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Advanced Corporate Finance
Live Session: State Contingent Pricing
Example: Incumbent Ltd. New Product Cash Flows will vary with
State of the Economy (undiversifiable) Competitors’ response (idiosyncratic) Other mean zero events
Conditional Forecasting is Better Separates risks that we do not understand
well… Undiversifiable (priced) risk factors – consider risk
aversion … from situations we can at least draw with
precision Idiosyncratic risk factors – only take expectations
Includes management and strategy into valuation “properly”
For tractability, we need to condition over a limited number of outcomes Easily identifiable risk strands Scenarios
Expected Cash Flows of Incumbent Ltd.
E[CF] Year 1 Year 2 Year 3 Year 4
Prob. of entry
20% 60% 100% 100%
Bull Market $102 $66 $30 $30
Average $48 $24 --- ---
Bear Market
$12 -$4 -$20 -$20
What are the probabilities of the market being bullish /bearish each year?
Conditional E[CF] No Competition With Competition
Bull Market $120 $30
Average $60 ---
Bear Market $20 -$20
PV
High
Hi-Hi
Mid
Low
Low-Low
Many States of the World, Many Prices
State Contingent Claims:
“The price today of a security that pays $1 if (and only if) state A happens, X years from now”
State Contingent Claims
Payoff of state contingent claim
Index Level
X = 1.4 times initial value
$1
What is the current price of this asset?
Where to get State Prices From? Digitals
Call or Put Spreads
Black Scholes Ph = DigitalH Pm = DigitalH – DigitalM Pl = Lend at Rf & Sell (Pm + Ph)
Spreads as a Source of State PricesPayoff of state contingent claim
Index Level
X = 1.4
$1
Payoff of buying call with Strike price X and selling call with strike X+1
Index Level
X
$1
X+1Payoff of buying call with Strike price X and selling call
with strike X+d
Index Level
X
$1
X+d
Black Scholes Pricing Formula
BS as a Source of State Prices (High)
BS as a Source of State Prices (Middle)
Payoff of state contingent claim
Index Level
X = 1.4 initial value
$1
X = initial value
PA = P X=PV(S) – P X=1.4xPV(S)
BS as a Source of State Prices (Middle)
Using SCC to calculate NPVs
SCC Year 1 Year 2 Year 3 Year 4
Bull $0.154613
$102 $66 $30 $30
Average $0.360469
$48 $24 --- ---
Bear $0.394 $12 -$4 -$20 -$20
PV (E[CF])
$48.386 $37.8 $15.7 -$2.679 -$2.435
PV
Pg
Pa
Pl
State Contingent Prices
Pg * Pg
Pg * Pa
Pa * Pa
Pl * Pa
Pl * Pl
Pl * Pg
State Contingent Prices Work as well as… … CAPM … APV … Fama-French 3/4/5 factor model … …
Regardless of what your theory on asset pricing is (no matter how inefficient you think markets are)
A set of state-contingent claim prices can represent your pricing kernel See Huang & Litzenberger (Prentice Hall, 1988) for
the formal proof
… and Better than Most If we do the math, the correct Present Value Is the value of each year 2 cash flow
discounted taking into account its two years of history
Only by making the strong assumption that cash flows react equally to Current economic conditions, than Past economic conditions
Can we claim a single discount rate These models cannot deal with
Term structure of interest rates Term structure of volatility, etc.
PV
Hi A & Lo B
Lo A & Hi B
Lo A & Lo B
Several drivers – Rainbow Options
High A&B
…..
PV
High
Hi-Hi
Mid
Low
Low-Low
State Contingent Strategy: Real Options
Scenario Building: What matters? 3 is not a crowd Think about black swams Be mindful of automatic stabilizers The Grasshoper and the Ant
Aesop v. Michelle Malkin
Part I: The Option to Abandon By the end of year 3 there is competition and
CF<0 PV if abandon after 2 years: $37.8 + $15.7 =
$53.5 Is it better if we abandon after 1 year if
competition enters during year 1? PV = $37.8 + PV(Year 2 | abandon if competition
in Yr 1) PV (…) = Pr (Do not abandon) * E(CF Yr2 if no
competition) Pr(Competion Yr2 | No Year 1 competition) = 0.5
From 0.6 = Pr (year 1 comp) + y * Pr (no year 1competition = 0.8)
The Option to AbandonConditional E(CF in Yr 2 | no competition in Yr 1)
With Competition
Without
Bull Market
0.5 x 30 + 0.5 x 120 = 75 $30 $120
Average 0.5 x 0 + 0.5 x 60 = 30 --- $60
Bear Market
0.5 x (-20) + 0.5 x 20 = 0 -$20 $20
The Value of the Project With fixed strategy ex-ante
$37.8 + $15.7 - $2.679 - $2.435 = $48.386 When abandoning at the end of year 2,
regardless $37.8 + $15.7 = $53.5
When abandoning at the end of year 2, or at the end of year 1 if competition enters $37.8 + $16.3 = $54.1
Part II: Strategy Meets Risk Analysis What if the probability of competitors’ entry
depends on the overall health of the economy? In most cases idiosyncratic factors are related to
priced factors
Year 1 Pr(Entry)
E(CF) Pr(Entry)
E(CF)
Bull Market 40% 84 = .6x120 + .4x30
20% 102 = .8x120 + .2x30
Average 20% 48 = .8x60 20% 48 = .8x60
Bear Market --- 20 20% 12 =.8x20
+ .2x(-20)
States of the World for non-diversifiers You may not care about “market prices for
states” Even if you have a strong view about the
probability of each state Just substitute the “market implied
probabilities” for each players’ subjective ones to price
This allows us to pinpoint the relevant set of differences between players…
… and opens up a world of opportunities for “win-win” contracting!
And that was our Objective!