Finance: Investment Risks, Portfolio Optimization, and Asset Allocation

Speculation

The assumption of considerable investment risk to obtain commensurate gain.

Considerable risk

Risk is sufficient to affect the decision.

Commensurate gain

Positive risk premium (expected return > risk-free alternative).

Gamble

To bet or wager on an uncertain outcome.

Fair Game

Risky investments with a risk premium of zero.

Risk Averse Investors

Reject investment portfolios that are fair game or worse.

Utility Score

The measure of welfare/satisfaction of an investor.

Utility (U)

U = E(r) − 1/2 Aσ.

E(r)

Expected rate of return.

A

Risk aversion.

σ

Standard deviation.

Certainty Equivalent rate

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

Risk neutral investors

Judge risky prospects solely by their expected rates of return.

Risk lover

Happy to engage in fair game and gambles; willing to accept lower expected returns on prospects with higher amounts of risk.

Risk-averse investors

Consider risky portfolios only if they provide compensation for risk via risk premiums.

Mean-variance Criterion

Selection of portfolios based on the means and variances of their returns.

E(ra) >= E(rb)

Portfolio A dominates Portfolio B.

Indifference Curve

Connects all portfolios with the same utility according to their means and standard deviations.

Capital Allocation

The choice between risky and risk-free portfolios.

Risky Asset Classes

Simplest way to control risk is to manipulate the ratio of risk assets to risk free assets.

Weight of Equity

Amount invested in risky equity ($) / total risky amount invested ($).

Weight of Risky Portfolio (y)

Amount invested in risky assets ($) / total market value of portfolio.

Weight of Risk-Free Portfolio (1-y)

Amount invested in risk-free assets / total market value of portfolio.

Weight of Asset Class in Complete Portfolio

Total amount invested in equity / total market value of portfolio.

Risk-Free Asset

One with a certain rate of return: often taken to mean short-term T-bills.

Risk Premium

E(rp) - rf.

Expected Return on the Complete Portfolio

E(rc) = y(E(rp)) + (1 - y)rf.

Risk of Complete Portfolio

σc² = y²σp.

Slope (Sharpe Ratio)

(E(rp) - rf)/Op.

Investment Opportunity Set

Set of feasible expected return and standard deviation pairs of all portfolios resulting from different values of y.

Capital Allocation Line (CAL)

A graph showing all feasible risk-return combinations of risky and risk-free assets.

Risk Tolerance and Asset Allocation

As the allocation to the risky asset increases, expected return increases and so does volatility.

MaxU

E(rc) - Aσc² = rf + y(E(rp) - rf) - Ay²σ²p/2.

Optimal Position in Risky Asset (y*)

y* = (E(rp) - rf) / Aσ²p.

Passive Strategy

Describes a portfolio decision that avoids any direct or indirect security analysis.

Capital Market Line (CML)

A capital allocation line provided by the market-index portfolio.

Investment Policy

The basic framework involves dividing the investment process into 4: Specifying objectives, Specifying constraints, Formulating policy, Monitoring and updating the portfolio as needed.

Accumulation Phase

Early to middle years with low net worth and a long time horizon.

Consolidation Phase

Mid-point and later where earning exceeds needs.

Spending Phase

Earnings have mostly ceased with a shorter time horizon.

Prudent Investor Rules

An individual confers legal title to property on another person.

Mutual Funds

Pools of investors' money.

Pension Funds (Defined Benefit)

Employer has an obligation to provide specified annual retirement benefit.

Endowment Funds

Orgs chartered to use their money for specific nonprofit purposes.

Life Insurance Companies

Should exceed the new money rate by sufficient margin to meet expense and profit objectives.

Types of Securities

Include underlying securities, bonds, common equity, preferred equity, derivative securities, structured products/hybrids.

Characteristics of Bonds

A security issued by a borrower that obligates the issuer to make specified payments to the holder over a specific period.

Liquidity

Ease and speed with which an asset can be sold and still fetch a fair price.

Investment Horizon

Planned liquidation date of the investment or a significant part of it.

Prudent Investor Rule

Investors who manage other people's money have a responsibility to restrict investments that would have been approved by a prudent investor.

Investment Policy Statement (IPS)

Strategic guide to the planning and implementation of an investment program.

Policy Statement Components

Include scope and purpose, governance, investment, return, and risk objectives, risk management.

Asset Allocation

Specify asset classes to be included in the portfolio.

Markowitz Portfolio Theory

Mathematical framework that's used to build a portfolio of assets that maximizes the expected return for the collective level of risk.

Optimal Asset Mix

Selecting the efficient portfolio that best meets risk and return objectives while satisfying constraints.

Investment Objectives - Return

Nominal vs. real, pre-tax vs. post-tax, stated return desired.

Investment Objectives - Risk

Investors' Risk Tolerance = willingness + ability.

Efficient Diversification

Investment decisions are viewed as a top-down process.

Security Selection

Selection of individual assets within each asset class.

Optimal Risky Portfolio

Combination of risky assets that provide the best risk-return trade-off (highest Sharpe ratio).

Diversification

Spreading a portfolio over many investments to avoid excessive exposure to any one source of risk.

Market Risk

Risk that remains even after extensive diversification.

Systematic Risk

Risk that is attributable to market-risk sources.

Unique Risk/Firm-specific Risk

Risk that can be eliminated by diversification.

Minimum-Variance Portfolio

Has a standard deviation smaller than that of the individual component assets.

Correlation Coefficients

Range of values for ρD,E: −1.0 ≤ ρ ≤ 1.0.

Portfolio Opportunity Set

The expected return-standard deviation pairs of all portfolios that can be constructed from a given set of assets.

Sharpe Ratio

Higher the Sharpe ratio, the greater expected return corresponding to any level of risk.

Markowitz Portfolio Optimization Model

A method to identify risk-return combinations available from the set of risky assets.

Minimum-Variance Frontier

Graph of the lowest possible portfolio variance that is attainable for a given portfolio expected return.

Efficient Frontier

The portion of the minimum-variance frontier that lies above the global minimum-variance portfolio.

Equally Weighted Portfolio

Portfolio where each asset has an equal weight (wi = 1/n).

Brokered Markets

A market where an intermediary (broker) offers search services to buyers and sellers.

Dealer Markets

Markets where traders buy and sell assets for their own accounts.

Bid Price

Price at which a dealer is willing to purchase a security.

Ask Price

Price at which a dealer will sell a security.

Bid-Ask Spread

The difference between a dealer's bid and ask prices.

Market Order

Order based on volume (quantity to buy or sell) for immediate execution.

Limited Order

Order based on price to buy or sell at a designated price or better.

Short Sell

Sell something you don't have, hoping the price falls, then buy it back for profit.

Short Sell Mechanism

Borrow stock through a dealer, sell it, and close out the position by buying back.

Types of Orders

Include market orders, limited orders, and stop-loss orders.

Buy Stop Loss

Shorting a stock

Commission

Fee to be paid to broker for making the transaction

Spread

Cost of trading with a dealer

Margin Trading

Using only a portion of the proceeds for an investment, and borrowing the remaining component

Minimum Margin

Minimum level the equity margin can be (30% set by the Securities Commission)

Margin Call

Call from the broker for more equity funds

Candlestick Chart

Shows the price movement of a security over a specific time period

Body of a Candlestick

Shows the range in price from open to close

Shadows/Tails of a Candlestick

Show max or min price during the period

Green Candlestick

Bullish sentiment; Close > open

Red Candlestick

Bearish sentiment; Close < open

Doji Candlestick

Occurs when open = close; Very small or almost nonexistent body

Bullish Confirmation

Strong green candle after Doji; Break above Doji high; Increased volume

Bearish Confirmation

Strong red candle after Doji; Break below Doji low; Volume spike

Hammer Candlestick

Bullish reversal candlestick that forms after a downtrend

Hanging Man Candlestick

Bearish warning that occurs after an uptrend

Support

Price area where buying pressure consistently outweighs selling pressure

Resistance

Price area where selling pressure consistently outweighs buying pressure