IFoA SA7 cheat sheet

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

Bond price sensitivity: modified duration ≈ Macaulay duration / (1 + y/m); ΔP/P ≈ −D_mod·Δy + ½·convexity·(Δy)².

Equity risk premium = expected equity return − risk-free rate; use long-dated index-linked gilt or swap yields as the risk-free proxy in sterling work.

Yield curve shapes: normal (upward), inverted, and humped; inverted curves historically precede recessions but are an unreliable timing signal.

Credit spread = corporate yield − government yield of matching maturity; spread widens with default probability, loss given default and illiquidity.

Money-market convention: sterling uses ACT/365, US dollar and euro use ACT/360; compounding frequency differences must be normalised before comparison.

Purchasing power parity and interest rate parity link currencies: covered parity implies forward premium ≈ domestic rate − foreign rate.

Emerging-market and high-yield assets carry higher volatility, political/convertibility risk and thinner liquidity than developed-market government debt.

Immunisation requires matching present value, duration and (ideally) convexity of assets to liabilities; it holds only for small parallel yield shifts unless cash flows are matched.

Redington immunisation condition: PV(assets) = PV(liabilities), D_A = D_L, and convexity of assets ≥ convexity of liabilities.

LDI structure: scheme holds growth assets plus a leveraged gilt/swap overlay; the overlay's notional is sized to hedge the interest-rate and inflation sensitivity of the liability.

Defined-benefit funding measures: technical provisions (ongoing), buy-out/solvency basis (prudent, insurer pricing), and accounting basis under IAS 19.

Surplus volatility ≈ (D_L·L − D_A·A)·Δy; a duration gap of zero minimises first-order surplus risk but leaves curve and basis risk.

Cash-flow matching removes reinvestment and price risk for matched liabilities but is costly and inflexible; duration matching is cheaper but needs rebalancing.

Insurers must hold capital against asset-liability mismatch; longer-tailed liabilities (annuities, liability claims) support longer-duration asset backing.

Trigger-based de-risking (funding-level steps) is common in UK pension schemes; each step shifts allocation from return-seeking to matching assets.

Fixed-coupon bond price = Σ C/(1+y)^t + R/(1+y)^n; accrued interest is excluded from the clean price and included in the dirty price.

Forward rate implied by spot curve: (1+s_2)² = (1+s_1)(1+f_{1,2}); bootstrapping recovers spot rates from coupon bond prices.

Black-Scholes call: C = S·N(d1) − K·e^(−rT)·N(d2), with d1 = [ln(S/K) + (r + σ²/2)T]/(σ√T) and d2 = d1 − σ√T.

Put-call parity: C − P = S − K·e^(−rT) for European options on non-dividend-paying stock.

Dividend-discount model: P = D1/(r − g) for constant growth; the terminal value dominates value for long-horizon high-growth stocks.

Interest rate swap value = PV of fixed leg − PV of floating leg; at inception it is zero, and par swap rate equates the two legs.

Credit default swap spread approximates annual default probability × loss given default under simplified assumptions; basis = CDS spread − bond spread.

Option greeks: delta = ∂V/∂S, gamma = ∂²V/∂S², vega = ∂V/∂σ, theta = ∂V/∂t, rho = ∂V/∂r.

Portfolio variance for two assets: σ_p² = w₁²σ₁² + w₂²σ₂² + 2w₁w₂ρσ₁σ₂; diversification benefit rises as ρ falls.

Markowitz efficient frontier: minimum-variance portfolio is the leftmost point; adding a risk-free asset produces the capital market line and tangency portfolio.

Risk budgeting allocates total portfolio risk (e.g. tracking error or VaR) across managers or factors rather than allocating capital alone.

Marginal contribution to risk: MCTR_i = (Σw)_i/σ_p; total risk contribution = w_i·MCTR_i, and contributions sum to portfolio volatility.

Tracking error = standard deviation of active return (portfolio − benchmark); information ratio = active return / tracking error.

Black-Litterman blends market-implied equilibrium returns with investor views, reducing sensitivity to estimation error in mean-variance optimisation.

Rebalancing to target weights controls drift in risk exposure but incurs transaction costs; calendar and threshold rules are the two common approaches.

Liquidity budgeting matches the proportion of illiquid assets to the scheme's expected benefit outgo and collateral calls over stress periods.

Value at Risk is not sub-additive in general and says nothing about the size of losses beyond the confidence level; expected shortfall is coherent.

Hedge ratio for a futures overlay: N = (target beta − current beta) × portfolio value / (futures price × contract multiplier).

Interest-rate swap overlay: pay-fixed swap duration ≈ swap maturity × fixed-leg annuity factor; notional sized to close the duration gap.

Basis risk arises when the hedging instrument and the hedged exposure are not identical (e.g. corporate bond vs government bond futures).

Currency hedge ratio: forward contract notional = foreign-currency exposure × hedge ratio; full hedge removes translation but not economic exposure.

Counterparty risk on OTC derivatives is mitigated by collateral (CSA), central clearing, netting and initial/variation margin.

Stress testing complements VaR: scenario shocks (rate +200bp, equity −30%, credit spread +300bp) reveal tail exposures VaR misses.

Options hedging: delta hedging removes first-order price risk but leaves gamma and vega exposure; dynamic hedging costs rise with volatility.

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

Modified Dietz approximates money-weighted return: (V_E − V_B − CF)/(V_B + Σ w_i·CF_i) with weights based on time in period.

Brinson attribution: allocation effect = (w_p − w_b)(r_b − r_total); selection effect = w_b(r_p − r_b); interaction = (w_p − w_b)(r_p − r_b).

Return decomposition: total return = income + capital gain + currency; currency effect ≈ (1 + local return)(1 + FX return) − 1.

GIPS require composites of all actual, fee-paying, discretionary portfolios, time-weighted returns and defined valuation frequency.

Benchmark must be specified, investable, measurable and consistent with the mandate; a peer-group benchmark is not investable.

Governance: statement of investment principles, clear delegation to managers, and documented monitoring of mandate breaches and style drift.

Attribution should distinguish asset allocation, stock selection and currency, and separate them from benchmark and fee effects.

Solvency II: SCR = min(BSCR, standard formula), with BSCR covering market, credit, life, non-life, health and operational risk, plus adjustment for deferred tax.

Solvency II own funds are split into tiers; tier 1 unrestricted (ordinary share capital, retained earnings) is the highest quality.

Solvency II market risk sub-modules include interest rate, equity, property, spread, currency and concentration risk; symmetric adjustment dampens equity shocks.

Matching adjustment allows firms to match illiquid liabilities with eligible assets and add a spread based on asset credit quality.

UK insurers now report under UK Solvency II (PRA); key changes include a lower risk margin and reformed matching adjustment.

Pension schemes: scheme funding (Part 3 of the Pensions Act 2004 in the UK) requires a funding objective, statement of funding principles and actuarial valuation.

UCITS/AIFMD rules govern fund diversification, liquidity and leverage limits; UCITS must hold diversified liquid assets and meet redemption obligations.

Reporting: Solvency and Financial Condition Report (SFCR) and Quantitative Reporting Templates (QRTs) are public and supervisory disclosures respectively.

Illiquidity premium compensates for inability to trade, valuation uncertainty and long lock-ups; it is hard to separate from leverage and selection effects.

Property valuation methods: income capitalisation (value = net income / yield), comparison and discounted cash flow; yields move inversely to values.

Private equity J-curve: early negative returns from fees and unrealised investments, then positive returns as exits occur; IRR overstates early performance.

Private equity IRR is sensitive to cash-flow timing; modified IRR or public-market equivalent (PME) is used for fair comparison with listed markets.

Infrastructure assets offer long-duration, inflation-linked cash flows suited to matching long-dated liabilities, but carry regulatory and political risk.

Hedge fund strategies: equity long/short, global macro, event-driven and relative value; returns depend on manager skill and leverage, not just beta.

Valuation of illiquid assets relies on periodic appraisals, so reported volatility is smoothed and understates true risk; correlations to listed markets are biased low.

Commitment-based funds require a pipeline of unfunded commitments; over-commitment risk arises if cash calls exceed available liquidity.

Loss aversion: losses are weighted roughly twice as heavily as equivalent gains, producing risk-seeking behaviour in loss domains.

Anchoring, herding, overconfidence and recency bias are common drivers of mispricing and poor allocation decisions.

Prospect theory value function is concave for gains, convex for losses, and kinked at the reference point; framing changes the reference point.

Disposition effect: investors sell winners too early and hold losers too long, contrary to tax-loss harvesting logic.

Actuarial profession: the Actuaries' Code requires integrity, competence, impartiality and compliance; conflicts of interest must be disclosed and managed.

TPR/IFoA guidance: advice to trustees must be objective, documented and based on adequate information; a conflict of interest can be managed but not ignored.

Ethical investment: trustees may consider non-financial factors where they do not conflict with financial duty; ESG factors are increasingly treated as financially material.

Professional judgement must be documented with assumptions, sensitivity analysis and clear communication to the client or trustee board.

Placeholder section retained only if a tenth domain is required by the exam syllabus; content mirrors domain 9 above.

Loss aversion: losses are weighted roughly twice as heavily as equivalent gains, producing risk-seeking behaviour in loss domains.

Anchoring, herding, overconfidence and recency bias are common drivers of mispricing and poor allocation decisions.

Prospect theory value function is concave for gains, convex for losses, and kinked at the reference point; framing changes the reference point.

Disposition effect: investors sell winners too early and hold losers too long, contrary to tax-loss harvesting logic.

Actuarial profession: the Actuaries' Code requires integrity, competence, impartiality and compliance; conflicts of interest must be disclosed and managed.

TPR/IFoA guidance: advice to trustees must be objective, documented and based on adequate information; a conflict of interest can be managed but not ignored.

Ethical investment: trustees may consider non-financial factors where they do not conflict with financial duty; ESG factors are increasingly treated as financially material.