CIMA cheat sheet

FV = PV x (1 + r)^n and PV = FV / (1 + r)^n; the periodic rate r must match the compounding frequency (a monthly rate with monthly periods).

Real return = (1 + nominal)/(1 + inflation) - 1, approximated as nominal minus inflation; nominal return bundles a real return, expected inflation and a risk premium.

The arithmetic mean overstates long-run compound growth; geometric mean = [product of (1 + ri)]^(1/n) - 1 is the correct measure of realised compound return.

Two-asset portfolio variance: variance_p = w1^2 x var1 + w2^2 x var2 + 2 x w1 x w2 x rho12 x sd1 x sd2; at rho = +1 diversification removes no risk.

Sharpe ratio = (Rp - Rf)/sd_p; it uses total risk, so it is the appropriate ranking measure when the portfolio is the investor's entire wealth.

Beta = Cov(Ri, Rm)/Var(Rm); beta captures only systematic risk, which cannot be diversified away and is the risk CAPM compensates.

Primary market issues raise new capital for the issuer (IPO, seasoned offering, new bond); secondary market trades transfer ownership between investors and generate no proceeds to the issuer.

Index weighting: price-weighted is dominated by high-priced shares, market-cap-weighted by the largest firms, equal-weighted requires periodic rebalancing back to equal weights.

Material nonpublic information may not be used or tipped; the mosaic theory permits combining public information with non-material nonpublic information, and conflicts must be disclosed or avoided.

Gordon growth model: P0 = D1/(r - g); it fails when g >= r and is highly sensitive to small changes in the spread (r - g).

Justified leading P/E = payout ratio/(r - g); justified trailing P/E = [payout ratio x (1 + g)]/(r - g).

Bond prices and yields move inversely; approximate percentage price change = -modified duration x change in yield + 0.5 x convexity x (change in yield)^2.

Modified duration = Macaulay duration/(1 + y/m); the Macaulay duration of a zero-coupon bond equals its time to maturity.

Yield to maturity assumes every coupon is reinvested at the YTM; the realised return equals the YTM only if the holding period equals maturity and reinvestment rates do not change.

Current yield = annual coupon/market price; it ignores the capital gain or loss to maturity, so it diverges from YTM whenever a bond trades away from par.

Call payoff at expiry for the buyer is max(0, S - K), put payoff is max(0, K - S); option value = intrinsic value + time value, and time decay erodes long option positions.

Alternative assets (private equity, real estate, hedge funds) carry illiquidity, valuation lags and appraisal smoothing, so reported volatility understates true risk and reported correlations understate stress co-movement.

Prospect theory: the value function is concave over gains, convex over losses and steeper for losses; outcomes are coded as gains or losses relative to a reference point, not to wealth level.

Loss aversion is commonly estimated near 2.0, meaning a loss of one unit requires roughly two units of gain to be equally acceptable.

The disposition effect - selling winners early and holding losers - raises turnover, defers tax losses and leaves the portfolio riskier than intended.

Overconfidence inflates the perceived precision of forecasts; it is associated with excessive trading, concentrated holdings and underestimated downside risk.

Representativeness with base-rate neglect causes extrapolation of recent fund returns, producing return-chasing flows and subsequent underperformance.

Anchoring to a purchase price or a past index level makes investors refuse to sell below the reference value even when fundamentals have deteriorated.

Mental accounting violates fungibility: dividends are spent as income while principal is treated as untouchable, ignoring that total return is what funds consumption.

Herding and feedback trading inflate bubbles; when the crowd reverses, correlated selling amplifies drawdowns beyond fundamental values.

Confirmation bias filters out contradicting evidence, contributing to home bias, familiarity bias and under-diversified portfolios.

The efficient frontier gives the maximum expected return for each level of risk; adding a risk-free asset produces the capital allocation line tangent to it at the maximum-Sharpe portfolio.

Two-fund separation: every efficient portfolio is a combination of the risk-free asset and the same tangency (optimal risky) portfolio; only the proportions differ.

At rho = +1 the risk-return trade-off is a straight line with zero diversification benefit; at rho = -1 portfolio variance can be driven to zero at a specific weight mix.

The CML plots expected return against total risk (standard deviation) and prices efficient portfolios only; the SML plots expected return against beta and applies to all assets.

CAPM: E(Ri) = Rf + beta_i x [E(Rm) - Rf]; alpha = actual return - E(Ri), so a positive alpha plots above the security market line.

Only systematic risk earns an expected premium in equilibrium; unsystematic risk is diversifiable and is not compensated.

IPS constraints are liquidity, time horizon, tax, legal/regulatory and unique circumstances; objectives are stated as a return requirement and a risk tolerance.

Rebalancing to target weights enforces contrarian trading; tolerance-band rules trade less frequently than calendar rules in a trending market.

Tracking error = standard deviation of (Rp - Rb); active risk is bounded by how far policy permits weights to deviate from benchmark weights.

Time-weighted return geometrically links sub-period returns and neutralises the effect of external cash flows; it is the standard basis for manager evaluation and composite reporting.

Money-weighted return is the IRR of the portfolio including the size and timing of contributions and withdrawals; with no external flows it equals the time-weighted return.

Sharpe = (Rp - Rf)/sd_p uses total risk; Treynor = (Rp - Rf)/beta_p uses systematic risk, so rankings can diverge when the two risk orderings differ.

Jensen's alpha = Rp - [Rf + beta_p x (Rm - Rf)]; it is beta-adjusted and therefore assumes the portfolio sits inside a diversified total holding.

Information ratio = (Rp - Rb)/tracking error; M-squared = Rf + (Rp - Rf) x sd_m/sd_p, restating return at benchmark volatility.

Attribution decomposes active return into allocation, selection and interaction effects; the allocation effect uses benchmark returns inside each segment.

Sortino ratio = (Rp - target)/downside deviation; it penalises only returns below the target, unlike Sharpe which penalises all volatility.

Capture ratios compare portfolio to benchmark returns in up and down markets; a favourable profile shows upside capture above 1.0 and downside capture below 1.0.

GIPS requires composites of all actual, fee-paying, discretionary portfolios, time-weighted returns and a defined set of prescribed disclosures and verification claims.

The consulting sequence is discovery and data gathering, then the IPS, then strategic asset allocation, then implementation, then monitoring and review.

Strategic asset allocation drives most of the long-run variability of portfolio returns; tactical tilts are short-horizon deviations measured against policy weights.

Risk tolerance combines ability (financial capacity, horizon, liquidity needs) and attitude (psychological willingness); the binding constraint is the lower of the two.

Manager due diligence assesses philosophy, process, people, performance and price, plus business and operational risk such as asset growth, key-person dependence and compliance.

Implementation shortfall = paper portfolio return - actual portfolio return; its components are delay cost, execution cost and opportunity cost on unfilled shares.

Market impact cost rises with order size relative to average daily volume; VWAP and POV algorithms trade to a schedule or a fixed participation rate respectively.

Fee structures combine an asset-based management fee with a performance fee subject to a high-water mark and sometimes a hurdle rate; fee drag compounds over the horizon.

Monitoring uses tolerance bands around policy weights; rebalancing triggers include a threshold breach, a large external cash flow and a scheduled review date.

Best execution and soft-dollar or commission arrangements must be disclosed; client brokerage may not fund research or services that benefit only the manager.