Investments final study guide

What is the definition of an investment?

A current commitment of money for a period of time to derive future payments that compensate for opportunity cost, inflation, and uncertainty.

What is the Holding Period Return (HPR)?

HPR = Ending Value / Beginning Value. A return multiple over the holding period (e.g. 1.10 = 10% gain).

What is the Holding Period Yield (HPY)?

HPY = HPR − 1 = (Ending Value / Beginning Value) − 1. Converts HPR into a percentage return.

How do you annualise an HPR and HPY?

Annual HPR = HPR^(1/n). Annual HPY = Annual HPR − 1, where n = number of years.

What is the Arithmetic Mean (AM) return and when is it used?

AM = Sum of all annual HPYs / n. Best used as the expected value for a single future year.

What is the Geometric Mean (GM) return and when is it used?

GM = [Product of all annual HPRs]^(1/n) − 1. Best measure of long-term historical performance.

When does AM equal GM, and when does AM exceed GM?

AM = GM only when all period returns are identical. When returns differ, AM is always greater than GM.

How is the expected rate of return calculated for a risky asset?

E(R) = Sum of [probability x possible return] for all outcomes. It is a probability-weighted average of all possible outcomes.

What is the initial margin requirement?

The proportion of the total transaction value that must be paid in cash by the investor (e.g. 50%). The remainder is borrowed from the broker.

What is the maintenance margin and what triggers a margin call?

The minimum required equity-to-total-value ratio after purchase (e.g. 25%). If equity falls below this level a margin call is issued requiring the investor to deposit cash or sell securities.

What are the five key assumptions of Markowitz Portfolio Theory?

1. Investments viewed as probability distributions. 2. Maximise one-period expected utility. 3. Risk measured by variance. 4. Decisions based solely on return and risk. 5. Higher returns preferred for a given risk level.

What is risk aversion and what evidence supports it?

Risk-averse investors choose the lower-risk asset when two assets offer equal returns. Evidence: widespread purchase of life, auto, health and disability insurance.

What is the formula for variance of an individual asset?

Variance = Sum of [probability x (possible return minus expected return) squared] for all outcomes.

What does covariance of returns measure?

How much two assets move together relative to their individual means over time. Positive covariance = same direction; negative = opposite directions.

What is the correlation coefficient and how is it derived from covariance?

r = Covariance(i,j) / (standard deviation i x standard deviation j). Ranges from -1 (perfect negative) to +1 (perfect positive).

What does a correlation of +1 vs -1 mean for portfolio risk?

r = +1 means no diversification benefit. r = -1 means maximum risk reduction possible. Low or negative correlation reduces portfolio standard deviation.

What is the formula for the standard deviation of a two-asset portfolio?

Portfolio SD = sqrt(w1^2 x var1 + w2^2 x var2 + 2 x w1 x w2 x Cov12).

What is the Efficient Frontier?

The set of portfolios offering maximum return for each level of risk, or minimum risk for each level of return. Rational investors only choose portfolios on this frontier.

What is the utility function used for portfolio selection?

U = E(r) - 0.5 x A x variance, where A = risk aversion coefficient (7 = conservative, 1 = aggressive). Optimal portfolio is where the indifference curve is tangent to the efficient frontier.

What is semi-variance as a measure of risk?

A measure that only considers deviations below the mean return. It captures downside risk only, ignoring upside volatility.

What are the seven assumptions of Capital Market Theory (CAPM)?

1. All investors are Markowitz efficient. 2. Borrow/lend at the risk-free rate. 3. Homogeneous expectations. 4. Same one-period horizon. 5. Assets infinitely divisible. 6. No taxes. 7. No inflation or interest rate changes.

What is the Capital Market Line (CML) and its equation?

E(R_port) = RFR + portfolio SD x [(E(R_M) - RFR) / market SD]. Shows the risk-return trade-off for efficient portfolios combining the risk-free asset and the market portfolio M.

What is the Market Portfolio M?

The tangency portfolio on the efficient frontier. In equilibrium it contains ALL risky assets in proportion to their market values. Only systematic risk remains in this portfolio.

What is the difference between systematic and unsystematic risk?

Systematic risk is caused by macroeconomic factors, affects all assets, and cannot be diversified away. Unsystematic risk is firm-specific and is eliminated through diversification.

What is the CAPM (Securities Market Line) equation?

E(R_i) = RFR + beta x [E(R_M) - RFR]. RFR = risk-free rate; beta = systematic risk; [E(R_M) - RFR] = market risk premium.

How is beta calculated?

Beta = Covariance(R_i, R_M) / Variance of the market. Measures the asset's sensitivity to market movements.

What is the key difference between the CML and the SML?

CML uses total risk (standard deviation) and applies to efficient portfolios only. SML uses systematic risk (beta) and applies to individual assets and all portfolios.

How are undervalued and overvalued assets identified on the SML?

Estimated return ABOVE the SML means underpriced (buy). Estimated return BELOW the SML means overpriced (sell). In equilibrium all assets lie exactly on the SML.

What does beta stability research show?

Individual stock betas are unstable over time. Portfolio betas are more stable. High-beta portfolios drift toward 1 and low-beta portfolios also drift up toward 1 over time.

What effect do size, P/E ratio and leverage have on returns beyond CAPM?

Size and P/E have an inverse impact on returns after controlling for beta. Financial leverage also explains cross-sectional returns. These are anomalies not captured by single-factor CAPM.

What are the three major assumptions of APT?

1. Capital markets are perfectly competitive. 2. Investors always prefer more wealth. 3. Asset returns are a linear function of K systematic risk factors.

What does APT NOT assume unlike CAPM?

APT does not require normally distributed returns, a quadratic utility function, or a mean-variance efficient market portfolio.

What is the APT equation and what do the terms mean?

How does APT differ from CAPM in structure?

CAPM has 1 risk factor, uses beta as sensitivity, and RFR as the zero-beta return. APT has K or more factors, uses b_ij as sensitivities, lambda_j as risk premiums, and lambda_0 as the zero-beta return.

What does SMB measure in the Fama-French model?

SMB (small minus big) = return premium earned by small-cap stocks over large-cap stocks. Captures the size effect.

What does HML measure in the Fama-French model?

HML (high minus low) = return premium earned by high book-to-market value stocks over low book-to-market stocks. Captures the value effect.

What is a multifactor model and how does it differ from APT?

The investor explicitly chooses the number and identity of risk factors. APT does not specify them. Equation: R_it = a_i + sum of [factor loading x factor return] + error term.

What are the six factors in the macroeconomic risk factor model?

Market index return, industrial production growth, change in inflation, unexpected inflation, unanticipated credit spread change, and unanticipated term structure shift.

What is an efficient market?

A market where security prices fully and rapidly reflect all available information, making it impossible to consistently earn above-average risk-adjusted returns.

What are the three premises supporting market efficiency?

1. Many competing rational investors independently analyse securities. 2. New information arrives randomly. 3. Investors rapidly adjust prices to reflect new information.

Define the three forms of the Efficient Market Hypothesis.

Weak form: prices reflect all historical market data. Semi-strong: prices reflect all public information. Strong: prices reflect all public and private information.

What trading strategies fail under each form of EMH?

Weak form: technical analysis fails. Semi-strong form: fundamental analysis fails. Strong form: even insider trading fails.

What is an autocorrelation test?

Tests whether today's return is linearly related to past returns. A significant relationship between current and past returns violates weak-form EMH.

What is a runs test?

Counts sequences of same-sign price changes. Fewer runs than expected by chance suggests positive price correlation, violating weak-form EMH. Eliminates the influence of extreme outliers.

What is the momentum effect?

Recent 1 to 12 month winners continue to outperform over the next 1 to 12 months (Jegadeesh and Titman, 1993). Challenges weak-form EMH.

What is the long-term reversal effect?

Over 3 to 5 years, past winners become losers and past losers become winners (DeBondt and Thaler, 1985). Markets overreact in the long run.

What is the disposition effect and how does it explain momentum?

Investors sell winners too soon and hold losers too long. Good news causes prices to rise slowly (under-reaction). Bad news causes prices to fall less than they should. Both create price momentum.

What is an abnormal return (AR)?

AR = security return minus market index return for the same period. Used in event studies to test whether markets adjust quickly to new information (semi-strong EMH test).

What is the January effect?

Stocks especially small-caps earn abnormally high returns in January, attributed to tax-loss selling in December followed by reinvestment. Challenges weak and semi-strong EMH.

What is passive equity portfolio management?

A long-term buy-and-hold strategy that replicates a market index. The manager is judged on how closely the portfolio tracks the index (tracking error), not on outperforming it.

What is active equity portfolio management?

Attempts to outperform a passive benchmark on a risk-adjusted basis by identifying mispriced securities and earning alpha.

What is alpha in active management?

Alpha is the excess return above what is expected for the portfolio's level of risk.

What are the three passive index construction techniques?

1. Full replication: buy every index security in exact proportions. 2. Sampling: buy a representative subset. 3. Quadratic optimisation: minimise tracking error using historical correlations.

What is tracking error?

The standard deviation of the return differential between the managed portfolio and the benchmark.

What are the four asset allocation strategies?

1. Integrated. 2. Tactical. 3. Strategic. 4. Insured.

What is the contrarian investment strategy?

Buy when most investors are most bearish and sell when most are most bullish.

What is the 130/30 strategy?

Long positions of 130% of original capital and short positions of 30%.

What is sector rotation?

Actively shifting portfolio weights between sectors based on the stage of the business cycle.

What is the inverse price-yield relationship for bonds?

As yield rises, bond price falls and vice versa.

What does bond duration measure?

Macaulay Duration measures the bond's interest rate sensitivity.

What is the Macaulay Duration formula?

D = Sum of [cash flow at time t x t / (1+yield)^t] divided by current bond price.

How should duration guide bond selection when rates are expected to change?

If rates are expected to fall, buy bonds with higher duration; if rates are expected to rise, buy bonds with lower duration.

What is a laddered vs a barbell bond strategy?

Ladder: stagger bond maturities evenly; Barbell: concentrate holdings in very short and very long maturities.

What is credit analysis in bond management?

Detailed analysis of the bond issuer to detect expected changes in default risk.

What are the two passive bond management strategies?

1. Buy and hold. 2. Indexing.

What is active bond management and what drives its success?

Active managers beat the benchmark through interest rate anticipation and valuation analysis.

What is a call option?

A contract giving the holder the right to BUY 100 shares at the preset exercise price before expiry.

What is a put option?

A contract giving the holder the right to SELL 100 shares at the preset exercise price before expiry.

What is a protective put strategy?

Hold shares and buy a put option to create a floor on portfolio value.

What is a covered call strategy?

Hold shares and write a call option to earn premium income.

What is a collar agreement?

Buy an out-of-the-money put and sell an out-of-the-money call on the same asset.

How many futures contracts are needed to hedge a portfolio?

n = (Portfolio Value x Portfolio Beta) / (Futures price x contract multiplier).

What is a long straddle and when is it profitable?

Buy a call and buy a put with the same strike and expiry; profits when the stock moves significantly.

What is a short straddle and when is it profitable?

Sell a call and sell a put with the same strike and expiry. Profits when the stock stays near the strike (low volatility).

What is a strangle and how does it differ from a straddle?

Buy an out-of-the-money call and an out-of-the-money put with the same expiry but different strike prices. Lower upfront cost than a straddle but requires a larger price move to profit.

What is a bullish spread vs a bearish spread?

Bullish spread: buy a lower-strike call and sell a higher-strike call, profiting from a moderate price rise. Bearish spread: sell a lower-strike call and buy a higher-strike call, profiting from a moderate price fall.

What is a butterfly spread?

Buy 1 call at a low strike, sell 2 calls at a middle strike, buy 1 call at a high strike. Profits if price stays near the middle strike. Less risk of large losses than a short straddle.

What are the key characteristics of hedge funds?

Large minimum investment; lightly regulated; not public funds; unorthodox strategies and assets; high fees; use leverage and derivatives; focus on absolute returns; low correlation with traditional assets.

What is a high water mark provision in hedge funds?

Performance fees are only charged once all past losses have been fully recovered. The fund NAV must exceed its previous peak before the manager earns a performance bonus.

What is the J-curve effect in private equity?

New PE funds typically show negative returns in early years due to fees and slow deployment, before turning positive as investments mature. The return pattern over time resembles the letter J.

What are the four categories of hedge fund strategies?

1. Equity-based (long/short, market neutral). 2. Arbitrage-based (fixed income, convertible, merger arbitrage). 3. Opportunistic (global macro, managed futures, distressed). 4. Multiple strategies (fund of funds).

What is long/short equity hedge fund strategy?

Identifies mispriced stocks and takes long positions in undervalued stocks and short positions in overvalued stocks. Reduces market exposure while seeking alpha from stock selection.

What is private equity?

Ownership interest in assets not publicly traded. It is illiquid, long-term, involves small investor groups, and typically funds new or restructuring businesses. Offers higher expected returns and diversification benefits.

What are the stages of venture capital funding?

1. Start-up. 2. Development (early growth). 3. Expansion. 4. Mezzanine finance (pre-IPO). The typical exit strategy is through an IPO.

What are the four key lessons from the LTCM collapse?

1. Too much capital exhausts finite arbitrage opportunities. 2. Overconfidence combined with leverage is dangerous. 3. Ensure exit options before problems arise. 4. Markets can remain irrational longer than you remain solvent.

What is the Sharpe ratio and what does it measure?

S = (average portfolio return - RFR) / portfolio standard deviation. Measures excess return per unit of total risk.

What is the Treynor ratio and when should it be used?

T = (average portfolio return - RFR) / portfolio beta. Measures excess return per unit of systematic risk.

What is Jensen's alpha and how is it interpreted?

Alpha = actual return minus CAPM expected return. Positive alpha means the manager outperformed on a risk-adjusted basis.

What is the Information Ratio?

IR = (average portfolio return minus average benchmark return) / standard deviation of excess returns. Measures consistent active outperformance relative to the active risk taken.

What is the Sortino ratio and how does it differ from Sharpe?

Sortino = (average return - minimum acceptable return) / downside risk (semi-deviation). Unlike Sharpe, it only penalizes downside volatility, not upside volatility.

What is the semi-deviation (downside risk) formula?

Semi-deviation = sqrt of [1/n x Sum of (return minus mean return) squared] where the sum only includes periods where return is below the mean.

What is the total rate of return formula for a mutual fund?

R = (Ending price + Dividends + Capital gain distributions - Beginning price) / Beginning price.

What are the two desirable attributes of a portfolio manager?

1. Ability to earn above-average risk-adjusted returns through superior security selection or market timing. 2. Ability to fully diversify the portfolio so that unsystematic risk is eliminated.

What is performance attribution analysis?

Decomposes a portfolio's outperformance into an allocation effect and a selection effect.

What are the six required characteristics of a good benchmark?

1. Unambiguous. 2. Investable. 3. Measurable. 4. Appropriate for the manager's style. 5. Reflective of current investment opinions. 6. Specified in advance.

What are the five Fundamental Principles of Performance Presentation Standards (PPS)?

1. Total return must be used. 2. Time-weighted rates of return must be used. 3. Portfolios valued at least monthly with geometrically linked returns. 4. All actual fee-paying accounts included in composites. 5. Performance calculated after deduction of trading expenses.

What is benchmark error and why does it matter?

Using the wrong risk-free rate or wrong market portfolio proxy distorts beta calculations and shifts the SML, leading to incorrect performance evaluation.