R53 — Portfolio Risk and Return: Part II

If βi > 1 → E(Return on asset i) ____ E(Return on market)

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Sharpe ratio of a portfolio is the slope of the ___ for that portfolio → can be compared to slope of ____

CAL CML * Remember, bigger slope/Sharpe ratio, better return for the same risk

As the number of stocks in a portfolio increases, the portfolio's systematic risk ____

Can increase or decrease

Active portfolio management

Investors who will not use the weights of the market portfolio because they think their estimates are better/more accurate than the market prices

The simplest factor model is a ____

Single-factor model

Single-factor model is also known as the ____

Single-index model

Two formulas for measuring beta using asset i and market m

1. Cov(i, m)/var(m) 2. corr(i, m) * (σi/σm)

Market model is used to estimate a security's/portfolio's ___ and to estimate the security's/portfolio's ____

Beta and abnormal return

Borrowing portfolios → ____ of market portfolio (left/right) Lending portfolios → ____ of market portfolio

Borrowing → Right Lending → Left

CAPM equation

Cost of Equity = RFR + beta (Market return - RFR)

General form of multifactor model estimates ____ above the ____ by taking sum of the multiple between ____ for each asset in the portfolio x ____ of each asset

Estimates expected return above the risk-free rate Sum of each factor sensitivity (or factor loading) for each asset multiplied by the expected value of that factor for that period

As the number of stocks in a portfolio increases, the portfolio's unsystematic risk ____ at a ____ rate

Decreases at a decrease rate * After 12-18 stocks, the portfolio achieves 90% of max. diversification possible

Return generating models are used to estimate the ____ on risky securities based on specific factors

Expected return

Fama and French multifactor model → estimates sensitivity of security returns using ____, ____, ____ (and ____)

Firm size Firm book value to market value ratio Return on market portfolio - the risk-free rate of return Price momentum

Higher Sharpe ratio → ____ risk-adjusted portfolio performance

Higher Sharpe ratio → better performance

Can individual firms/securities have systematic and unsystematic risk or only portfolios will have them?

Individual firms/securities will also have systematic and unsystematic risk

Passive investment strategy

Invest in an index of risky assets as proxy for market portfolio → for investors who believe market prices are informationally efficient

Homogeneous expectation assumption (modern portfolio theory)

Investors all have the same estimates of risk (σ), return (E), and correlations (ρ) with other risky assets for all risky assets

What's the difference between Sharpe ratio and M-squared measure?

M-squared measure provides the same portfolio rankings as the Sharpe ratio but is stated in percentage terms

Multifactor models most commonly use ____ factor along with ____ factors but rarely use ____ factors.

Macroeconomic factors (e.g. GDP, inflation) and fundamental factors (e.g. earnings, firm size), but not statistical factors (no basis in finance theory)

What does the Treynor measure do?

Measures a portfolio's excess return per unit of systematic risk (Sharpe ratio is total risk)

What does the Sharpe ratio measure and what is it useful for?

Measures excess return per unit of total risk (Treynor is systematic risk) Useful for comparing portfolios on a risk-adjusted basis

If there are multiple CAL lines for an individual investor, each CAL having different risk and return (三條線的斜率不一樣), the best CAL for this investor is the one that ____

Offers the greatest expected utility (highest expected return) given the same risk (斜率最大的)

Attribution analysis: analysis of the sources of returns difference between active portfolio returns and those of a ____. Portfolio with greater risk than the ____ is expected to produce ____ returns over time.

Passive benchmark portfolio Benchmark portfolio, higher returns over time

Main application of CAPM and SML: To find the security's ____ based on the security's exposure to ____ and then to determine whether a security is ____

Required rate of return, market risk, properly valued

Single-factor model uses ____ as its only risk factor

Return on the market

Assumptions of CAPM

Risk aversion Utility maximizing investors Frictionless market (no taxes/transaction costs/other impediments to trading) One-period horizon Homogeneous expectations Divisible assets (all investments are infinitely divisible) Competitive markets (investors take the market price as given and no investor can influence prices with trade)

Market risk premium (definition and formula)

Risk premium of market portfolio. Difference between market return and return on risk-free rate

Implication of homogeneous expectations → all investors face ____ efficient frontier of risky portfolios and will therefore have the same ____ and ____

Same efficient frontier of risky portfolios Same optimal risky portfolio and CAL

Using least-square regression to estimate beta by regressing returns on the asset → regression line formed is the ____

Security characteristics line

Plot expected returns against COVi, mkt (so using covariance between the asset's returns and the market's return as measure of risk instead of using σ) → resulting line of the relationship between expected return and risk measured by β (systematic risk) is the ____

Security market line (SML)

Beta in the context of the market model measures ____

Sensitivity of an asset's return to the return on the market index * Standardized measure of the covariance of the asset's return with the market return

In CAPM, beta is defined as a _____ and measures the relationship between a security's excess return and the excess returns to the ____

Standardized measure of systematic risk, market portfolio

Total risk =

Systematic risk + Unsystematic risk

Equilibrium security returns depend on a stock's/portfolio's ____ risk, not its ____ risk as measured by standard deviation

Systematic risk, not total risk

What is Jensen's alpha?

The difference between a portfolio's return and the return of a portfolio on the SML that has the same beta

Capital allocation line (CAL) (Definition)

The line of possible portfolio risk and return combinations given the risk--free rate and the risk and return of a portfolio of risky assets

Capital market line (CML)

The optimal CAL for all investors under the assumption of homogeneous expectations

Sharpe ratio and M-squared measure → based on ____ Treynor measure and Jensen's alpha → based on ____

Total risk Systematic (beta) risk

CML → measures risk with ____ and only ____ portfolios will plot on CML SML → measures risk with ____ and ____

Total risk (standard deviation) and only efficient portfolios (on efficient frontier) Bata (systematic risk) and all properly priced securities/portfolios will plot on SML

Forecast return v.s. CAPM required return: Forecast > Required → ____ Forecast = Required → ____ Forecast < Required → ____

Undervalued Properly valued Overvalued * 如果你想成undervalued → need higher projected return to 'catch-up' to required return

An investor can expect to get one unit of market risk premium in additional return (above risk-free rate) for every ____

Unit of market risk σM *你的risk是市場market risk σM的多少倍數 就能得到多少market risk premium

For individual securities, if risk is primarily from: - Firm specific factors → Higher ____ risk - Macro/market factors → Higher ____ risk

Unsystematic risk (firm-specific factors) Systematic risk (e.g. Ferrari and Harley Davidson)

Why shouldn't an investor expect to receive additional returns for bearing unsystematic risk?

Unsystematic risk can be eliminated for free through diversification

Difference between unsystematic and systematic risk

Unsystematic risks are risk that can be eliminated by diversification and systematic risky are the risk that remains which cannot be diversified aways

Implication of combining a risk-free asset with a portfolio of risky assets → σP for the portfolio will be ____

WA x σA → Weight of risky assets in the portfolio x σ for the risky asset

Determining the optimal risky portfolio and optimal CAL (CML) assuming homogeneous expectations (Steps)

a.) Assume homogeneous expectations → all investors face same estimates of risk, return, and correlations with other risky assets for all risky assets b.) Because of homogeneous expectations, all investors also face the same efficient frontier of risky portfolios c.)Risk-free asset stays the same (Rf) d.) To form the capital market line (CML), use the risk-free asset return and draw a tangential line with the efficient frontier e.) This CML is the optimal CAL for any investor with the market portfolio f.) The optimal risky portfolio (market portfolio) is where the CML and market efficient frontier intersects g.) Each individual investor can then choose a different portfolio weights for the risk-free asset and the risky (tangency) portfolio (using the same risky portfolio) to suits their risk-averseness and/or expected return;;

Security market line equation

an equation that shows the relationship between risk as measured by beta and the required rates of return on individual securities

Security Market Line (SML)

graphical representation of the expected return-beta relationship of the CAPM