Investment Inputs and Tools
This domain tests the quantitative tools used to evaluate investments: return and risk measurement, time value of money, valuation, portfolio theory, and performance measurement. Questions often require a calculation or a choice between competing measures.
Return and risk measurement
Holding-period return (HPR) = (ending value - beginning value + income) / beginning value. The arithmetic mean averages periodic returns; the geometric mean is the compound annual growth rate and is lower when returns vary. Standard deviation measures total volatility; beta measures sensitivity to the market. Sharpe ratio = (portfolio return - risk-free rate) / standard deviation; it measures excess return per unit of total risk. Correlation ranges from -1 to +1; diversification benefits are greatest when correlation is low.
Time value and valuation
Future value = present value x (1 + r)^n; present value discounts future cash flows. NPV discounts all project cash flows at the required return; accept positive NPV. IRR is the discount rate making NPV zero; it can mislead when comparing projects of different scale or with nonconventional cash flows. DCF valuation discounts expected cash flows; a bond price is the present value of coupons and principal.
Portfolio and performance tools
CAPM: expected return = risk-free rate + beta x market risk premium. Performance attribution decomposes return into allocation and selection effects. Time-weighted return removes the effect of external cash flows; money-weighted return, or IRR, reflects the investor's actual cash-flow timing.
Worked example
An investor buys a share for 50, receives a 2 dividend, and sells for 55. HPR = (55 - 50 + 2) / 50 = 14%. If the risk-free rate is 3% and the return's standard deviation is 20%, Sharpe = (14% - 3%) / 20% = 0.55. If beta were 1.2 and the market risk premium 5%, CAPM required return = 3% + 1.2 x 5% = 9%. The 14% realized return exceeded the required return, but that alone does not prove skill.
Traps
- Using the arithmetic mean for multiperiod growth.
- Confusing standard deviation (total risk) with beta (systematic risk).
- Mixing time-weighted and money-weighted returns when the client controls cash flows.
- Treating IRR as always superior to NPV.
- Forgetting that correlation, not just the number of holdings, drives diversification.