CFA level 1

Holding period return

HPR = (End Value - Beginning Value + Dividends) / Beginning Value

Continuously Compounded rate of return

R = ln(End Value / Beginning Value)

Value of Perpetual Bonds

V = PMT / r

Geometric Mean

[n-th root of: (1+r₁)(1+r₂)…..(1+r_n)] - 1

Coefficient of Variation

CV = s / X bar

Roy’s Safety first ratio (want the maximum)

(mean - threshold) / sd

Correlation Coeff

rho_A,B = Cov_A,B / sd_Asd_B

Forward and Spot exchange rate

Forward rate = Spot rate * (1 + R_price) / (1 + R_base)

Forward and Spot exchange rate with CPI

Forward rate = Spot rate * (CPI_base) / (CPI_{price currency})

Activity Ratios

Inventory Turnover = COGS / Average inventory

Days of Inventory on Hand = 365 / Inventory Turnover

Receivables Turnover = Revenue / Average Receivables

Days of sales outstanding = 365 / Receivables Turnover

Payables turnover = COGS / Average Payables

Number of days payable = 365 / Payables Turnover

Working Capital Turnover = Revenue / Average working Capital

Fixed asset turnover = Revenue / average fixed net assets(tangible)

Total asset turnover = Revenue / average total assets

Profitability Ratios

Gross Profit Margin = Gross profit / Revenue

Operating Profit Margin = Operating income / Revenue

Pre-tax Margin = EBT / Revenue

Net Profit Margin = Net Income / Revenue

ROA = Net Income / Average total Assets

Operating ROA = Operating income (EBIT) / average total assets

Return on invested capital = after tax operating profit / average long term capital

ROE = Net Income / Average total equity

Return on Common equity = (NI - preferred dividends) / Average common equity

Liquidity Ratios

Current Ratio = Current Assets / Current Liabilities

Quick Ratio = (Current Assets - Inventory) / Current Liabilities

Cash Ratio = (Cash + Short term marketable securities / Current Liabilities

Solvency Ratios

Debt to asset ratio = Total debt / Total Assets

Debt to capital Ratio = Total debt / (Total debt + Total Equity)

Debt to equity Ratio = Total debt / Total Equity

Financial Leverage Ratio = Average total assets / Average total equity

Interest Coverage = EBIT / Interest Payments

Fixed charge coverage = (EBIT + lease payments) / (interest payments + lease payments)

DuPont

2 step: ROE = ROA * Financial Leverage

3 step: ROE = Net Profit Margin * Total Asset Turnover * Financial Leverage

Impairment for US GAAP and IFRS

US GAAP: impairment if book value > un-discounted expected future cash flows (but if we have fair value use that instead)

IFRS: impairment if book value > present value of expected future cash flows

Operating Vs Finance lease

Operating: temporary, no ownership risks

Finance: lessor removes the asset from the balance sheet

• Must be a finance lease if the PV of lease payments >= the value of leased asset

• If the lessor has no other use for asset

Broker call price (share price on margin call) and leverage ratio

Call price = P₀ * (1 - initial margin) / (1 - maintenance margin)

Leverage ratio = 1 / (1 - initial margin)

Operating Profit and Leverage

Operating Profit = [Q * (P - VC)] - FC

Degree of operating leverage (DOL) = % change of operating profit / % change of sales

Degree of financial leverage (DFL) = % change in net income / % change operating profit

Bond Value

P₀ = D₁ / (r - g)

g = ROE * (1 - dividend payout)

div payout = 1 - retention rate

Discount and Add on Yield

Discount Yield = (Assumed days in a year / Days till maturity) * ((FV - PV) / FV)

Add on Yield = (Assumed days in a year / Days till maturity) * ((FV - PV) / PV)

Macaulay Duration, Modified Duration, Money Duration

Macaulay Duration: Discount all PV => find weighting of Each PV => multiply by time to receive CF => sum up

Modified Duration = Macaulay Duration / (1 + YTM/payment periods per year)

Approx Modified Duration = (V^- - V⁺) / (2V₀∆YTM)

Money Duration = Modified Duration * Bond Price

Convexity and % ∆ in price

Convexity = t(t + 1) / (1 + r)²

Weighted Convexity: Find PV weighting of CF => multiply by convexity => sum up

Approx Convexity = (V^- + V⁺ - 2V₀) / (∆YTM²V₀)

% ∆ in price = -annual modified duration * (∆YTM) + 0.5(∆YTM²)(Convexity)

Effective Duration and Convexity and % ∆ in price

Effective Duration(used for bonds with embedded options) = (V^- + V⁺) / (2∆curveV₀)

Effective convexity = (V^- + V⁺ - 2V₀) / (∆Curve²V₀)

% ∆ in price = -annual effective duration * (∆Curve) + 0.5(Effective convexity)(∆Curve²)

Standards of Conduct

1. Professionalism

   1. Knowledge of the law

   2. Independence and Objectivity

   3. Misrepresentation

   4. Misconduct

   5. Competence

2. Integrity of Capital Markets

   1. Material non-public information

   2. Market Manipulation

3. Duties to clients

   1. Loyalty, prudence, and care

   2. Fair dealing

   3. Suitability

   4. Performance representation

   5. Preservation of Confidentiality

4. Duties to Employers

   1. Loyalty

   2. Additional Compensation

   3. Responsibilities of supervisors

5. Investment analysis, recommendation, and actions

   1. Diligence and reasonable bias

   2. Communication with clients and prospective clients

   3. Record retention

6. Conflict of interest

   1. Avoid or disclose conflicts

   2. Priority of transactions

   3. Referral fees

CFA Code of Ethics

1. Act with Integrity

2. Place client interest above your own

3. Use reasonable care/independent judgement

4. Practice and encourage Professionalism

5. Maintain Competence

6. Promote market integrity

7. Preserve Confidentiality