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 1Year 2Year 3Year 4 Prob. of entry20%60%100% Bull Market$102$66$30 Average$48$24--- Bear Market$12-$4-$20 What are the probabilities of the market being bullish /bearish each year? Conditional E[CF]No CompetitionWith 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 Prices Payoff 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+1 Payoff 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 P A = P X=PV(S) – P X=1.4xPV(S)

BS as a Source of State Prices (Middle)

Using SCC to calculate NPVs SCCYear 1Year 2Year 3Year 4 Bull$ $102$66$30 Average$ $48$24--- Bear$0.394$12-$4-$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: $ $15.7 = $53.5  Is it better if we abandon after 1 year if competition enters during year 1?  PV = $ 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 Abandon Conditional E(CF in Yr 2 | no competition in Yr 1) With Competition Without Bull Market 0.5 x x 120 = 75$30$120 Average0.5 x x 60 = 30---$60 Bear Market 0.5 x (-20) x 20 = 0-$20$20

The Value of the Project  With fixed strategy ex-ante  $ $ $ $2.435 = $  When abandoning at the end of year 2, regardless  $ $15.7 = $53.5  When abandoning at the end of year 2, or at the end of year 1 if competition enters  $ $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 1Pr(Entry)E(CF)Pr(Entry)E(CF) Bull Market40%84 =.6x x30 20%102 =.8x x30 Average20%48 =.8x6020%48 =.8x60 Bear Market %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!