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!