Real Options in decision making under uncertainty

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Real Options in decision making under uncertainty
Chandra Poojari
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Outline

• Acknowledgments.
• Introduction.
• Terminologies in Option pricing.
• Decision making under uncertainty- common
  pitfalls.
• Comparison of pricing real options- dynamic
  programming and arbitrage.

3
Acknowledgements

• Paper titled Option theory and modelling under
  uncertainty by Daniel S. Crsitiansen and Stein
  W. Wallace.
• Investment under uncertainty by Dixit and
  Pindyck

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Introduction

• Well developed in Finance.
• Investment under uncertainty by Dixit and
  Pindyck (1994)
• Rich set of vocabulary

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Introduction
Temporal Context

• Resolution of uncertainty over time- event tree.
• Explicit description of future decisions-flexibili
  ty.

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Introduction
Temporal Context- an Event tree
Decision points
Random outcomes
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Terminologies in Options pricing
American option
European option
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Terminologies in Options pricing
Net present value approach
Initial investment Rs. 100 million Time 5
years Expected cash inflow each year Rs. 25
million Risk adjusted discount rate 12
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Terminologies in Options pricing
Options embedded in a project

• Abandonment option This is an option to sell or
  close down a project. This is an American put
  option on the projects value.
• Expansion option This is the option to make
  further investments and increase the output if
  conditions are favourable. It is an American call
  option on the value of additional capacity.
• Contraction option This is the option to reduce
  the scale of a projects operation. It is an
  American put option on the value of the lost
  capacity.
• Option to defer One of the most important
  options open to a manager is the option to defer
  a project. This is an American call option on the
  value of the project.
• Option to extend Sometimes it is possible to
  extend the life of an asset by paying a fixed
  amount. This is a European call option on the
  assets future value

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Decision making under uncertainty- common pitfalls
Investing in a factory
We are considering building a factory either at
Mumbai or Kolkata. The future demand for the
product manufactured by this factory is
uncertain, it may be either high or low. We know
that a plant in Mumbai is quite profitable if we
build the factory of the right capacity but quite
unprofitable if they have to adapted to demand of
different capacity. The location of the factory
in Kolkata, on the other hand, is not as
profitable as the one in Mumbai but they can
easily be modified to remain profitable when we
have guessed wrong.
Profit for the different configuration and demand
scenarios
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Decision making under uncertainty- common pitfalls
Building a factory
Location
Factory
Demand
Profit
High
10
Large
Low
-6
Mumbai
High
-3
Small
Low
5
High
6
Large
Kolkata
Low
2
High
1
Small
Low
3
The Event tree
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Decision making under uncertainty- common pitfalls
Deterministic thinking - Scenario based solutions
Location
Factory
Demand
Profit
High
10
Mumbai
Large
Low
-6
Large
High
-3
Small
Low
5
Small
Kolkata
6
High
Large
Low
2
Large
High
1
Small
Low
3
Small
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Decision making under uncertainty- common pitfalls
Stochastic solution
Profit for the different configuration and demand
scenarios
The IQ of hindsight is very high
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Comparison of pricing real options dynamic
programming and arbitrage
Ignoring some of the costs
An investment in a real asset
340
Now
Future
200
140
Net pay-off
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Comparison of pricing real options- dynamic
programming and arbitrage
Ignoring some of the costs
Option to wait
Loss of money due to late entrant 40
An investment in a real asset
300
Now
Future
200
100
Value of the project 100 (300-200) in favorable
scenario, 0 otherwise
Value of the project 0.5(100)0.5(0)50
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Comparison of pricing real options- dynamic
programming and arbitrage
Ignoring some of the costs
Value of the project Value of Option to wait
Value of the project Value Exercised now
Value of flexibility
50 40 Value of flexibility
Value of flexibility10 units
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Comparison of pricing real options- dynamic
programming and arbitrage
Ignoring some of the costs
Option to wait
Higher variance
An investment in a real asset
440
Now
Future
200
40
Net pay-off
Value of the project 200 in favorable scenario,
0 otherwise Value of project 0.5(200) 0.5(0)
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Comparison of pricing real options- dynamic
programming and arbitrage
Dynamic programming based approach
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Comparison of pricing real options- dynamic
programming and arbitrage
Valuation by Arbitrage using replication argument
It is an American Call option- when to invest
before or after the resolution of uncertainty
Properties of an underlying Asset Dividend
40 Return in favorable state 300 Return in
unfavorable state 100 Exercise price
200 Market price 240 (if not there will be
arbitrage opportunity)
W price of the option to wait to invest.
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Comparison of pricing real options- dynamic
programming and arbitrage
Valuation by Arbitrage using state prices
Let
be the state prices for the favorable and
unfavorable states.
Investment
Safe asset
Since the option pays 100 in the favorable and
zero in the unfavorable one, its value according
to the state prices is
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Comparison of pricing real options- dynamic
programming and arbitrage
Adjustment for time
Consider the time value of money
The payments received and the cost incurred at
different time in the future needs to their
equivalent present value for comparison.
10
100
?
90.91
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Comparison of pricing real options- dynamic
programming and arbitrage
Adjustment for time
Dynamic programming
Value of the project
Expected value of the project
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Comparison of pricing real options- dynamic
programming and arbitrage
Adjustment for time
Arbitrage pricing
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Comparison of pricing real options- dynamic
programming and arbitrage
Valuation by Arbitrage by state prices
Let
be the state prices for the favorable and
unfavorable states.
Investment
Safe asset
Since the option pays 100 in the favorable and
zero in the unfavorable one, its value according
to the state prices is
25
Thank you
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Decision making under uncertainty- common pitfalls
Adjustment for risk
Dynamic programming
Specify an appropriate discount
Discount the investment at
Discount the safe asset
Discount the option
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Decision making under uncertainty- common pitfalls
Adjustment for risk
Arbitrage pricing
There is premium on risk
Influence of an asset on the entire portfolio
The expected rate of return of an asset depends
on how it varies relative to other assets..
covariance.
Let the expected rate of return be
W
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Decision making under uncertainty- common pitfalls
Adjustment for risk
Arbitrage pricing
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Decision making under uncertainty- common pitfalls
Advantages/Disadvantages
Dynamic programming
Easy to apply -makes an adhoc assumption about
the discount rate
Arbitrage approach
Easy to apply -makes an adhoc assumption about
the discount rate