CFA Finance Ratio

Finance Ratio:

ROE = NI / Equity
ROA = NI / Assets
ROIC = NOPAT / invested capital
  - investment focus
  - invested capital = debt + equity - cash

ROCE = EBIT / Capital Employed
  - pretax, operating focus

Financial Leverage Ratio (Equity Multiplier) =  Avg Total Assets / Avg Total Equity

Asset Turnover = Sales / Assets
Inventory Turnover = COGS / Average Inventory

Interest Coverage Ratio = EBIT/Interest Expense

RI = ((ROIC - WACC) * Assets)
RI = (ROE - r) * BV
RI = NI - r*BV

EVA = NOPAT - WACC * Total Assets

EBIT - Interest Expense = Pretax profit
Pretax profit - tax = NI

Accounting Profit = Normal Profit + Economic Profit

Cash Conversion Cycle
CCC = DOH + DSO - DPO
the smaller the number, the better it is

Good Will:

EQUITY METHOD:

Full Goodwill –> Fair Value - Book Value of Net Identifiable assets (same under IFRS and US GAAP)

And then we allocate the above calculated difference (i.e. the excess purchase price) to subsidiary’s those assets whose fair values exceed their book values. What we get after allocation is the goodwill which is essentially same as the difference between subsidiary’s fair value and parent’s proportionate share of net identifiable assets.

ACQUISITION METHOD:

Full Goodwill –> Fair value of entity - Fair Value of Identifiable Net assets (same under IFRS and US GAAP)

Partial Goodwill –> Purchase Price - Proportionate share of Fair Value of Identifiable Net Assets (only under IFRS)

CFA Level 1 - Part 6 Derivatives and Alternative Investment

Forward

Forward contract : constant price, variable value, price is stated in the contract. At initiation, value is zero. Value of long position is (spot price of underlying - forward price)

Forward rate agreement (FRA)
                                                   
                                         (underlying rate at expiration - forward rate) (days/360)
FRA payoff:  notional principal[-------------------------------------------------------]
                                                     1+underlying rate at expiration(days/360)

FRA notation
1 X 3  expires in 1 month , underlying rate 60 day LIBOR

3 X 6  expires in 3 month , underlying rate 90 day LIBOR

Commodity Forward
Convenience yield, storage cost

For consumer of commodity
continuous form: F = S*e^([r+s-c]t)
discrete form: f0(T)  = S0(1+r)T+FV(storage cost,0,T) - FV(convenience yield,0,T)
s- storage cost
c- convenience yield
cost of carry is (funding costs + storage costs - convenience yield)*T

Future

Contango: current spot price < future price
Backwardation: current spot price > future price

The movement of price as future is expiring. For backwardation, future price converge to prevailing spot price.

Commodity
The relationship between risk free rate, storage costs and convenience yield.

Futures price = spot price(1+r) + storage cost - convenience yield

rolled yield: rolling short term contract into a longer term contract, profit from higher spot price

rolled yield: the difference between the spot price of commodity and futures price in contract. It futures price below spot price, the price of futures contract rolls up to the spot price as futures contract near maturity. The price convergence earns the futures contract bearer a positive roll yield. This explanation is called the theory of storage.

Option

Option profit = π
π = Max(0, S_t-X) - C₀ (profit to call buyer)
    X: strike proce, S_t: share price at time T , C₀ : option price

π = -Max(0, S_t-X) + C₀ (profit to call seller)

π = Max(0, X-S_t) - P₀ (profit to put buyer)

π = -Max(0, X-S_t) + P₀ (profit to put seller)

Option intrinsic value
  call option = underlying current share price - strike price
  put option = strike price - underlying current share price

Option price = intrinsic value + time value
  time value depends on underlying's volatility

European option: exercise only on expiration day

Option value
european call option  c_t >= max[0, S_t- X/(1 + r_f)^t]
american call option  C_t >= max[0, S_t- X/(1 + r_f)^t]

european put option p_t >= max[0, X/(1 + r_f)^t - S_t ]

american put option P_t >= max[0, X - S_t ]

Interest Rate Option                    
  value = notional principal [expiry rate - exercise rate] (days/360)
                                           
Put Call parity (European option only)
  fiduciary call = protective put
  c₀ + X/(1 + r_f)^t= p₀ + S₀
   X treasury bond, S₀ stock, c₀ call option

Put Call Forward parity
  p₀  = c₀ +(X - F(0,T))/(1 + r_f)^T
  X-F(0,T)  bond face value, X exercise price of option, F(0,T) forward price


covered call

protective put

Swap
Swap: value of swap at initiation is zero to both parties at initiation
  interest rate swap V_fix = V_floating

Currency swap:
  For example, Target wants to expand in Europe. They borrows $10mil in US from bondholders, go to Deutsche Bank, and change to €9mil.

Interest rate swap:
  value = notional principal [rate] (days/360)
  For example, GE takes floating rate loan from BofA. It can change the floating rate payment to fixed rate payment by entering into a interest rate swap with JPM.

Eurodollar: dollar deposited outside the US

CFA Level 1 - Part 5 Equity and Fixed Income

Markets
Market execution mechanisms
1) quote driven markets
    customers trade with dealers
2) order driven markets
   use rules to match buyers to sellers
3) brokered markets

Equity Indexing
Index weighting
1) Price weighting
               Pi
  wi = ----------
         Σ_i=1ⁿPi
2) Equal weighting
            1
  wi = -----
            N

3) Market capitalization weighting
               QiPi
  wi = -------------
         Σ_i=1ⁿQiPi

Need of rebalancing for equal weighting
                                                          total shareholder's equity
book value of equity per share = ----------------------------------
                                                         total  shares outstanding


Need to understand the below:
price return of price weighting
price return of equal weighting
total return of equal weighting
price return of market cap. weighting
total return of market cap. weighting


                                                         365
Day Sales Outstanding (DSO) = --------------------
                                                    credit sales/AR

                                                         365
Day Inventory on Hand (DOH) = -----------------
                                                     COGS/Avg Inv

                                                              365
Day payable Outstanding (DPO) = -------------------
                                                          purchase/AP


Operating cycle = DSO + DOH
Cash conversion cycle:  DSO + DOH - DPO

Receivable turnover = credit sales / AR
Inventory turnover = cogs / avg inventory
Receivable turnover = purchases / avg payable

cogs = beginning inv + purchase - ending inv

Equity valuation
Present value model
  dividend discount model
                        Dt
  Vi = Σ_t=1^∞-----------
                       (1+r)^t

                        Dt            Pn
  Vi = Σ_t=1ⁿ----------- + --------
                       (1+r)^t       (1+r)ⁿ

  gordon growth
                   D1
      Vi =   ---------
                  r - g
     g = b * roe
     b: ( 1 - dividend payout ratio)
     g: growth rate
     roe : return on equity

  multi stage dividend growth model

  FCFE model
                          FCFEt
  Vi = Σ_t=1^∞-------------
                             (1+r)^t

Multiplier model
  P/E = p/ (r - g)  p: dividend payout ratio
  P/B
  P/CF
  enterprise value multiple
     EV = debt + preferred stock + common stock - cash
     EV/EBITDA

Asset based model
  estimate the fair value of the companies asset and liabilities
  useful for companies that do not have high level of intangibles or off the book assets

  assets + liabilities
  -------------------------  = asset based value
   shares outsanding

Margin Call:
based on equity in the position
short sell margin call:

 maintenance margin = (Price + initial margin value - current value) / current value

long position margin call:

 maintenance margin = (current value - Price + initial margin value) / current value

Bonds:
tenor: term to maturity
current yield : annual coupon / bond price
yield to maturity : internal rate of return
   higher the ytm, lower the bond price

bond indenture: the bond legal contract
debentures: a type of bond, can be secured or unsecured

Callable bonds
  american call: call at any time on the first cal date
  european call: only once
  bermuda call: call on specified dates

Putable bonds:
  a put provision has value to bondholders

Commercial paper:
  issue $50,000, 180 day USCP, 5%
  interest : 50,000 * 0.05 * 180/360

Contingency provisions:
   clauses in indenture: call provision, put provision, conversion provision

Bond price <--------> market discount rate
                     inverse

Bond price <---------> coupon
                 low coupon, more price volatile
                 given changes in ytm

Bond price <----------> maturity
               longer term bonds, more price volatile

Bond price, market discount rate is CONVEX relationship

Price and yields:
  PVfull = PVflat + AI ,  PVfull : dirty price, PVflat : clean price

  AI = t/T * PMT  , t/T : fraction of the coupon period that has gone by

  PVfull = PV*(1 + r)^t/T

Matric pricing
  use interpolation to find the bond price , from other bond price of tenor and coupon

Z-spread
  yield spread over government spot curve, zero volatility spread
                PMT                   PMT+FV
  PV =  ------------- + --- + ------------
            (1+z₁+Z) ¹             (1+z_n+Z)^N

 z1 .. z_n : benchmark spot rates

Duration: bond price sensitivity to ytm or yield curve
Macaulay Duration
Modified Duration = MacDur / (1+r)
                                    PV_- - PV₊
Approx ModDur = ----------------------
                                 2(ΔYield)(PV₀)

%ΔPVfull = -AnnualModDur * ΔYield

coupon rate ↑ --> MacDur ↓

time to maturity↑ --> MauDur↑

ytm ↑ --> MacDur ↓


                                       PV_- - PV₊
Effective Duration = ----------------------
                                    2(ΔCurve)(PV₀)

Money Dur = AnnualModDur * PVfull

ΔPVfull = -MoneyDur * ΔYield

PVBP = estimate of change in full price given a 1bp change in ytm
                                      PV_- - PV₊
                   PVBP = ----------------------
                                           2

                                     PV_- - PV₊ - 2*PV₀ 
Approx Convexity   = ----------------------
                                      (Yield)²*(PV₀)

ΔPVfull = -MoneyDur * ΔYield + 1/2 * MoneyConv * (ΔYield)²

%ΔPVfull = -AnnualModDur * ΔYield + 1/2 * AnnualModConv * (ΔYield)²


Bonds with embedded option (or floating rate bond) uses effective duration to measure interest rate risk -> effective duration allows for changes in bond's cash flow

Macaulay Dur inversely related to coupon rate, ytm

Macaulay Dur positively related to time to maturity

Convexity is a positive attribute for a bond

more convex --> price ↑ more when interest rate ↓

return impact = -(ModDur * Δspread) 1/2 * ModConv * (Δspread)²

credit migration risk: risk that a bond issuer's creditworthiness may lower

market liquidity risk: risk that the price of investor transact is different from price of market

CFA Level 1 - Part 4 Corporate Finance and Portfolio Management

Corporate Finance

Capital Budgeting

  NPV : Σ_t=1ⁿCF_t/(i + r)_t - outlay

  IRR  : Σ_t=1ⁿCF_t/(i + r)_t = outlay

  Payback Period : number of years to recover original investment, based on cashflows

  Discounted Payback Period : number of years to recover original investment, based on discounted cashflows

  NPV profile: shows a project's NPV graph as function of various discount rates

  Profitability Index = PV of future cash flow / initial investment
                                 = 1 +  ( NPV / initial investment )

Cost of Capital
  WACC = w_dr_d(1 + t) + w_pr_p + w_er_e

Cost of Preferred Stock
 P_p = D_p/r_p

Cost of Debt
  calculate the ytm of bond

Cost of Equity
  cost of debt + risk premium
  CPAM: r_i = r_f +  β(r_m-r_f)
  PV model: P₀ = D₁/(r_e-g)

Pure play method
  Unlevered beta of the company:
  β_u,comparable or called β_assets

  Levered beta of the company:
  β_L,comparable or called β_equity 

  Find unlevered beta:
  β_u,comparable = β_L,comparable / [1 + (1 - Tcomparable)Dcomparable/Ecomparable]

  Lever this beta to get β_project
  β_L,project = β_u,comparable [1+ (1 - Tproj)Dproj/Eproj]

Leverage
Degree of Operating Leverage (DOL): measure of operating risk
Operating leverage involves using a large proportion of fixed costs to variable costs in the operations of the firm.


             % change Operating Income
DOL =  -------------------------------------
                % change sales
                     Q(P-V)                 P: price
         = ------------------------     V: variable operating cost
                 Q(P-V) - F               F: Fixed operating cost

   Fixed operating cost, such as factory depreciation

Degree of Financial Leverage (DOL): measure of financial risk

               % change net Income
DFL =  --------------------------------------
              % change Operating Income
                     Q(P-V)                 P: price
         = ------------------------     V: variable operating cost
                 Q(P-V) - F -C          C: Fixed financial cost

  Fixed financial cost, such as interest payment

                  EBIT
DFL = ------------------------
             EBIT - Interest

Since interest is a fixed expense, DFL magnifies returns.

DTL  = DOL x DFL
                     Q(P-V)                 P: price
         = ------------------------     V: variable operating cost
                 Q(P-V) - F -C          F: Fixed operating cost

Break-Even Point         Operating Breakeven Point
                  F + C                                   F
    Qbe = ---------------         Qobe = -----------
                  P - V                                   P - V

Dividend Payment Chronology:
  dividend declaration date:
     the day dividend is declared
  ex-dividend date ( ex-date ) :
     the 1st day that a share trades without dividend
  holder of record date:
     two business days after the ex-dividend date, the date that a shareholder listed in the corp. record will be deemed to have ownership of the shares for purpose of receiving the upcoming dividend
  payment date:
     the day company sends out dividend payment

treasury stock: shares that have been issued and then repurchased

money market yield:
    FV - Price               360
    -------------  * ------------------------------------
        Price           number of days to maturity

bond equiv. yield: state bond yields into annual yield
    FV - Price               365
    -------------  * ------------------------------------
        Price            number of days to maturity

Portfolio risk and return:
                                                Pt + Dt
     holding period return: R = ----------  - 1
                                                    Po

                                                    1
     arithmetic/mean return: R = ---- Σ_t=1^T Rt
                                                    T

     geometric mean return:  R = ^T√π_t=1^T (1+ Rt) - 1

Portfolio Management

For two asset portfolio,

  σ_p ²= w₁²σ₁²+ w₂²σ₂ ² + 2w₁w₂ COV(R1,R2)

  COV(R1,R2) = ρ₁₂σ₁σ₂

Efficient Frontier is combinations of 2 stocks

Utilities Theory and Indifference Curves

Capital Allocation line: risk free asset + risky portfolio
Capital Market line: risk free asset + market portfolio

    E(Rp) = Rf + σ_p/σ_m [E(Rm) - Rf]

CML with different lending and borrowing rates


systematic risk: risk that cannot be avoided
non-systematic risk: risk that is local

total variance = systematic variance + non-systematic variance

beta: it is a measure of volatility or systematic risk, of a security or a portfolio, compared to market as a whole

  βi = ρ_imσ_i/σ_m        E(Ri) = Rf + β_i [E(Rm) - Rf]

Security market line: use systematic risk, applies to any security
CAL, CML: use total risk, applies to efficient portfolio only

Portfolio performance evaluation:
  Sharpe ratio = (Rp-Rf)/σ_p
  Treynor ratio = (Rp-Rf)/β_p
  M-squared(M²) = (Rp - Rf)σ_m/σ_f - [E(Rm) - Rf]
  Jensen's Alpha = Rp - [Rf + β_p(E(Rm) - Rf)]

Application of Sharpe ratio
The greater a portfolio's sharpe ratio, the better its risk adjusted performance has been. If the addition of a new security lowers the sharpe ratio, it should not be added to the portfolio.

CFA Level 1 - Part 3 Financial Statement Analysis

Financial Statement
Balance sheet: statement of financial position

Income statement: P&L statement

Other comprehensive income:
Other comprehensive income is the difference between net income as in the Income Statement and comprehensive income, and represents the certain gains and losses of the enterprise not recognized in the P&L Account. It is particularly valuable for understanding ongoing changes in the fair value of a company's assets. Items that are other comprehensive income:

• Available-for-sale securities fair value changes that were previously written down as impaired
• Available-for-sale securities unrealized gains and losses
• Foreign currency transaction gains and losses that are hedges of an investment in a foreign entity
• Pension or post-retirement benefit plan gains or losses

Other comprehensive income + net income = comprehensive income

Statement of changes in equity:
Statement of changes in equity, often referred to as Statement of Retained Earnings in U.S. GAAP, details the change in owners' equity over an accounting period by presenting the movement in reserves comprising the shareholders' equity.

Cash flow statement
Financial notes
Management discussion and Analysis
Auditor Report

retained earning = opening re + net income - dividend

NWC = CA - CL
NOWC = (CA - cash) - (CL - interesting bearing debt)
change in NWC = CA - (CL - interesting bearing debt)

Accruals
Unearned(deferred) revenue: company receives cash before earning the revenue, it is a liability
Unbilled(accrued) revenue: company earns revenue before receive the cash, it is an asset
Prepaid expense: company pays cash payment before recognizing expense, it is asset

Accrued expense: company incurs expense but not yet paid, as of end of accounting period, it is liability.

Revenue Recognition
Long term contract
  IFRS:
   percentage of completion on prorated basis:
                      spent cost
   revenue = --------------- * sales price
                      total cost

  installment method:
                         profit
   revenue = --------------- * downpayment
                      selling price 

if outcome of the contract is not sure
  US GAAP: completed contract method. only at contract completion
  IFRS: cost recovery. revenue = cost spent

Earnings per share:
                                       NI - preferred dividend
  Basic EPS = ---------------------------------------------------------
                       weighted avg number of shares outstanding

                                                     NI
 Diluted EPS = ----------------------------------------------------------------------------------------------
(preferred          weighted avg number of shares outstanding +  converted common shares
shares)

                                                   NI - preferred dividend
 Diluted EPS = -------------------------------------------------------------------------------------------------            
 (stock                weighted avg number of shares outstanding +  (new share issued at option
 option)             exercise  - share purchase with cash received upon exercise)*year proportion

                                          NI + after tax interest - preferred dividend
Diluted EPS = ------------------------------------------------------------------------------------------
(convertible      weighted avg number of shares outstanding +  converted common shares
bond)

Financial Assets:

available for sale, measured at fair value
  unrealised gains/losses recognised in other comprehensive income
held for trading, acquired for purpose of selling
    measured at fair value, unrealised gains/losses are recognised as profit/loss on the income statement

Liquidity ratio (short term)
                            current asset
  current ratio = ---------------------
                            current liabilities
                        cash + AR + marketable securities
  quick ratio = ---------------------------------------------
                            current liabilities
                           cash  + marketable securities
  cash ratio = ----------------------------------------------
                            current liabilities

Solvency ratio (long term)
                                debt
  debt to equity = ------------
                               equity

                                     total assets
  financial leverage = ----------------
                                     total equity

                                    debt
  debt to capital = ------------------
                                 debt +  equity

Cash flow statements
In IFRS:
  interest paid    operating/financing
  interest recd    operating/investing
  dividend paid   operating/financing
  dividend recd   operating/investing

Financial Analyis
  total asset turnover = revenue / avg total assets

  ROA =  NI / avg total assets
                  NI           revenue                  avg total assets
  ROE = ----------- * ------------------- *  -----------------------------
              revenue     avg total assets      avg shareholder equity

Inventory
IFRS: LIFO is not allowed

Inventory cost should not include:

• abnormal waste 
• storage costs 
• administrative overheads unrelated to production 
• selling costs 
• foreign exchange differences arising directly on the recent acquisition of inventories invoiced in a foreign currency 

  Transportation cost incurred to ship inv. to customers are an expense, and may not be capitalised in inv. Inventory cost does not include storage cost (unless part of production process), all admin cost, selling cost. These costs are treated as expenses and recognized in the income statement.

IFRS measure inventory as lower of cost or net realisable value (NRV)
  net realisable value = selling price - cost of selling

IFRS can recover previous write-down inv. but to the original write-down value

Any write-down to NRV should be recognized as an expense in the period in which the write-down occurs. Any reversal should be recognized in the income statement in the period in which the reversal occurs

COGS = beginning inv + purchase - ending inv

Long-lived Assets
depreciation methods:
  straight-line method
  accelerated method
  units of production method:
                         original cost - residual value
per unit cost =  ----------------------------------
                                total production

year 1: units produced * per unit cost
year 2: units produced * per unit cost
year 3: etc.

IFRS
- Cost model, historical cost minus accumulated depreciation
- Revaluation model, revalue at fair value less accumulated depreciation (not allowed under US GAAP)

  Revaluation model:

• Increase in carrying amount goes to other comprehensive income, accumulated in equity under account called "revaluation surplus"
• Loss in carrying amount show in income statement

US GAAP
  for machinery
- cost model

For investment property
- IFRS: cost model or fair value model
  fair value model, no depreciation, fair value changes in P/L
- US GAAP: historical cost model

Impairment of assets (unexpected decline in asset value)
IFRS:
- Impairment is recorded when an long-lived asset's carrying amount exceeds the higher of the asset's value in use (discounted present value of the asset's expected future cash flows) and (fair value - costs to sell).
- The impairment loss is measured as the amount by which the asset's carrying amount exceeds its recoverable amount.
- If so happens,  reduce carrying amount to the higher of value in use or (fair value - cost to sell)
- possible to reverse impairment loss

US GAAP:
- compare carrying amount with undiscounted expected future cash flows
- cannot reverse impairment loss

Should include capitalised interest in the calculation of interest coverage ratio, will provide better picture of solvency, eg,  EBIT / interest payment

Expenditures related to long -lived assets are capitalised as part of cost of the assets if provide benefits beyond one year. Otherwise, expenditures are expensed as incurred.

Interest cost related to acquire or construct asset that is long-lived must be capitalised.

Tangible assets - depreciation
Intangible assets - amortization

Income Taxes

for temporary differences, consider:

deferred tax assets / deferred tax liabilities

deferred tax assets: taxes that have been recognised for tax reporting purposes but not yet on income statement

deferred tax liabilities: taxes that is on income statement but not yet payable under the regulations

- accounting profit on income statement
- taxable income subject to income tax
- tax base of asset / liability is the amount the asset / liability is valued for tax purposes, carrying amount is the amount valued to accounting principles.
- deferred tax assets must be assessed for their recover probability, if will be recovered partly, the carrying amount should be reduced.

For US GAAP, it is done through valuation allowance. For valuation allowance, it happens when there is doubt on company's ability to pay the tax in future.

- higher reported tax expense relative to taxes paid will increase deferred tax liability
- lower reported tax expense compared to taxes paid will increase deferred tax asset
- if the deferred tax asset or liability is reversible (the result of timing difference), the deferred tax is a future asset or liability
- if the deferred tax will not reverse in the future, it should be treated as equity
- tax credit that reduce taxes is permanent difference, it does not cause deferred tax.

Long-Term Liabilities

• bonds payable

- issued at premium (interest expense reflects interest payment less amortization of the premium),
  carrying amount > face value
  interest expense < coupon payment
- issued at discount(interest expense reflects interest payment plus amortization of the discount),
  carrying amount < face value
  interest expense > coupon payment

eg, 1,000,000 face value, sales proceeds 957,876
  market interest rate 6%, 5% interest payment
interest payment = 5%*1,000,000
interest expense = 6%*957,876

interest payment -> IFRS, operating or financing cash outflow
   US GAAP, operating cash outflow
interest expense -> income statement

debt extinguishment: net carrying amount of the bond (including bond issuance cost) less the amount required to redeem the bond

• leases

financial(capital) lease
- financial lease is economically similar to borrowing money and buying an asset. lessee reports lease asset and lease payable on balance sheet. On income statement, lessee report interest expense on the debt, and maybe depreciation expense.
- the lessor reports sale of an asset (remove the asset), and record lease receivable

operating lease
- lessee record lease expense on income statement, lease payment on operating cash flow
- lessor record lease rental income on income statement

financial lease has higher debt and expenses than operating lease.

lease payment for interest expense -> operating cash outflow
lease payment for lease liability -> financing cash outflow

Financial Report Quality

• fraud triangle

1. incentive or pressure
2. opportunities
3. rationalise the behaviour

fraud from cash flow statement:
- securitizing of receivables: boost operating cash flow, gain on income statement.
- tax benefits from stock options:reduce tax return reflecting difference between strike price and market price of option, reduce tax payable, increase equity of balance sheet
- financing payables: use 3rd party to pay the payables, and pay the 3rd party later, re-classify account payable to short term loan
- stretch payables: improve cash flow from operations

CFA Level 1 - Part 1 Ethics and Quantitative Methods

Ethics and Professional Standards

Code of Ethics and Standards of Professional Conduct

Guidance for Standards I-VII

  Standards I - Professionalism
    A. Knowledge of the Law
      eg. Applicable law - report violation is not compelled unless such disclose is mandatory under applicable law
    B. Independence and Objectivity
      eg. Travel funding
      eg. allocate shares in over-subscribed IPOs to personal account of investment managers
     eg. pressure on sell-side analyst by buy-side clients
    C. Misrepresentation
      eg. Verify outside information
      eg. Plagiarism
      eg. Work completed for employer
        the firm can use ex-employee's prior analysis without providing attribution
      eg. prohibit assurances on an investment
    D. Misconduct
      eg. background check on prospective employers
      eg. list of violations and assoc. disciplinary actions

  Standards II - Integrity of Capital Markets
    A. Material non-public information
      eg. Non-public info can be used for conducting due diligence, cannot be used to trade securities of the firm
     eg. info disseminated to select group of investors is nonpublic, not necessary to wait for slowest method of delivery
      eg. Mosaic theory
        can use mosaic info in analyst research report, the investment research reports not required to make public
     eg. investment research reports
           no need to make respected analyst report work of material non public info
      eg. Firewall elements
      eg. Source of Information
      eg. A prohibition on all types of proprietary activity when a firm has possession of material nonpublic information is not appropriate.
         proprietary trading procedures, firm acts as market maker can continue to trade
     eg.   CFA member/candidate should encourage the issuing company to make the information public. CFA member/candidate, however, is under no obligation to disseminate the information himself.
    B. Market Manipulation

  Standards III - Duties to Clients
    A. Loyalty, Prudence, Care
      eg. soft commission policies
      eg. proxy voting policies
    B. Fair Dealing
      eg. treat all clients fairly when disseminate investment recommendation or taking investment action. not equally
            allocate IPOs on pro-rata basis to all suitable clients
            trade allocation procedures must be fair/equitable
     eg. different level of service should not be offered to clients selectively
           the different service level should be disclosed to clients
     eg. members may provide more personalised service to clients for a premium fee
    C. Suitability
      eg. understand client risk profile
    D. Performance Presentation
      eg. consider the knowledge of audience to whom the presentation is addressed
    E. Preservation of Confidentiality
      eg. members and candidates must keep client info confidential unless client permits disclosure

  Standards IV - Duties to Employers
    A. Loyalty
    B. Additional Compensation Arrangements
      eg. disclose other benefits from third parties
    C. Responsibilities of Supervisors

  Standards V - Investment Analysis, Recommendations and Actions
    A. Diligent and Reasonable Basis
    B. Communication with Clients and Prospective Clients
    C. Record Retention
        eg. up to 7 years

  Standards VI - Conflicts of Interest
    A. Disclosure of Conflicts
    B. Priority of Transactions
      eg. personal trading secondary to trading for clients
    C. Referral Fees

  Standards VII - Responsibilities as a CFA institute member or candidate
    A. Conduct as members and candidates in the cfa program
    B. Reference to cfa institute, the cfa designation and the cfa program

Global Investment Performance Standards (GIPS)

  firms must meet all requirements set forth in the GIPS standards, and cannot claim partial compliance
  third party verification enhances the credibility of the GIPS compliance

Quantitative Methods

Time value of money
  FV = PV(1+r)   - single period
  FV = PV(1+r)ⁿ - any number of periods
  FV = PVe^rn         - continuous compounding

effective annual rate
         ear = (1 + period rate)ⁿ -1
          n: number of compounding period in a year
         ear = e^rn -1 , for continuous compounding

annuity - finite                     perpetuity - infinite

ordinary annuity - first cash flow one period from now
annuity due - first cash flow happens immediately (t=0)

Annuity formula
     FV = A[(1+r)ⁿ-1]/r

     PV = A[1-(1+r)^-n]/r

Perpetuity formula
     PV = A/r

Discounted Cash flow Applications
   bank discount basis (for T-Bill)
       D = F * R_bd * t/360
         F: face value
         D: dollar discount difference between face value of T-Bill and price
         t: remaining days to maturity

  holding period yield
      hpy = (P₁ - P₀ +D₁) / P₀

  effective annual yield
      eay = (1 + hpy)^365/t -1

  money market yield
      r_mm = hpy * 360/t

  bond equivalent yield: double the semiannual ytm
  (annual percentage rate)

  time weighted return - use geometric mean
    return = [(1+hpy₁)(1+hpy₂)(1+hpy₃)] ^1/3 - 1
      hpy1 : hpy for year 1

Statistics
statistical inference: make estimates about a larger group from a smaller group that is actually observed

sample statistic: a statistic computed from a sample

measurement scales:
  nominal scales: categorise data, no rank
  ordinal scales: sort and order data
  interval scales: ranking data, differences between scale are equal
  ratio scales:  have a true zero point as the origin

median divides a distribution in half
quartiles into quarters
quintiles into fifths
percentiles into hundredths

mean absolute deviation  = Σⁿ_i=1 | x_i - x̄ | / (n)
population variance  = Σⁿ_i=1 (x_i - x̄)² / (n)
sample variance  = Σⁿ_i=1 (x_i - x̄)² / (n-1)

coefficient of variation : CV =  s/x̄

sample skewness: positively skewed, negatively skewed

lognormal distribution is skewed to the right (positively skewed)

kurtosis: shows the probability of extreme outcomes
               shows peakness of a distribution

Probability
Empirical probability: based on historical data and observation
Subjective probability: based on subjective judgement
A priori probability: based on logical analysis

Conditional Probability
          P(A|B) = P(AB) | P(B)

Joint Probability
          P(AB) = P(A|B)P(B)
          P(AB) = P(BA)
          P(A or B) = P(A) + P(B) - P(AB)

Independent Events
          P(AB) = P(A)P(B)
          P(A|B) = P(A)     P(B|A) = P(B)

Total Probability Rule
          P(A) = P(AS) + P(AS^C)
          P(A) = P(AS₁) + P(AS₂) + ... + P(AS_n)
              P(A) is mutually exclusive and exhaustive

Baye's formula
          using the occurrence of event to infer the probability of the scenarios generating it
          update probability based on new info
          P(A) = P(B|C)/P(B) * P(C)

Counting
         labeling problem:  n! / n1!n2! n3! .... nk!
       
         combination: nCr = n!/(n-r)!r!
   
         permutation: nPr = n!/(n-r)!

Odds:
        odds of E = P(E)/[1 - P(E)]
        odds against E = [1 - P(E)]/P(E)


Probability Distributions

Discrete random variable -> probability function

Continuous random variable -> probability density function

Binomial probability
  p(x) = n!/(n-x)!x! * p^x(1-p)^n-x

Binomial distribution
  X ~ B(n,p)

Normal distribution: most used probability density function, kurtosis of 3
  X ~ N(μ, σ²)

Standard normal distribution (μ = 0, σ= 1)

standardizing a RV X : Z = (x -μ)/σ    standard normal RV, Z(0,1)

Mean variance analysis
    SFRatio = [E(Rp) - R_L] / σ _p    (safety first ratio)

    R_L - safety level

Coefficient of variation , CV = S/x̄

Monte Carlo Simulation
  generate large number of random samples from specific probability distribution to represent the risk

Sampling and Estimation

Sampling methods:

• simple random sampling
• systematic sampling: The sampling starts by selecting an element from the ordered sampling frame at random, and then every k^th element in the frame is selected
• stratified sampling: the process of dividing members of the population into homogeneous subgroups before sampling

distribution of sample mean: central limit theorem
  population (μ, σ²) of any distribution
  sample,  mean x̄ , (μ, σ²/n) when sample size is large , n> 30
                                approximate normal distribution

standard error: Sx = S/ √n
                         σx = σ/√n

Confidence Interval
  given probability 1-α , degree of confidence that interval contains the parameter is 100(1-α)%

  x̄ ± Z _α/2 σ/√n   --> 100(1-α)%  (confidence interval for population mean)

    Z _α/2  -- standard normal distribution

  90% - Z_0.05 = 1.65
  95% - Z_0.025 = 1.96
  99% - Z_0.005 = 2.58

  x̄ ± Z _α/2 σ/√n   (population variance is unknown, large sample size)

  x̄ ± t _α/2 σ/√n   (population variance is unknown, large sample size or small sample size but population is normally distributed)

Data mining bias (data snooping bias): finding models by repeatedly searching for patterns
Sample selection bias : survivorship bias
look ahead bias:
time period bias: time period used makes data time period specific

Hypothesis Testing

1. stating the hypothesis
    null hypothesis, H₀, the hypothesis to be tested, H₀ is considered true unless evidence proves it to be false
    alternative hypothesis, H_a, the hypothesis accepted when H₀ is rejected

two sided hypothesis
H₀ : θ=θ₀
H_a : θθ₀

one sided hypothesis
H₀ : θθ₀
H_a : θθ₀

2. define test statistics
       x̄ - μ
      ------------
        s/√n

choose test distribution:  t-test
                                            Z-test
                                           X² test
                                            F-test

3. specify the significance level
    reflect how much sample evidence to reject H₀

reject false H₀
reject true H₀                -- type I error
do not reject false H₀ -- type II error
do not reject true H₀

4. state the decision rule
    statistically significant           ----> reject H₀
    not statistically significant    ----> do not reject H₀

eg. two sided test, 0.05 significant level, H₀ : θ=θ₀
   Z_0.025 = 1.96   ,  Z_-0.025 = -1.96
   Z < -1.96 or Z > 1.96   ---> reject H₀

eg. one sided test, 0.05 significant level, H₀ : θθ₀
   Z_0.05 < 1.645   ,
   Z > 1.645    ---> reject H₀

5. collect data, calculate test statistic

6. make statistical decision

7. make investment decision


p-value, smallest level of significant that H₀ can be rejected

p-value < sig. level --> reject H₀

p-value close to zero, H₀ should be rejected

single mean : t-test, Z-test
         x̄ - μ
      -------------
        s/√n             (n-1) df

difference between means: t-test

single variance:  X²-test
       (n - 1) s²
X²= -----------------
          σ²               (n-1) df

difference between variance: F-test
           s₁²                  (n₁-1) df1
 F= -------------
          s₂²               (n₂-1) df2


Technical Analysis

• Chart Pattern

  head and shoulders: price target = neckline - ( head - neckline)
  inverse head and shoulders: price target = neckline + (neckline - head)

• Technical Indicator

  moving average:
    golden cross: short term moving average cross underneath a long term moving average
    death cross: short term moving average cross above a long term moving average

  bollinger bands: upper boundary band, lower boundary band

  momentum indicators:
    momentum oscillators: overbought, oversold
      M = V/Vx * 100    V - last closing price
                                     Vx - closed price x days ago
      M = (V - Vx) * 100

    relative strength index

    stochastic oscillator  :
      > 70 overbought
      < 30 oversold

    moving average convergence/divergence (MACD)
      difference between short term and long term moving average of price

• Sentiment Indicator

    flow of funds indicators
      arms index (TRIN) = advanced number / declined number
                                         ------------------------------------------------
                                         advanced volume / declined volume

• Cycles

  Kondratieff wave: (K wave)
    54 year economic cycle

• Elliott wave theory

  5 up waves, impulse wave
  3 down waves, corrective wave
  1.618 golden ratio -> fibonacci ratio
  relationship among wave heights is fibonacci ratio