CFA Level 1 Important Formulas: Last-Minute Revision Guide

CFA Level 1 preparation requires a strong command of formulas. Many questions in Quantitative Methods, Financial Statement Analysis, Corporate Issuers, Fixed Income, Equity, Derivatives, and Portfolio Management are formula-based. During the final revision stage, candidates should revise formulas in a structured way.

This CFA Level 1 important formulas revision guide covers key formulas that are useful for last-minute preparation. These formulas help candidates revise returns, risk, probability, hypothesis testing, regression, ratios, valuation, bonds, derivatives, and portfolio concepts.

Holding Period Return

Holding Period Return measures the return earned during a specific holding period. It includes capital gain and dividend income.

Formula:

HPR = (P1 – P0 + D) / P0

Here, P0 is the initial price, P1 is the final price, and D is the dividend received.

For example, if an investment of ₹100 becomes ₹130 and gives ₹5 dividend, the HPR will be 35%. HPR does not need annualisation unless the question asks for it.

Annualized Return

Annualized return converts a short-term return into a yearly return. It is useful when returns are given for months or quarters.

Formula:

Annualized Return = (1 + R)^(12/m) – 1

Here, R is the return for m months. If a return is given for 3 months, it can be converted into an annual return using this formula.

Geometric Mean Return

Geometric mean is used when returns are given for multiple periods. It gives a more realistic average return because it considers compounding.

Formula:

Geometric Mean = [(1 + R1)(1 + R2)…(1 + Rn)]^(1/n) – 1

This formula is useful when returns include both positive and negative values.

Harmonic Mean

Harmonic mean is used when the average price has to be calculated, especially when equal amounts are invested at different prices.

Formula:

Harmonic Mean = n / Σ(1/xi)

It is commonly used in finance for average cost or average share price calculations.

Sample Variance and Standard Deviation

Variance measures the spread of data around the mean. Standard deviation is the square root of variance.

Sample Variance Formula:

s² = Σ(xi – x̄)² / (n – 1)

For population variance, the denominator is n instead of n – 1.

Downside Deviation

Downside deviation measures only negative deviations from a target return. Positive deviations are ignored.

Formula:

Downside Deviation = √[Σ(xi – target)² / (n – 1)]

This formula helps measure downside risk.

Coefficient of Variation

Coefficient of Variation compares risk with the average return.

Formula:

CV = Standard Deviation / Average Return

A lower CV is preferred because it shows lower risk per unit of return.

Expected Value

Expected value gives the weighted average outcome based on probabilities.

Formula:

E(X) = Σ Pi × Ri

Here, Pi is the probability and Ri is the return in each state.

Conditional Probability

Conditional probability measures the probability of one event happening when another event has already happened.

Formula:

P(A|B) = P(A and B) / P(B)

This is useful in probability questions and Bayes theorem-based problems.

Covariance

Covariance shows how two variables move together.

Formula:

Cov(X,Y) = Correlation(X,Y) × σX × σY

Another formula is:

Cov(X,Y) = Σ(xi – x̄)(yi – ȳ) / (n – 1)

If covariance is positive, both variables move in the same direction. If it is negative, they move in opposite directions.

Portfolio Return

Portfolio return is the weighted average return of all assets in the portfolio.

Formula:

Rp = w1R1 + w2R2 + … + wnRn

For two assets:

Rp = wsRs + wbRb

Portfolio Variance

Portfolio variance measures total portfolio risk.

Formula:

σp² = ws²σs² + wb²σb² + 2wswbρsbσsσb

This formula includes weights, individual risks, and the correlation between assets.

Roy’s Safety First Ratio

Roy’s Safety First Ratio compares portfolio return with a target return.

Formula:

Safety First Ratio = (Rp – T) / σp

Here, T is the target return. A higher ratio is preferred.

Standard Error of Mean

Standard error measures the accuracy of the sample mean.

Formula:

SE = σ / √n

As sample size increases, standard error decreases.

Hypothesis Testing Errors

Hypothesis testing includes two common errors.

Type I Error: Rejecting a true null hypothesis.

Type II Error: Failing to reject a false null hypothesis.

Power of test is calculated as:

Power = 1 – β

Test Selection in CFA Level 1

Candidates should remember the basic test selection rules.

Use the Z-test when the population variance is known.

Use the t-test when the sample standard deviation is used.

Use the chi-square test for one variance.

Use the F-test for comparing two variances.

For the correlation test, degrees of freedom are:

df = n – 2

Regression Formula

Regression explains the relationship between dependent and independent variables.

Formula:

y = b0 + b1x

Here, b0 is the intercept and b1 is the slope.

Intercept Formula:

b0 = ȳ – b1x̄

Slope Formula:

b1 = Cov(X,Y) / Var(X)

R-Squared

R-squared shows how much variation is explained by the regression model.

Formula:

R² = SSR / SST

It can also be calculated as:

R² = Correlation²

Basic EPS

Basic EPS measures earnings available to common shareholders.

Formula:

Basic EPS = (Net Income – Preference Dividends) / Weighted Average Number of Shares

Diluted EPS is always less than or equal to Basic EPS.

Cash Flow from Operations

Under the direct method, CFO is calculated as cash inflows minus cash outflows.

Formula:

CFO = Cash Received from Sales – Cash Paid for Expenses, Suppliers, Interest, and Taxes

A useful shortcut is that an increase in current assets reduces cash, while an increase in liabilities increases cash.

Free Cash Flow

Free Cash Flow shows cash available after operating and investment needs.

Formula:

FCF = Net Profit + Non-cash Charges – Change in Working Capital – Capital Expenditure + Interest After Tax

Liquidity Ratios

Liquidity ratios measure the ability to meet short-term obligations.

Current Ratio:

Current Ratio = Current Assets / Current Liabilities

Quick Ratio:

Quick Ratio = (Cash + Marketable Securities + Receivables) / Current Liabilities

Defensive Interval Ratio:

Defensive Interval Ratio = Liquid Assets / Average Daily Expenditure

Activity Ratios

Activity ratios measure how efficiently a company uses assets and manages working capital.

Receivable Turnover:

Receivable Turnover = Sales / Average Receivables

Inventory Turnover:

Inventory Turnover = Cost of Goods Sold / Average Inventory

Payable Turnover:

Payable Turnover = Purchases / Average Payables

Days Sales Outstanding:

DSO = 365 / Receivable Turnover

Days of Inventory:

Days of Inventory = 365 / Inventory Turnover

Cash Conversion Cycle:

Cash Conversion Cycle = Days of Inventory + Days Sales Outstanding – Days of Payables

Profitability Ratios

Profitability ratios measure the earning ability of a company.

Gross Profit Margin:

Gross Profit Margin = Gross Profit / Sales

Operating Profit Margin:

Operating Profit Margin = Operating Profit / Sales

Net Profit Margin:

Net Profit Margin = Net Profit / Sales

Return on Assets:

ROA = Net Profit / Average Total Assets

Return on Equity:

ROE = Net Profit Margin × Asset Turnover × Financial Leverage

This is the three-step DuPont formula.

WACC

Weighted Average Cost of Capital measures the overall cost of financing.

Formula:

WACC = wd × kd × (1 – t) + we × ke

Here, wd is debt weight, kd is cost of debt, t is tax rate, we is equity weight, and ke is cost of equity.

CAPM

CAPM calculates the required return on an asset.

Formula:

Ri = Rf + βi(Rm – Rf)

Here, Rf is the risk-free rate, β is beta, and Rm – Rf is the market risk premium.

If the actual return is above the Security Market Line, the stock is undervalued. If the actual return is below it, the stock is overvalued.

Dividend Discount Model

The one-stage Dividend Discount Model is used to value a stock with constant growth.

Formula:

P0 = D1 / (r – g)

Here, D1 is the expected dividend, r is the required return, and g is the growth rate.

Important condition: r must be greater than g.

Justified Leading P/E Ratio

Formula:

P/E1 = (1 – b) / (r – g)

Here, b is the retention ratio.

Margin Call Price

Margin call price shows the price at which a margin call will occur.

Formula:

Margin Call Price = Pmarket × (1 – Initial Margin) / (1 – Maintenance Margin)

Accrued Interest

Accrued interest calculates interest earned between coupon dates.

Formula:

Accrued Interest = Coupon × Days Held / 365

Forward Rate Formula

Forward rates are calculated using spot rates.

Formula:

(1 + s4)^4 = (1 + s2)^2 × (1 + f2,2)^2

This helps calculate a two-year forward rate after two years.

Duration and Convexity

Duration measures bond price sensitivity to interest rate changes.

Modified Duration Formula:

Modified Duration = Macaulay Duration / (1 + YTM)

Approximate price change can be calculated as:

ΔP ≈ – Duration × Δy + 1/2 × Convexity × (Δy)²

Expected Loss

Expected loss is used in credit risk.

Formula:

Expected Loss = Probability of Default × Loss Given Default

Credit spread is often linked with expected loss.

Futures Valuation

Formula:

Value = S + PV(Cost) – PV(Benefit) – PV(Future Price)

Here, S is spot price. Costs and benefits are adjusted using present value.

Option Payoff Formulas

Call Option Payoff:

max(0, S – X)

Put Option Payoff:

max(0, X – S)

Here, S is the stock price, and X is the strike price.

Payoff is different from profit. Profit is calculated after subtracting the premium.

Put-Call Parity

Formula:

C + PV(X) = P + S

Or:

C = P + S – PV(X)

Here, C is the call price, P is the put price, S is the spot price, and PV(X) is the present value of the strike price.

Risk-Neutral Probability

Risk-neutral probability is used in binomial option pricing.

Formula:

p = (1 + rf – d) / (u – d)

Here, u is the up factor, d is the down factor, and rf is the risk-free rate.

Candidates should revise formulas with small examples. This helps in understanding the application. Do not only memorise formulas without knowing the terms used in them.

During the final days, focus more on returns, risk, probability, ratios, WACC, CAPM, DDM, bond formulas, and option payoffs. These areas are commonly used across different CFA Level 1 topics.

Also, practice calculator-based questions. Formula knowledge is useful only when candidates can apply it quickly in the exam.