CS Executive · Corporate Accounting and Financial Management

Security Analysis: formula sheet

Full chapter guide

Key formulas

Undervalued security: Intrinsic value > Market price; Signal to buy. Intrinsic value comes from fundamental analysis.
Overvalued security: Intrinsic value < Market price; Signal to sell or avoid.
Fairly priced security: Intrinsic value = Market price; No gain expected from trading on valuation alone.
Fundamental analysis layers: Economy → Industry → Company (EIC); Top-down order. State all three layers in answers.
Forms of market efficiency: Weak: past prices | Semi-strong: all public information | Strong: all information including private; Each form includes the one before it.
Holding period return: Return = (D + (P1 − P0)) ÷ P0; D is dividend or interest received, P0 is the purchase price, P1 is the end price. Multiply by 100 for a percentage.
Expected return (with probabilities): E(R) = Σ (pi × Ri); Multiply each possible return by its probability and add. Probabilities must total 1.
Expected return (historical data, equal weight): Average return = ΣR ÷ n; Use when past returns are given without probabilities.
Variance (with probabilities): σ² = Σ pi × (Ri − E(R))²; Take the deviation from expected return, square it, weight it by probability, then add.
Standard deviation: σ = √σ²; Same unit as return, so it is easier to interpret. Higher σ means higher risk.
Variance (historical, sample): σ² = Σ (R − average)² ÷ (n − 1); Use n instead of (n − 1) if the question treats the data as the whole population. Follow the question or state your assumption.
Coefficient of variation: CV = σ ÷ E(R); Risk per unit of return. Use it to compare securities with different expected returns. Lower is better.
Value of a redeemable bond: V0 = Σ [I ÷ (1 + kd)^t] + M ÷ (1 + kd)^n, t = 1 to n; I = annual interest (coupon rate × face value), kd = required return, M = redemption value, n = years to maturity.
Annuity-factor form: V0 = I × PVIFA(kd, n) + M × PVIF(kd, n); Use the present value tables given in the exam. This is the fastest way to compute the value.
Irredeemable (perpetual) debenture: V0 = I ÷ kd; Use when there is no maturity date and interest continues forever.
Zero-coupon bond: V0 = M ÷ (1 + kd)^n; No interest is paid. The whole return comes from the gap between price and redemption value.
Semi-annual interest: V0 = (I ÷ 2) × PVIFA(kd ÷ 2, 2n) + M × PVIF(kd ÷ 2, 2n); Halve the interest and the rate, and double the periods. Use only when interest is paid twice a year.
Current yield: Current yield = (Annual interest ÷ Current market price) × 100; Ignores the capital gain or loss at maturity.
YTM (approximate): YTM ≈ [I + (M − P) ÷ n] ÷ [(M + P) ÷ 2]; P = current price. A close estimate, not exact. Use it as a starting rate for trial and error.
YTM by interpolation: YTM = r1 + [(V1 − P) ÷ (V1 − V2)] × (r2 − r1); V1 is the value at the lower rate r1 and V2 the value at the higher rate r2. P must lie between V1 and V2.
Macaulay duration: D = Σ [t × PV(CFt)] ÷ Σ PV(CFt); The denominator is the bond's present value (its price at that yield). t is the year of the cash flow.
Modified duration and price change: Modified duration = D ÷ (1 + y); % change in price ≈ − Modified duration × change in yield; A linear estimate that works for small changes in yield. The minus sign shows prices fall when yields rise.
Dividend discount model (finite holding): P0 = D1 ÷ (1 + ke) + D2 ÷ (1 + ke)² + … + Dn ÷ (1 + ke)ⁿ + Pn ÷ (1 + ke)ⁿ; Use when you are given dividends for a few years and an expected selling price.
Zero growth (constant dividend): P0 = D ÷ ke; Dividend stays the same forever.
Gordon's growth model: P0 = D1 ÷ (ke − g); Valid only when ke > g. D1 = D0 × (1 + g).
Growth rate from retention: g = b × r; b is the retention ratio and r is the return on equity (ROE). Use when growth is not given directly.
Implied cost of equity: ke = D1 ÷ P0 + g; Rearranged Gordon's model, used when market price is given.
P/E valuation: Value per share = EPS × P/E ratio; P/E ratio = market price per share ÷ EPS.
Earnings capitalisation: Value per share = EPS ÷ required earnings yield; Same as using P/E = 1 ÷ earnings yield.
Irredeemable preference share: P0 = Preference dividend per share ÷ kp; Fixed dividend perpetuity.
Redeemable preference share: P0 = Σ Dt ÷ (1 + kp)ᵗ + Redemption value ÷ (1 + kp)ⁿ; Discount the dividends and the redemption amount at the required return.
Simple moving average (SMA): SMA = (P1 + P2 + ... + Pn) ÷ n; P is the closing price of each of the last n periods. Drop the oldest price and add the newest to roll it forward.
Moving average crossover rule: Price > moving average: buy signal. Price < moving average: sell signal.; Signal comes when the price line crosses the average line. Short average crossing above long average is also a buy signal.
Relative Strength Index (RSI): RSI = 100 − [100 ÷ (1 + RS)], where RS = average gain ÷ average loss; Commonly over 14 periods. Above 70 is read as overbought, below 30 as oversold.
Dow Theory trends: Primary (1 year or more) > Secondary (weeks to months) > Minor (under about 3 weeks); Learn the three trends and their durations.
Volume confirmation rule: Price up + volume up = strong. Price up + volume down = weak.; Applies the same way to downtrends.
Weak form efficiency: Price today reflects all past prices and volumes; Technical analysis cannot produce consistent abnormal returns. Supports the random walk idea.
Semi-strong form efficiency: Price today reflects all publicly available information; Neither technical nor fundamental analysis gives consistent abnormal returns. Insiders may still gain.
Strong form efficiency: Price today reflects all information, public and private; Even insider information gives no abnormal return. Generally regarded as the least realistic form.
Random walk: Pₜ = Pₜ₋₁ + random change (unpredictable); Successive price changes are independent. Past changes do not help forecast future changes.
Abnormal return: Abnormal return = Actual return − Expected return; EMH says consistent positive abnormal returns are not available using the information set of that form.
Nesting of forms: Strong ⊃ Semi-strong ⊃ Weak; If a stronger form holds, the weaker forms hold too.
Expected return of a portfolio: Rp = Σ (wi × Ri); wi is the proportion invested in security i. Weights must add up to 1.
Expected return of a security from probabilities: E(R) = Σ (Pi × Ri); Pi is the probability of outcome i.
Variance and standard deviation: σ² = Σ Pi × (Ri − E(R))²; σ = √σ²; Standard deviation is the usual measure of total risk.
Two-security portfolio risk: σp = √(w1²σ1² + w2²σ2² + 2 × w1 × w2 × ρ12 × σ1 × σ2); ρ12 is the correlation coefficient. Equivalent: replace ρ12σ1σ2 with covariance Cov12.
Correlation: ρ12 = Cov12 ÷ (σ1 × σ2); Lies between −1 and +1. At +1 there is no diversification benefit; at −1 risk can be reduced to zero with right weights.
Beta of a security: β = Cov(Ri, Rm) ÷ σm² = ρim × σi ÷ σm; σm² is the variance of market returns.
Portfolio beta: βp = Σ (wi × βi); A simple weighted average.
CAPM: Ke = Rf + β × (Rm − Rf); (Rm − Rf) is the market risk premium. Ke is the required return.
Security market line: Required return = Rf + β × (Rm − Rf); Same equation as CAPM, plotted against beta. Intercept is Rf; slope is the market risk premium.

Quick revision

Fundamental analysis studies economy, industry and company; technical analysis studies price and volume.
Expected return = Σ (probability × return).
Standard deviation is the square root of variance, and it measures total risk.
Bond value = present value of interest payments + present value of redemption value, discounted at the required return.
Zero-coupon bond value = redemption value ÷ (1 + r)ⁿ.
Constant growth model: P₀ = D₁ ÷ (k − g), valid only when k > g.
D₁ = D₀ × (1 + g).
Dow Theory describes primary, secondary and minor trends in the market.
Weak form efficiency says past prices cannot predict future prices; semi-strong adds public information; strong adds all information including private.
CAPM: Expected return = Rf + β × (Rm − Rf).
Beta measures systematic risk, which diversification cannot remove.
Diversification reduces unsystematic risk only.

Common mistakes

Saying technical analysis studies the company's financial statements. Fix: Remember: technical looks at prices and volume only. Financial statements belong to fundamental analysis.
Writing intrinsic value and market price as the same thing. Fix: Intrinsic value is your estimate of worth. Market price is what the share trades at. The gap between them drives the decision.
Taking the simple average of returns when probabilities are given Fix: If probabilities are given, always use the weighted sum Σ p×R.
Forgetting to take the square root, so variance is reported as standard deviation Fix: Write σ² and σ on separate lines. Variance is in squared percent; standard deviation is in percent.
Using the market price or the required return to calculate the annual interest. Fix: Interest is always coupon rate × face value. The required return is used only for discounting.
Adding the redemption value in every year, or forgetting to add it in the last year. Fix: Treat interest as an annuity for n years and the redemption value as a single sum at year n.
Using D0 instead of D1 in Gordon's model Fix: Check the wording. If it says 'has just paid' or 'last dividend', multiply by (1 + g) first.
Forgetting to discount the sale price in the DDM Fix: Discount the expected price at year n by (1 + ke)ⁿ, the same way as the dividend of that year.
Mixing up support and resistance Fix: Support is the floor under falling prices. Resistance is the ceiling over rising prices.
Treating Dow Theory trends as one trend Fix: Always name all three: primary, secondary and minor, with duration and role.

Exam tips

Learn the comparison of fundamental and technical analysis as a five-point list. It is the most likely written question on this topic.
Always include economy, industry and company when you explain fundamental analysis.
Link each efficiency form to the method it challenges. This shows depth beyond definitions.
Write a short conclusion on combining the approaches. ICSI-style answers reward a clear closing line.
Keep short notes to about one third of a page. Use headings for each approach and bullet points for tools.
Write the table in full. Marks are given for each step, so a correct method with a small arithmetic slip still scores.
Learn the systematic and unsystematic lists with one example each. Theory questions often ask for the difference with examples.
State the formula before substituting. Add a one-line conclusion naming the less risky or preferred security.