General framework for valuation of risky securities intrinsic value and market value

1

• General framework for valuation of risky
  securities -- intrinsic value and market value

2
Three perspectives on discounted cash flow (CAPM)
valuation of assets with uncertain future cash
flows

• valuation -- any attempts to determine the
  underlying worth or intrinsic value of any
  capital asset
• worth -- is related to the benefit from
  consumption enabled by the assets future payoffs
  or future cash flows
• relationship between future cash flows and worth
  -- is described by some model or function that
  transforms cash flow payoffs into units of value,
  e.g. the CAPM
• three perspectives on these concepts

3
I. Underlying worth or intrinsic value

• underlying worth or intrinsic value -- the value
  that would be created in an open and competitive
  market with full information about the
  probability distribution of future payoffs --
  Pei0
• full information -- the information set created
  with full disclosure of what is known at the
  point of the valuation (t0) --
• information set -- -- would include all
  things useful to the prediction of
• amount and timing of future cash flows
• beta -- uncertainty of flows
• risk free rate
• market price of risk

4
underlying worth --neither right nor left hand
side observable
5
II. Market price

• market price -- the value for which the security
  sells in the open market, the market price
  created through the interplay of actual supply
  and demand -- Pmi0
• public information -- the market uses only the
  information set publicly revealed, but focuses in
  on the same items that give rise to underlying
  worth cash flow expectations, their timing,
  beta, risk free rate, market price of risk --
• rationale for describing Pmi0 -- the market
  realizes that since underlying value is the value
  that ultimately will be revealed (on average in
  the long run) the focus of rational market
  participants must be on those same factors.
  Thus, it must be

6
market price (left hand side observable, but not
right hand side)
7
III. Personal value

• personal value -- the value estimate of the
  investor -- Pki0
• public information and proprietary analysis --
  the investor focuses on public information (re
  FCF, E(ri), etc), which ultimately would affect
  market price, and supplements the public info
  with proprietary analysis(insight, intuition,
  modeling, etc)
• rationale -- since market price is determined by
  all investors who are trying to determine
  underlying value, the investor must also.

8
personal value (both sides observable)

• corollary k can generate abnormal normal (risk
  adjusted) returns only by being better at
  predicting underlying value, Pei0, than is m

9
defining under- and over-valuation

• Fact from the definitions,
• if Pei0 gt Pmi0 -- market has under-valued
  asset
• if Pei0 Pmi0 -- market is in equilibrium
• if Pei0 lt Pmi0 -- market has over-valued
  asset
• Therefore, it follows that, since k is estimating
  e,
• if Pki0 gt Pmi0 -- investor believes market has
  under-valued the asset
• if Pki0 Pmi0 -- investor believes market has
  correctly valued the asset
• (its in equilibrium)
• if Pki0 lt Pmi0 -- investor believes market has
  over-valued the asset
• If investor beliefs are more accurate than market
  consensus, then investor can generate abnormal
  return.

10
Valuing Fixed Income Securities(bonds, notes
mortgages, and other senior claims)
11
Characteristics of Bond Markets

• small on exchanges large in O-T-C trading
• corporates and treasuries quoted without accrued
  interest but settlement (confirmation slip)
  includes accrued interest
• quoted in 1/32s of a dollar, and in 100 par
  value -- 103 and 17/32s for a bond at 1035.31.
• US Treasury market volume is extremely large,
  agency debt quite large, corporate and municipal
  markets have much lower turnover than equities
• market value of corporates is about 2 trillion,
  market value of treasuries is -- well, you know
  what that is from the size of the national debt

12
Valuation methods and techniques
Two fixed income security valuation techniques
are widely used in the financial markets

• I. Absolute Value
• II. Relative Value

13

• I. Absolute Value - FCF/DCF (CAPM) valuation --
  in all respects equivalent to the valuation of
  equities -- based on estimating FCFs and an
  appropriate discount rate, E(ri)
• FCFs are a function of issuers ability to pay
  now and in future -- dependent on
• issuers expected cash flows,
• issuers assets, and access to financial markets
• issuers willingness and ability to comply with
  indenture contract
• E(ri) is determined in the same way as for
  equities -- bonds and stock trade in one,
  integrated market -- beta is relevant and
  determined by comovement of the securitys return
  with the market return -- a function of
• interest rate risk (duration risk, maturity risk)
• cash flow risk (default risk)

14
value of a straight debt security is

• E(Interest) or E(Prin) -- are not the promised
  sums unless the security is default free --
  greater the default expectations the lower the E(
  ) -- thus E( ) reflects the possibility of
  default (the center of the probability
  distribution of cash flows)
• E(ri) -- reflects the risk due to the possibility
  of default (the deviation of possible cash flows
  from their expected values and the comovement of
  those deviations with similar market deviations)
  and the possible variation in bond price due to
  changes in interest rates (SML)

15

• default risk -- is related to the firms
  creditworthiness (ability to pay) -- by custom,
  for convenience, and for those investors
  restricted to a grade of security each issue is
  rated by one or more of four rating agencies
• Standard Poors (AAA, AA, A, BBB, BB, B , CCC,
  CC, C, D, NR) (P-1,P-2) (Credit Watch)
• Moodys (Aaa, Aa, A, Baa, Ba, B, Caa, Ca, C)
• Duff Phelps
• e.g. consider the following latent risks
• bad (good) news on employment and take home pay
  reduces (increases) Dillards revenues and
  squeezes (pushes up) margins -- cash flow
  expectations are reduced (increased) and firm
  finds it more difficult to meet its obligations
  to debtholders -- debt beta is high
• Dillards expands into New York and Boston where
  its store layouts are not (are very) suitable to
  the high rise malls common in those locations,
  cost rise (fall) making those units unprofitable
  (profitable)

16

• duration risk -- measures the exposure to
  interest rate risk through the average length of
  time before receipt of expected cash flows
• duration defined -- for security i

17

• duration for a newly issued 8 coupon security
  with no default risk and 10 years to maturity
  (with all principal repayments at maturity) is
• beta -- on any fixed income security, therefore,
  is a function of default and duration
• beta f (default risk, duration)

18
(No Transcript)
19

• II. Relative value -- yield to maturity, ry,
  defined from current market price and promised
  payments to solve for an IRR
• free cash flows are those promised by the
  contract and not those rationally expected from
  the issuer
• yield to maturity will overstate expected (CAPM)
  returns for any security with a possibility of
  default -- the greater the default the greater
  the overstatement
• thus, at most, y-t-m can be used for relative
  comparisons only

20
(No Transcript)
21
sample yields to maturity
22
value of a complex (debt and equity components to
it) security is