Portfolio Theory - Investments Exam 1

In a world of certainty

there would be no risk

Risk Averse Investors are willing to consider

•risk-free assets

•speculative positions with positive risk premiums

How can we assess return levels and dispersion simultaneously?

assigning utility values

Utility

Score assigned to competing portfolios on the desirable expected return and risk of those portfolios

•Desirability increases with return and decreases with risk

We can interpret the utility score of risky portfolios as

certainty equivalent rate of return

certainty equivalent rate

the rate that a risk-free investment would need to offer to provide the same utility as a risky portfolio

Risk-neutral investors

make decisions on the basis of expected returns, ignoring risk

•certainty equivalent rate is equal to the expected rate of return

indifference curve

•connects all portfolio points with the same utility value

•Equally preferred portfolios will lie in the mean-standard deviation plane

Estimating Risk Aversion

1)Use questionnaires

2)Observe individuals' decisions when confronted with risk

3)Observe how much people are willing to pay to avoid risk

Risk-free asset

actual return equals the expected return in all future states

•It is generally assumed that only the government can issue default-free bonds.

•T-bills often viewed as "the" risk-free asset

•Money market funds are often also considered risk-free in practice

The expected return on the complete portfolio

is the risk-free rate plus the weight of P times the risk premium of P

Passive strategy

describes a portfolio decision that avoids any direct or indirect security analysis

•Capital Market Line

•A natural candidate for a passively held risky asset would be a well-diversified portfolio of common stocks such as the S&P 500

Capital Market Line (CML)

is the capital allocation line formed from one month T-bills and a broad index of common stocks (e.g. the S&P 500).

correlation coefficient = 1

•Perfectly positively correlated

•no diversification

•no risk reduction is possible.

correlation coefficient = -1

•perfectly negatively correlated

•a perfect hedge is possible

•the standard deviation of the minimum variance portfolio is zero.

The minimum variance portfolio

is the portfolio composed of the risky assets that has the smallest standard deviation (the portfolio with the least risk).

Correlation Effects

•The risk reduction possible through diversification depends on correlation.

•The risk reduction potential increases as the correlation coefficient approaches -1

•If r = +1.0, no risk reduction is possible.

•If r = 0, σP may be less than the standard deviation of either component asset.

•If r = -1.0, a riskless hedge is possible.

Sharpe Ratio

-the slope of CAL

•Our Goal: Maximize the slope of our CAL for any possible risky portfolio, P.

Markowitz Portfolio - security selection

•The first step is to determine the risk-return opportunities that are available.

•All portfolios that lie on the minimum-variance frontier from the global minimum-variance portfolio and upward provide the best risk-return combinations

•We now search for the Capital Allocation Line (CAL) with the highest reward-to-variability ratio (E[r]/s)

separation property

tells us that the portfolio choice problem can be separated into two independent tasks

1)Determination of the optimal risky portfolio which is purely mechanical (in theory).

2)Asset allocation of the complete portfolio to T-bills or the risky portfolio depending on personal preference.

Total Risk

systematic risk + unsystematic risk

Systematic Risk

risk factors common to the whole economy, nondiversifiable risk; also called market risk

Unsystematic Risk

a risk that affects at most a small number of assets. Also, unique or asset-specific risk

SIngle-Index model Variance

= Systematic risk and firm-specific risk

SIngle-Index model covariance

= product of betas x market index risk

CAPM

is the main equilibrium pricing model that underlies a significant portion of modern financial theory

•It is derived using the principles of diversification combined with a number ofother simplifying assumptions

CAPM History

•CAPM was introduced by Jack Treynor(1961-1962), William Sharpe (1964), John Lintner (1965) and Jan Mossin (1966) somewhat independently.

•It was heavily dependent on the earlier work of Harry Markowitz on diversification and modern portfolio theory.

CAPM Assumptions

•Individual investors are price takers

•Single-period investment horizon

•Investments are limited to traded financial assets

•No taxes and transaction costs

•Information is costless and available to all investors

•Investors are rational mean-variance optimizers

•There are homogeneous expectations

Market Portfolio

All investors hold the same portfolio of risky assets

•Contains all risky securities

•The proportion of each security is its market value as a % of the total market's value

The risk premium provided by the market depends on the

average risk aversion of all the market participants

The risk premium on an individual security is a

function of the covariance of returns with the assets that make up the market portfolio.

Market Risk Premium

the slope of the SML - the difference between the expected return on a market portfolio and the risk-free rate

-The risk premium on the market portfolio will be proportional to its risk and the degree of risk aversion of the investor

Is the CAPM Valuable?

The CAPM is still widely used to explain the returns on risky assets. This means:

•Without any security analysis, alpha (α) is assumed to be zero.

•Positive and negative alphas are revealed only by superior security analysis.

The CAPM is still considered the best _____________ description of security pricing

theoretical

Extensions of the CAPM

•Merton's Multi-Period Model and hedge portfolios

•Incorporation of the effects of changes in the real rate of interest and inflation

•Consumption-based CAPMs

•Rubinstein, Lucas, and Breeden

•Investors allocate wealth between consumption today and investment for the future

•Zero-Beta Model

Zero-Beta Model

•Helped explain positive alphas on low beta stocks and negative alphas on high beta stocks

Fama and French observed that two classes of stocks have tended to do better than the market as a whole:

(i) small caps and (ii) stocks with a high book-to-market ratio (BtM, customarily called value stocks, contrasted with growth stocks).

The CAPM uses only beta to describe the returns of a portfolio or stock. (T/F)

True

SML and HML

they measure the historic excess returns of small caps and "value" stocks over the market as a whole.

Illiquidity Premium

Discount from fair market value the seller must accept to obtain a quick sale.

•Measured partly by bid-asked spread

•As trading costs are higher, the illiquidity discount will be greater.

Liquidity Risk

•In a financial crisis, liquidity will often unexpectedly dry up.

•When liquidity in one stock decreases, it tends to decrease in other stocks at the same time.

•We expect investors demand compensation for this liquidity risk

---•This suggests the existence of liquidity betas

RMW and CMA stand for

"robust minus weak" profitability and "conservative minus aggressive" investment policies

-part of F&F 5 factor model