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security market line (def, equ, chart)
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SML vs CML (risk measure, application, definition, slope) table
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beta (def and change in beta, equ)
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Risks in PE Investing (9)
liquidity risk - not publicly traded
competition environment risk - fewre deals with good prospects
agency risk - principal agent conflict
capital risk - withdrawal of capital due to increase busienss/financial risk
regulatory risk - adverse gov't regulation
tax risk - treatment of returns changes
valuation risk - reflects subjective judgement
diversification risk - poorly diversified across stage, vintage, and strategy
market risk - long term factors such as interest rates/exchange rates
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Costs of PE Investing (8)
Transaction costs - due diligence, bank financing, legal
fund setup-up costs: usually amortized over life of fund
admin costs - custodian, transfer agent, and accounting costs
audit fees: reporting
Management fee = 2% typical
performance fee = 20%
dilution costs : resulting from additional rounds of financing and stock options
placement fees: as much as 2% upfront fee or annual trailer paid to placement agents
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PE Structure
limited partnership provides funding, no active role, limited liability. GP liable for all debts and unlimited liability, 10-12 year lives
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PE Terms (7)
"qualified" investors only with > $1.0 mm in assets
management fees: 1.5-2.0%
carried interest - GP's share of profits
Ratchet - allocation of equity between shareholders and fund management
Hurdle Rate - IRR target before GP can receive carried interest (7-10%)
Target fund size - Signals GP's ability to raise funds, below is negative signal
Vintage: year fund was started
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PE Valuation
NAV with frequent adjustments
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PE Due Diligence
Evaluation of past performance, trends and magnitude
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financial performance of PE Funds (how measured) 2
GIPS since inception IRR
money-weighted return
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Paid-in-Capital (PIC)
percent of capital used by GP
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Distributed to PIC (DPI)
measure LP realized return, cash on cash return
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Residual Value to PIC (RVPI)
measure LP's unrealized return
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Total value to PIC -
measure LP's realized and unrealized return, sum of DPI and RVPI
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carried interest (equ)
Carried Intereset % x (NAV before distributions - committed capital)
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NAV before distributions (equ)
NAV before distributions = previous year NAV after distribution + capital called down - management fee + operating results
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NAV after Distributions (equ)
NAV after distributions = NAV before distributions - carried interest - distributions
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Distributed to PIC (DPI) equ
DPI = cumulative distributions / paid in capital
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Residual Value to PIC (RVPI) equ and def
measures LP's unrealized return
RVPI = NAV after distributions / paid-in-capital
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Total Value to PIC (TVPI)
measures LP's realizsed DPI and unrealized RVPI returns
DPI+RVPI = TVPI
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post-money valuation (equ)
POST = FV / (1+r)^N
the value of the firm today to be future value in X years
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Pre-money valuation (equ)
PRE = POST - INV
value before investment
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required fractional ownership (equ)
f = INV / POST
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shares required for PE firm
Svc = S founders [f/(1-f)]
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stock price per share (equ)
p = INV / Svc
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investor's future wealth (W) equ
W=INV x (1+r)^N
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required fractional ownership for the PE firm (equ)
f = W / FV
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POST-money valuation (IRR) equ
post = P x (Spe + Se)
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contango
 - when futures price > spot prices
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backwardation
futures prices < spot prices
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futures price (equ)
future price = spot price x (1+r)^(T-t)
r = risk free rate
(T-t) represents the time from today (t) to the contract maturity (T) in years
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Roll yield:
roll yield is the return from closing out a maturing futures contract at one price and entering into another contract at another price
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main arguments against commodity futures as asset class (5)
1) commodity prices have tended to decline in the long run
2) roll yield is not guarangeed (and may be eliminated)
3) rolling costs reduce returns
4) rebalancing, rather than any change in the asset price, drives returns
5) commodity futures do not produce cash flows
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main arguments for commodity futures as asset class
short-term portfolio diversification benefits - counter cyclical
long-term - natural hedge against inflation
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Basic HF characteristics
leverage changes in freq and amount used having a significant impact on return and risk of the fund
varied hedging techniques such as short selling with unlimited loss potential, and buying puts with only a premium loss in a rising market
style drifts:
portfolio turnover: rises rapidly during market turmoil
very difficult to evaluate HF performance
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3 hedge fund benchmarks
1) broad based market indexes
2) hedge fund indexes
3) risk free rate
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types of hedge fund risk (7)
short HF history
credit spreads - can narrow or widen for extended periods and became a significant risk factor for FI funds
inter-market correlations - FI correlated with equities
intra-market correlations - even "zero-beta" arb funds have exposure
style drift/leverage: risk-return tradeoff not favorable for manager straying from style that reflects particular expertise, leverage increases risk
fraud risk - manager misrep quals, too good to be true, probably is
operational risk: deficient procedures, counterparty risk
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Meaure risk?
standard deviation: doesn't capture non-symmetrical distribution
maximum drawdown - largest loss in HF history
-doesn't give probability of loss
Value-at-risk - Provides an estimate of both the magnitute and probability of left tail loss over a time horizon
-prediction of future based historical data
-assumes normal distribution
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Default Risk
type of credit risk
borrower does not repay obligation
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Credit spread risk
type of credit risk
credit spread increases, bond value falls and/or bond underperforms benchmark
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downgrade risk
type of credit risk
issue downgraded; bond value falls and/or bond underperforms benchmark
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4 c's of credit analysis
1) Character: management integrity, qualifications, track record, corporate gov structure
2) covenants: terms/conditions of issue restricting some of management's discretion
-affirmative: will do
-negative: can't do
3) collateral: assetss offered as security
4) capacity to pay: ability to generate cash or liquidate assets to repay obligations
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Capacity to Repay factors (5)
industry trends
regulatory environment
operating and competitive position
financial position and liquidity sources
company structure
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Short term solvency ratios (def)
measure firm's ability to liquidate short term assets to meet short term obligations
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current ratio
short term solvency ratio
current ratio = current assets / current liabilities
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acid test ratio or quick ratio
short term solvency ratio
(current assets - inventories) / current liabilities
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capitalization ratios (financial leverage)
measure use of debt in capital structure
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LT debt-to-cap ratio
LT Debt / (LT debt + minority interest - SH's equity)
capitalization ratios (financial leverage)
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Coverage ratios
firm's ability to repay debt out of operating CF
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EBIT Coverage ratio
Coverage ratios
EBIT / annual interest expense
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EBITDA coverage ratio
Coverage ratios
EBITDA / annual interest expense
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S&P Framework (14)
Net income
+ depreciation
+/- other noncash items
Funds from operations
-increase in NWC
Operating Cash Flow
-capital expenditures
Free operating cash flow
- cash dividends
Discretionary cash flow
-acquisitons
+ asset disposals
+other sources (uses)
Prefinancing cash flow
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3 cash flow analysis ratios
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debt service coverage
[free operating cash flow + interest] / [interest + annual principal repayment]
higher better
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debt payback period
total debt / discretionary cash flow
lower better
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3 issues with high yield bond debt structure
1) floating rate: makes scenario analysis under different rates necessary
2) short-term: means analysis of ability to pay off/rollover is necessary
3) seniority: bank debt is repaid first in bankruptcy
point: high yield borrowers typically have more bank debt
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high yield bond, corporate structure issue
high-yield issuers frequently structured as holding companies
requires analysis of subs
do debt convenants have restrictions on dividends to parent? Asset sale? Intercompany loans?
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4 steps of credit analysis for Asset-backed securities
1) collateral quality - most important
2) seller/servicer quality: higher quality means higher rating
3) CF stress/payment structure: CF/repayemnt complex: "Waterfall"
4) legal structure: special purpose entity (SPE)
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municipal bond credit - Tax backed debt def and 4 factors to analyze
secured by some form of tax revenue
1) issuer's debt structure (debt per capita)
2) budgetary policy (balanced budget?)
3) local tax and intergovernmental revenue availablity (tax collection rates)
4) issuer's socioeconomic environment (employment trends)
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municipal bond credit - Revenue Bonds def and 3 factors to analyze
finance specific projects; backed by revenue or specific tax revenue
analysis similar to corp bonds
1) project revenue: Amont, reliability
2) flow of funds structure: will debt repayment be the primary use of rev
3) other covenants (rate covenante, additional bonds test)
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sovereign bond credit analysis - def and 2 risks
debt of foreign national govt
economic risk: ability to meet debt obligations
Political risk: willingness to meet debt obligations
-political stability
-integration into global economy
-internal and external security risks
-form of gov't/degree of participation
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sovereign bond credit analysis
two ratings assigned to each national gov't
government has more control over local currency debt repayment (tax policy, domestic spending)
local currency depreciation increases difficulty of repaying foreign currency debt
(one rating for local currency, one for foreign currency)
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Rating #1 (sov. Debt)
local currency debt ratings
1) political stability
2) income base and growth
3) economic infrastructure
4) tax and budgetary discpline
5) monetary policy
*ceiling of rating 2
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Rating # 2 (Sov. Credit)
balance of payments
external balance sheet
external debt obligations
economic/fiscal policies
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Types of credit - corporate, ABS, tax-based muni, revenue muni, sovereign KEY FACTORS (table)
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2 views of liquidity
traditional view: measured using money aggregates
liquidity as appetite for risk viewed as function of risk aversion. Putting money in shadow bank
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shadow banks
marginal sources of liquidity such as hedge funds, REITs, CDOs, etc
incentive for investors to withdraw when risk increases
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2/28 adjustable rate def(3)
borrowerer puts no money down
interest payments are optional
interest rate is a 2-year teaser that adjusts up
free "at-the-money" option
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3 steps in Minsky's financial instability hypothesis
the hedge unit
the speculative unit
the ponzi unit
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the Hedge Unit
levered investment
backed by sufficient income-generating capacity
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Speculative Unit
riskier than a hedge unit
backed by enough cash flow to pay interest, but not principal
less stable as borrower is speculating that interest rates wont rise and property will not decline
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The Ponzi Unit
riskiest
asset cash flow can't cover interest or principal
speculating that the property value will rise
2006 marginal unit of debt was a ponzi unit in U.S. mortgage markets
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3 factors affecting treasury returns
Factor:interest rate risk measured with
- Rate changes: effective duration
- slope changes: key rate duration
- curvature changes: key rate duration
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bootstrapping
calculating spot rates from securities with different maturities using yields on Treasury bonds from the yield curve
treasury bond yields -> bootstrapping -> spot rate curve (theoretical)
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several options of yields to calculate term structure (4)
all on-the-run treasury securities
on-the-run + selected other treasureies
all treasury securities
treasury strips
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Swap rate curve (LIBOR Curve)
yield curve: typically based on treasury securities
swap rate curve: yield curve based on series of fixed-rate quotes on interest rate swaps
point: increasingly preferred as benchmark
-not affected by government regulation
-more comparable across countries
-quotes at more maturities
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3 term structure theories (why yield curve is shaped what way)
1) pure expectations theories: same return over any investment horizon
2) liquidity theory
3) preferred habitat theory
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Pure expectation theory
main idea: forward rates are solely a function of expected future spot rates
implication: long-term rates = complex mean of future expected short-term rates
problem: assumes no interest rate uncertainty; fails to recognize:
-price risk (if horizon < maturity)
-reinvestment risk (if horizon > maturity)
yield curve implications:
upward sloping: short term rates are going to rise
flat: interest rates stay
downward: interest rates falling
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Liquidity Theory
Main idea: implied forward rate = expectations + liquidity premium
larger for longer maturities
can't tell what expectation are from upward sloping curve (since it could all be liquitiy premium)
however, can say that downward means ST rates expected to fall
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Preferred Habitat Theory
Main idea: implied forward rate = expectations + premium
premium not directly related to maturity
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Effective Duration
measures price risk for small parallel shifts in yield curve
problem: most yield curve shifts have non-parallel charateristics
solution: use key rate duration, measures impact of non-parallel shifts
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Duration Impact equ
D impact = -1 * D * change in Yield
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rate duration
sensitivity of price to changes in single spot rate
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binomial interest rate model
tree of up or down interest rate moves (50% each)
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Nominal Spread
difference between bondyield and yield on comparable-maturity government treasury security
=~z-spread
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z-spread
spread added to each rate on spot rate curve that makes PV of bond CFs equal to market price
spread from each spot rate that makes up for greater discount rate used in market
use for any bond without option
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Option-adjusted spread (OAS)
spread added to each rate in binomial rate tree that makes bond value calculated from binomial model equal to market price
OAS = Z-spread - cost of embedded option
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over or under valued?
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Benchmark interest rates
interpretation of spread depends on benchmark rates used to create interest rate tree
-U.S. treasury or
- Bond sector with higher credit rating
-specific issuer
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backward induction methodology
value bond by moving backward from last period to time zero
things to know:
-value at maturity
-value at any node is average PV of two possible values from next period
-discount rate is forward rate for that node
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call rule:
when firm will exercise call option
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call price:
limit for each node's value
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embedded calls (equ)
investors get a discount equal to call value
Vcall = Vnoncallable - Vcallable
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embedded puts (equ)
V put = V putable - V nonputable
investors pay premium equal to put value
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rate volatility increases? What happens to call/puts
value of embedded call increases, value of callable bond falls
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risks when benchmark = specific issuer
only option risk
ibm bond vs. ibm bond
OAS only shows liquidity
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risks when benchmark = higher-rated bond spread
credit risk and options risk
OAS only represents credit
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Effective Duration (equ) and Effective convexity (equ)
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convertible bond def
bond convertible into fixed number of shares
can't use binomial interest rate model, since depends on stock, not interest rates
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conversion ratio
number of shares per bond
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market conversion price
effective price per share when converting
-market price of bond/conversion ratio
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Conversion value
market price of stock after conversion x conversion ratio
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straight value
PV of CFs if not convertible
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minimum value of a convertible bond
greater of conversion value and straight value
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market conversion premium
market conversion price - market price of stock
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market conversion premium ratio (equ)
market conversion premium / market ratio
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premium payback period
period needed to offset market conversion premium with coupons: market conversion premium / favorable income difference
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favorable income difference (equ)
(ann. $ coupons - [CV ratio x ann. Divs]) / CV ratio
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Premium over straight value: (equ)
(MV of bond / straight value) -1
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(noncallable/nonputtable) convertible bond value equ
BV = straight bond + call on stock
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callable convertible bond value (equ)
CCBV = straight bond + call on stock - call on bond
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CCBV if rate increases? Stock vol increases? Rates volatility increases? rates increase?
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CV bonds does what to downside risk
limits downside rirsk
if stock price is low convertible is still worth something as a bond
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Conditional prepayment rate (CPR)
generic annaul prepayment rate
based on historical rates and expected future economic conditions
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CPR equ
SMM = 1 - (1-CPR)^(1/12)
single monthly mortality rate
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100 PSA def
assumes CPR = .2% for first month
increasing by .2% up to month 30
6% there after
200 PSA = 2 x (CPR of 100 PSA)
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3 main factors affecting prepayments
1) prevailing mortgage rates
2) housing turnover
3) characteristics of underlying mortgages
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characteristics of underlying mortgages (2)
seasoning: prepayments increase as loags season
property location: prepayments are faster in some locations
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Housing turnover
increases as rates fall
increases as economic activity rises
-personal income increases, more refinancing/prepayments
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prevailing mortgage rates
spread between current mortgage rates and original mortgage rates
most important factor, when rates fall, refinancing increases
Path of mortgage rates => refinancing burnout
known as "path dependence"
implication: can't value MBS with the binomial model
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Contraction Risk
average life decreases when rates fall and prepayments increase
lower rates lead to more financing
more financing shortens average MBS life
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Extension Risk
average life increases as rates rise and prepayments fall
rates rise causing prepayment to decline
average MBS life lengthens
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two typical structures of CMOs
sequential pay structure
PAC/support structure
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CMOs
Collateralized Mortgage Obligations
created for investors having different risk needs
CFs reallocated to different tranches, each with different contraction/extension risks
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Basic sequential pay CMO
tranches retired sequentially
all tranches receive interest
shortest receives all principal until paid off
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Risk for long/short tranche
Tranche A (shortest)
high contraction risk, low extension risk
tranche B, opposite
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PAC CMO Structure
PAC tranches: "Guaranteed" principal payments based on sinking fund schedule
PAC tranche has more predictable CFs and average life
support tranche: provides prepayment protection to PAC tranches
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Stripped MBS
principal and interest allocated to separate tranches
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Principal-only strips
receive only principal payments, POs win if rates fall
CF stream increases over time as principal payments increase
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Interest-only strips
receive only interest payments
IOs win if rates rise
CF stream decreases over itme as interest payments decrease
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Agency vs. non-agency (3)
agency: MBS based on underlying loans with gov't guarantee (Fanny may)
non-agency: issued by private entities (Goldman)
non-agency have more credit risk and therefore need credit enhancement
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Commercial MBS (2)
backed by income-producing real estate
apartments, warehouses, shopping centers, hotels
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difference in commercial MBS
vs. residential
non-recourse loan, meaning that analysis is of property income, not borrower metrics
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debt-to-service coverage ratio
loan-to-value ratio
debt-to-service coverage ratio = NOI / debt service (want high)
loan-to-value ratio = mortgage / appraised value (want low)
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CMBS: call protection (2)
1) loan level
-prepayment lockout (2-5 years)
-defeasance
-prepayment penalty points
-yield maintenance charges
2) CMBS structure
-sequential tranches
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asset securitization parties (4)
seller: originates assets/receivables and sells to issuer
issuer SPV: sells ABS securities; buys receivables
investors: buys securities; receives CFs
servicer: collects payments
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two types of tranching
1) prepayment tranching: just like mbs, tranche to redistribute prepayment risk
2) credit tranching
-abs have credit risk , require credit enhancement
-tranching can redistribute
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amortizing assets
payments include principal and interest
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non-amortizing assets
like credit cards: no scheduled principal payments means no prepayment risk
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credit enhancements
type 1: external credit enhancements
1) corporate guarantee by seller
2) bank letter of credit
3) bond insurance
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credit enhancements
type 2) internal credit enhancements
1) reserve funds: cash reserve funds
2) overcollateralization: face value < underlying collateral value
3) senior/subordinated structure: risk tranching
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HEL ABS def and 2 types
Home equity loan
first lien on property owned by borrower with marginal credit history
2 types:
1) closed end: fixed rate, fully amortizing loans
2) open end: revolving equity lines
prepayment and tranching similar to MBS
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Why prepayments not sensitive to rates in HEL or Auto loan
prepayments not sensitive to rates because
-little savings
-high depreciation in early years
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Auto Loan ABS
prepayments significant, but not related to interest rates
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Collateralized debt obligations
ABS collateralized by pool of debt obligations
below investment grade corporate bonds, EM bonds, distresssed, MBS and ABS, etc
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Typical CDO Structure
Senior tranches:70-80% of deal, floating rate
mezzanine tranches: fixed coupon
equity tranche: provides prepayment and credit protection
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Cash flow yield
discount rate that makes market price equal to PV of cash flows (like IRR)
major deficiencies:
-reinvestment assumption: reinvestment risk
-assumed held to maturity = price risk
-CF will be realized = prepayment risk
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zero-volatility spread (z-spread)
spread added to each treasury spot rate, so price = PV of CF
CFY vs. z-spread
CFY: considers one interest rate
Z-spread: considers one interest rate path
-not adequate for valuing BS
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monte carlo simulation model
def, mbs value, oas
computer simulates many rate paths
for each path: MBS value = PV of CF along path
need prepayment model
MBS value = average of path values
OAS: spread so model value = market price
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buy signal using OAS (2)
large OAS
low option cost
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Duration
measures interest rate risk
larger duration = more interest rate risk
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convexity
refines estimate
larger convexity = lower interest rate risk
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When to use which spread measure
nominal-never
z-spread: non callable bonds
OAS: binomial - callable bonds, CFs not path dependent
OAS: Monte Carlo - MBS, CFs are path dependent
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