IFoA SP5 flashcards

32 cards. Read the term and the definition here. The deck at the top of this page is optional.

Sharpe ratio

Excess portfolio return per unit of total volatility: (rp − rf)/σp. It uses total risk, so it is appropriate when the portfolio is the investor's entire holding rather than one component of a diversified fund.

Treynor ratio

Excess return per unit of systematic risk: (rp − rf)/βp. It suits ranking portfolios that sit within a larger diversified fund, where idiosyncratic risk is assumed to be diversified away.

Jensen's alpha

The realised return minus the CAPM-required return: αp = rp − [rf + βp(rm − rf)]. A positive alpha indicates outperformance after adjusting for the portfolio's exposure to market risk.

Information ratio

Active return divided by active risk, where active return is portfolio return minus benchmark return and active risk is the standard deviation of that difference (tracking error).

Modified duration

Macaulay duration divided by (1 + y/m) for m coupons per year. It approximates the percentage price change for a small parallel shift in yields: ΔP/P ≈ −D*·Δy.

Convexity adjustment

The second-order term in bond price sensitivity: ΔP/P ≈ −D*·Δy + ½·C·(Δy)². Convexity makes price rises for a yield fall larger than price falls for an equal yield rise.

Macaulay duration

The present-value-weighted average time to receipt of a bond's cash flows. It is measured in years and equals the maturity of a zero-coupon bond with the same yield.

Immunisation

A liability-matching strategy that sets asset present value equal to liability present value and asset duration equal to liability duration, so the surplus is protected against small parallel yield shifts.

Redington immunisation conditions

Present value of assets equals present value of liabilities, duration of assets equals duration of liabilities, and asset convexity exceeds liability convexity so the surplus is locally convex in yields.

Duration gap

The difference between asset duration and the duration of liabilities scaled by the liabilities-to-assets ratio. A positive gap means net worth falls when interest rates rise.

Liquidity preference theory

Forward rates exceed expected future spot rates because investors demand a term premium for holding longer-dated bonds; the yield curve therefore has an upward bias.

Expectations theory

Long-term yields equal the geometric average of expected future short-term rates, so forward rates are unbiased predictors of future spot rates and the curve shape reflects rate expectations only.

Market segmentation theory

Yields in each maturity segment are set independently by supply and demand from investors confined to that segment, so curves can be any shape regardless of rate expectations.

Preferred habitat theory

Investors prefer particular maturities but will leave their habitat if compensated by a sufficient term premium, combining segmentation with a yield-responsive element.

Forward rate from spot rates

(1 + s2)² = (1 + s1)(1 + f1,2), so f1,2 = (1 + s2)²/(1 + s1) − 1. It is the break-even one-year rate that makes the two-year spot investment equivalent.

Yield to maturity

The single constant discount rate that equates a bond's cash flows to its price. It assumes coupons are reinvested at that same rate and the bond is held to maturity.

Spot rate curve

The set of yields on zero-coupon bonds at each maturity. It is the correct discounting basis for pricing cash flows, unlike the yield to maturity of coupon bonds.

CAPM security market line

E[ri] = rf + βi(E[rm] − rf). Assets plot on a straight line in beta-return space; assets above the line offer positive alpha and assets below offer negative alpha.

Beta

Covariance of asset and market returns divided by market variance. It measures sensitivity to systematic risk, which cannot be diversified away and is therefore the only risk priced by the CAPM.

Arbitrage pricing theory

E[ri] = rf + Σk βik·λk. Expected return is a linear function of exposures to several unspecified systematic factors, with no-arbitrage rather than mean-variance optimisation as the foundation.

Two-asset portfolio variance

σp² = w1²σ1² + w2²σ2² + 2w1w2ρ12σ1σ2. Lower correlation reduces variance for given weights, which is the mathematical source of diversification benefit.

Minimum-variance portfolio

The portfolio on the efficient frontier with the lowest possible standard deviation. For two assets its weight in asset 1 is (σ2² − ρσ1σ2)/(σ1² + σ2² − 2ρσ1σ2).

Efficient frontier

The set of portfolios offering the highest expected return for each level of risk. Portfolios below it are inefficient because a higher return is attainable at the same volatility.

Capital market line

The line from the risk-free rate through the tangency portfolio. It shows the risk-return trade-off for efficient portfolios combining the risk-free asset with the market portfolio.

Systematic versus idiosyncratic risk

Systematic risk affects all assets and is priced; idiosyncratic risk is asset-specific and can be removed by diversification, so it earns no expected return premium.

Real versus nominal return

Real return = (1 + nominal)/(1 + inflation) − 1. It measures the change in purchasing power and is the appropriate target for liabilities expressed in today's prices.

Asset allocation

The split of a portfolio among asset classes such as equities, bonds and property. It is the primary driver of a fund's long-run risk and return profile.

Active versus passive management

Passive management tracks a benchmark at low cost; active management deviates from the benchmark to add alpha, judged by information ratio and tracking error.

Tracking error

The standard deviation of the difference between portfolio and benchmark returns. It quantifies active risk and constrains how far a manager may deviate from the benchmark.

Value at risk

The loss that will not be exceeded over a stated horizon with a stated probability. It reports a single quantile and says nothing about the size of losses beyond it.

Duration matching versus cash flow matching

Duration matching immunises against small parallel shifts using one aggregate statistic; cash flow matching buys bonds whose cash flows exactly meet each liability, removing interest rate risk entirely.

Credit spread

The yield on a corporate bond minus the yield on a comparable government bond. It compensates for default risk, recovery uncertainty and liquidity, and widens in stressed markets.