tangency portfolio is

market portfolio

SML depicts the relationship between

Systematic risk and return (beta and return)

CML depicts the relationship between

total risk and return

Systematic risk is measured with

beta

CAPM relates the returns on...

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

Investors are compensated for

systematic risk but not unsystematic (firm specific risk)

Unlike other points on Tobin frontier, the tangency portfolio is

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.

CAPM says that

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

Beta in CAPM =

Covar/var

What does CAPM say about alpha?

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"

Ex Ante Meaning

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)

Ex Post Meaning

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

Can we test CAPM?

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

CAPM's market portfolio cannot...

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

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

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

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

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

All existing CAPM tests only tell us

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

A true market portfolio should include

all assets in the universe!