Portfolio Management: Module 53: Systematic Risk and Beta, CAPM and the SML

M-squared

(M2) measure produces the same portfolio rankings as the Sharpe ratio but is stated in percentage terms. It is calculated as (RP−Rf)σMσP−(RM−Rf).

Portfolio Beta

(Weighted average)(Bi)

Individual Asset Beta

(correlation with market index) x [(standard deviation of asset) / (standard deviation of the return on index)] OR (covariance with index) / (market variance)

CAPM security selection via SML

+ Buy assets above the line + Sell below the line

Capital Asset Pricing Model (CAPM)

+ CAPM: the expected return on an asset based only on the asset's systematic risk or beta + CAPM is also used to determine the required return on an asset on the asset's systematic risk (beta) + Required return and expected return are the same in equilibrium

CAPM Applications

+ Performance evaluation: analyze risk and return of the active manager's portfolio + Attribution analysis: analyze sources of the difference between an active manager's portfolio returns and the benchmarks portfolio's returns + Calculating risk-adjusted return measures: Sharpe Ratio of P2 is slope of CAL; (compare to the slope of CML)

systematic risk (market risk)

+ caused by macro factors: interest rates, GDP growth, supply shocks + measured with covariance of returns and returns on the market portfolio

Assumptions of Capital Market Theory

+ investors use mean-variance framework + Unlimited lending and borrowing at Rf + Homogeneous expectations + one period time horizon + divisible assets + frictionless markets: no taxes, no transactions costs or restrictions on short selling + no inflation and unchanging interest rates + capital markets are in equilibrium + investors are price takers + investors are rational, risk averse, and maximize expected utility

Returns Generating Models

+ the market model has a single risk factor, the return on the market + the asset beta (Bi) is the sensitivity of its returns to this risk factor + Asset returns are a linear function of market returns

CML versus SML

+CML has only efficient portfolios and only two assets plot on the line + CML is based on total risk (standard deviation) +CML: Slope is the Sharpe Ratio + ALL asset or portfolio plots on the SML in equilibrium + SML is based on systematic risk (beta)

When you increase the number of stocks in a portfolio

+unsystematic risk will decrease at a decreasing rate +systematic risk can be increased by adding higher-beta stocks or decreased by adding lower-beta stocks

Risk factors (F) of three types:

- Macroeconomic factors: GDP growth, inflation etc - Fundamental factors: earnings, earnings growth, firm size, research expenditures etc - Statistical factors: no basis in finance theory

Abnormal return =

Actual return - expected risk-adjusted return

Difference between Capital Market Line and Security Market Line

CML: uses total risk (standard deviation, systematic risk + unsystematic risk) SML: uses beta (market risk)

Forecast Returns w. CAPM

Calculate HPR: Expected Return = [(P1 - P0 + Dividend) / P0] Calculate CAPM: Required Return If CAPM > HPR: Overvalued, want to sell If CAPM < HPR: Undervalued, want to buy CAMP = HPR: appropriately valued and would be plotted on the SML

CAMP (SML equation)

E(Ri) = Rf + Bi[E(Rmarket)-Rf] + Beta is a measure of systematic risk + Beta is the standardized covariance of an asset's returns iwth returns on the market portfolio: Bi = Covi,market / variance

Single Index Model

E(Ri) − Rf = βi ×[E(Rm) − Rf]

Multi-factor models

E[Ri]-Rf = βi,1E[F1]+βi,2E[F2]+...+βi,K E[FK] • The factors (F's) are the expected values of each risk factor • The betas (βi,K) are the asset's factor sensitivities or factor loadings for each risk factor

Sharpe Ratio

Excess return per unit of total risk: Sharpe Ratio = E(Rportfolio) - Rf / standard deviation ** higher Sharpe Ratio is better

CAPM (Capital Asset Pricing Model)

Kcs = Rrf + B(Rm-Rrf)

Combing a Risk-Free Asset with a Risky Asset

P(Er): (Wr)(Rr) + (Wrf)(Rrf) P(sd)= (Wr)(standard deviation)

Treynor Measure

RP−Rf / βP the excess returns per unit of systematic risk and compares to the slope of the SML + used for well diversified investors (big mutual funds)

market model

Ri = αi + βiRm + ei Ri = return on Asset i Rm = market return βi = slope coefficient αi = intercept ei = abnormal return on Asset i

The Farma-French (FF) Three Factor Model

Risk factors are: 1. Firm Size 2. Book-to-market ratio 3. excess return on the market portfolio Carhart added a fourth factor: + momentum **Explains US equity returns better than the market (single index) model**

The Market Portfolio contains

all risky assets in existence **It does not contain any risk-free assets.

All portfolios on the capital market line

are perfectly positively correlated **Since the line is straight, the math implies that the returns on any two portfolios on this line will be perfectly, positively correlated with each othe

Investors seeking to take on more risk will

borrow at the risk-free rate to purchase more of the market portfolio

Unsystematic risk (firm-specific risk)

can be reduced/ eliminated by holding well-diversified portfolios

Risk of portfolio vs. number of assets in the portfolio

diversification reduces unsystematic risk Total Risk: unsystematic risk + systematic risk Market Risk

Market Beta

is always 1 + Beta > 1: aggressive asset (tech companies) + Beta < 1: defensive asset (utility companies)

risk-adjusted performance (M2)

is the additional return that could have been earned by leveraging the active portfolio (borrowing at Rf) so that its risk is equal to that of the market portfolio **want M2 > 0

Risk premium

is the product of the Beta and the factor loadings

Anything that is NOT on the Security Market Line is

mispriced

Calculating Beta (βi)

often estimated as the slope of a characteristic line, a regression of asset returns on market returns Bi = slope = Cov market / variance of the market

approximate risk free rate =

real risk-free rate + inflation premium

Only systematic (market) risk is

rewarded with higher expected returns

Two types of risk

systematic risk and unsystematic risk

M-squared for a Portoflio

the excess return % on such a leveraged portfolio differs from the return on the market portfolio by the vertical distance M2

Capital Allocation Line

the risk-return combinations resulting from combing a risk-free asset with a portfolio of risky assets

Sharpe Ratio as Slopes

the slope of the CAL for that portfolio and can be compared to the slope of the CML, which is the Sharpe ratio for portfolios that lie on the CML

Capital Market Line

under the assumption of homogeneous expectations, the optimal CAL for all investors * Capital Market Line has two assets plotted on CML: Market portfolio M and risk-free asset **along this line, expected portfolio return is a linear function of portfolio risk

The point of tangency along CML

where the efficient frontier intersects with CML more risk: use borrowing Less risk: use lending

Jensen's Alpha

αP = Rp − [Rf + βP(RM − Rf)] * Different than CAMP because using Portfolio Beta The % return above the equilibrium return for a portfolio with beta = Bp the difference between a portfolio's actual rate of return and the equilibrium rate of return for a portfolio with the same level of beta (systematic) risk