R02 is the CII Diploma's investment principles paper, and it is the most calculation-heavy of the multiple-choice R0 units. There is no formula sheet in the exam, so every equation below needs to be at your fingertips on the day.
This is the complete cheat sheet. Every formula you need for R02, with what each symbol means, a quick worked example, and a link to a deeper walkthrough where one exists.
1. CAPM, Capital Asset Pricing Model
E(Rᵢ) = R_f + βᵢ × (R_m − R_f)
Expected return on a share = risk-free rate + beta × equity risk premium.
Quick example: R_f = 4%, R_m = 9%, β = 1.4 → 4% + (1.4 × 5%) = 11%.
2. Gordon Growth (Dividend Discount) Model
P₀ = D₁ / (r − g)
Share price = next year's dividend ÷ (required return − dividend growth rate).
Quick example: D₁ = 5p, r = 8%, g = 3% → 0.05 / (0.08 − 0.03) = £1.00.
Only valid when r > g. If g ≥ r the model breaks down.
Full Gordon Growth walkthrough →
3. Redemption Yield (Gross Redemption Yield)
GRY ≈ [Coupon + (100 − Price) / n] ÷ Price
Where n = years to maturity.
Quick example: 5% coupon, price £95, 5 years to redemption → [5 + (100 − 95)/5] ÷ 95 = 6.32%.
Full redemption yield walkthrough →
4. Modified Duration
% Price change ≈ −Modified Duration × Δy
Used to estimate the % change in a bond's price for a given change in yield.
Quick example: Modified duration 6.2, yields rise 0.5% → price falls about 6.2 × 0.5% = 3.1%.
Full modified duration walkthrough →
5. Sharpe Ratio
Sharpe = (R_p − R_f) ÷ σ_p
Excess return per unit of total risk (standard deviation). Higher is better.
Quick example: Fund return 9%, R_f = 3%, σ = 12% → (9 − 3) ÷ 12 = 0.50.
Full Sharpe ratio walkthrough →
6. Information Ratio
IR = (R_p − R_b) ÷ Tracking Error
Active return per unit of active risk (relative to a benchmark). Used to judge active manager skill.
Quick example: Fund 8%, benchmark 6%, tracking error 4% → (8 − 6) ÷ 4 = 0.50.
Full information ratio walkthrough →
7. Money-Weighted vs Time-Weighted Return
Money-weighted return (MWR) is the IRR of actual cash flows in and out of a portfolio, influenced by contribution timing. Use it to measure the investor's experience.
Time-weighted return (TWR) chains together the growth of each sub-period between cash flows and removes the impact of contribution timing. Use it to measure the manager's skill.
8. Price-to-Earnings (P/E) Ratio
P/E = Price per share ÷ Earnings per share
A quick valuation metric showing how much investors pay for each £1 of earnings. R02 may give you the share price and EPS and ask for the P/E, or give you the P/E and one of the other two variables.
Quick example: Share price £5.00, EPS 25p → 5.00 ÷ 0.25 = 20×.
R02 often tests whether a P/E is high or low relative to a sector average, or asks you to value a share given its EPS and a benchmark P/E.
9. Holding Period Return (HPR)
HPR = (Income + (P₁ − P₀)) ÷ P₀
The total return, income plus capital gain, over a single holding period.
Quick example: Buy at £2.00, sell at £2.20, dividend 10p → (0.10 + 0.20) ÷ 2.00 = 15%.
9. Real Return (Fisher Equation)
(1 + Real) = (1 + Nominal) ÷ (1 + Inflation)
For quick estimates: Real return ≈ Nominal return − Inflation.
Quick example: Nominal 7%, inflation 3% → 1.07 ÷ 1.03 − 1 = 3.88% (approximation gives 4%).
10. Standard Deviation and Variance
Standard deviation (σ) is the square root of variance. R02 won't ask you to calculate σ from raw data, but you must know:
- Higher σ = higher total risk
- σ is the denominator of the Sharpe ratio
- σ assumes returns are normally distributed. A key R02 critique
11. Beta
β = Covariance(asset, market) ÷ Variance(market)
You won't compute beta from covariances in R02, but you must know that β = 1.0 moves with the market, β > 1 is more volatile, and β < 1 is less volatile. Beta is the input to CAPM.
12. Correlation Coefficient
Correlation ranges from −1 to +1
- +1: assets move exactly together (no diversification benefit)
- 0: uncorrelated
- −1: perfectly negatively correlated (maximum diversification benefit)
You won't calculate it, but R02 routinely tests the implications of correlation for portfolio risk.
What R02 actually tests
A typical R02 sitting will include roughly 20-30 calculation questions out of 100. The exam never asks you to recite a formula in the abstract. It gives you three numbers and asks you to compute the fourth. That means you need to be able to rearrange every equation above to solve for any unknown.
The fastest route to bankable marks is:
- Learn each formula by writing it out, not by reading it.
- Practise rearranging, solve for beta in CAPM, solve for g in Gordon Growth.
- Do at least 50 timed calculation questions in the two weeks before your exam.
A note on accuracy
R02's multiple-choice answers are usually spaced widely enough to make rounding errors safe, but not always. Carry at least four decimal places through your working and only round at the final step.
Bottom line
These thirteen formulas cover essentially every calculation that R02 has thrown at candidates over the last six years. Master them, drill the rearrangements, and the calculation portion of the exam stops being the part you fear and becomes the part you bank.