IFoA SP10 cheat sheet

Real return ≈ nominal return − inflation; Fisher: (1+nominal) = (1+real)(1+inflation).

Nominal yields embed expected inflation plus an inflation risk premium; index-linked bonds strip out expected inflation but retain real yield and inflation-risk compensation.

Central bank policy rates transmit via the yield curve, credit spreads, FX and equity discount rates; duration measures the price sensitivity of a bond to a 1 bp parallel shift.

Regulatory capital frameworks (Solvency II SCR, Basel, IAS 19 for pension liabilities) shape asset demand and therefore equilibrium prices.

Liquidity premium: illiquid assets trade at a yield premium that compensates for transaction costs and forced-sale risk.

Business cycle: equities typically lead the cycle, credit spreads widen before default rates rise, and government bonds rally in risk-off phases.

Investor time horizon, tax position and liability profile determine the relevant risk-free benchmark, not a single market index.

Term structure theories: pure expectations (forward rates are unbiased), liquidity preference (upward bias), segmented markets (supply/demand by maturity).

Equity risk premium = expected equity return − risk-free rate; historical excess returns are a noisy estimator of the forward premium.

Bond pricing: price = Σ C/(1+y)^t + F/(1+y)^n; Macaulay duration = Σ t·PV(CF_t)/price, modified duration = Macaulay/(1+y/m).

Convexity adjustment: ΔP/P ≈ −D_mod·Δy + ½·C·(Δy)²; convexity is valuable when yields fall and costly when they rise.

Credit spread decomposition: expected default loss ≈ PD × LGD; the remainder is risk premium and liquidity compensation.

Property valuation approaches: income capitalisation (value = net income / yield), discounted cash flow, and comparable transactions.

Alternative assets (private equity, infrastructure, hedge funds) report smoothed valuations, understating volatility and correlation with listed markets.

FX: covered interest parity links forward premium to the interest rate differential; uncovered parity is a long-run, not short-run, relationship.

Commodities: roll yield from futures curve shape (backwardation positive for long holders) plus spot return plus collateral return.

Surplus = assets − liabilities; the surplus-efficient frontier minimises surplus risk for a given expected surplus return.

Immunisation: match present value, duration and convexity of assets to liabilities; requires duration matching and convexity of assets ≥ liabilities.

Cash flow matching (dedication) removes reinvestment and interest rate risk for fixed, certain liability outflows.

LDI: use swaps, repo and long-dated bonds to extend duration without requiring full physical bond funding.

Pension scheme funding: technical provisions discount rate, deficit recovery plan and sponsor covenant jointly determine the risk budget.

Solvency II: SCR uses a 1-in-200 one-year VaR; matching adjustment and volatility adjustment reduce eligible own funds volatility.

Liability relative optimisation: minimise tracking error against the liability benchmark, with constraints on asset class weights and liquidity.

Stochastic ALM output is a distribution of surplus; decision rules select portfolios on ruin probability, contribution volatility and expected return.

Dividend discount model: P = D1/(r−g); Gordon growth requires r > g and a stable payout/retention assumption.

Free cash flow to firm: FCFF = EBIT(1−t) + depreciation − capex − Δ working capital; discount at WACC.

WACC = (E/V)·k_e + (D/V)·k_d·(1−t); use market values, not book values, for weights.

Relative valuation: P/E, EV/EBITDA and P/BV are only comparable across firms with similar growth, risk and accounting policies.

Bond valuation with credit: discount at risk-free rate plus spread; expected loss = PD × LGD × exposure, adjusted for recovery timing.

Property: capitalisation rate = net operating income / value; equivalent yield solves the IRR of the term-and-reversion cash flows.

Private equity valuation uses DCF or multiples, then applies discounts for lack of marketability and control.

Real options add value to projects with staged investment, abandonment or expansion flexibility; value = static NPV + option premium.

Portfolio variance = wᵀΣw; for two assets σ_p² = w1²σ1² + w2²σ2² + 2w1w2ρσ1σ2.

Diversification benefit depends on correlation, not on the number of holdings alone; marginal risk contribution = w_i·(Σw)_i / σ_p.

Mean-variance optimisation is highly sensitive to expected returns; constraints, resampling or Black-Litterman views stabilise weights.

Strategic asset allocation sets long-term policy weights; tactical asset allocation deviates within permitted ranges.

Risk budgeting allocates risk rather than capital; equal risk contribution equalises each asset's marginal risk contribution.

Liquidity budgeting: match illiquid asset commitments to expected cash outflows and collateral calls.

Rebalancing: calendar-based versus threshold-based; wider bands reduce trading cost but allow drift from policy weights.

Factor exposures (value, size, momentum, quality, low volatility) explain much of active return and should be controlled in construction.

VaR at confidence α: the loss not exceeded with probability α over a horizon; it ignores the size of tail losses beyond the threshold.

Expected shortfall (CVaR) = average loss in the worst (1−α) tail; it is sub-additive and coherent, unlike VaR.

Black-Scholes call: C = S·N(d1) − K·e^(−rT)·N(d2); put-call parity: C − P = S − K·e^(−rT).

Delta = ∂V/∂S; gamma = ∂²V/∂S²; vega = ∂V/∂σ; theta = ∂V/∂t; hedge ratios use these sensitivities.

Interest rate swap: fixed-for-floating; value = PV of floating leg − PV of fixed leg, discounted on the appropriate curve.

Basis risk arises when the hedging instrument and the hedged exposure do not move perfectly together (e.g. asset swap versus cash bond).

Counterparty credit risk: exposure (mark-to-market), probability of default and recovery; collateral and netting reduce it.

Stress testing complements VaR: apply historical and hypothetical scenarios to portfolio and to liability simultaneously.

Time-weighted return removes the effect of external cash flows; money-weighted return (IRR) reflects the investor's actual experience.

Modified Dietz approximates money-weighted return: (V_end − V_start − net flows) / (V_start + Σ w_i·flow_i).

Attribution: total excess return = allocation effect + selection effect + interaction; Brinson-Hood-Beebower uses benchmark weights.

GIPS requires composites of all fee-paying discretionary portfolios, defined policies and at least five years of performance (or since inception) for compliant presentation.

Risk-adjusted measures: Sharpe = (R_p − R_f)/σ_p; Treynor = (R_p − R_f)/β_p; information ratio = active return / tracking error.

Governance: statement of investment principles, clear delegation, conflicts of interest policy and independent oversight of valuation.

Custody and asset segregation protect client assets; reconciliation and independent pricing support NAV accuracy.

Stewardship: voting and engagement records should be documented and reported to beneficiaries.