Monday, December 26, 2016

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)

Monday, December 12, 2016

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, St-X) - C0 (profit to call buyer)
    X: strike proce, St: share price at time T , C: option price

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

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

π = -Max(0, X-St) + 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  ct >= max[0, St- X/(1 + rf)t]
american call option  Ct >= max[0, St- X/(1 + rf)t]

european put option pt >= max[0, X/(1 + rf)- St ]

american put option Pt >= max[0, X - St ]

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 + rf)t= p0 + S0
   X treasury bond, Sstock, c0 call option

Put Call Forward parity
  p0  = c+(X - F(0,T))/(1 + rf)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 Vfix = Vfloating

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

Sunday, December 11, 2016

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 = ----------
         Σi=1nPi
2) Equal weighting
            1
  wi = -----
            N

3) Market capitalization weighting
               QiPi
  wi = -------------
         Σi=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 = Σt=1-----------
                       (1+r)t

                        Dt            Pn
  Vi = Σt=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 = Σt=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+zn+Z)N

 z1 .. zn : 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