Transcript This paper

Real Options, Risk Governance,
and Value-at-Risk (VAR)
What is a real option?
Real options exist when managers can
influence the size and risk of a project’s
cash flows by taking different actions during
the project’s life in response to changing
market conditions.
 Alert managers always look for real options
in projects.
 Smarter managers try to create real
options.

2
Introduction to Real Options
Alternative, yet complementary, approach to
DCF-based Capital Budgeting.
 Many corporate investments (especially
“strategic” ones) have embedded options.
 Overlooking these options can lead to
under-valuing investment projects.
 Using Real Options approach can improve
project management as well as valuations.

3
Types of Real Options


Abandonment
Contraction



Temporary suspension
Permanent




Switch / Transition



Change Product Mix
Change Input Mix
Technical Obsolescence
Wait / Timing
Expansion



Resolve Uncertainty
Identify Demand
Existing Products
New Geographic Markets
Growth


New Products
R&D
4
Four Procedures for
Valuing Real Options
1.DCF analysis of expected cash flows,
ignoring the option.
2.Qualitative assessment of the real option’s
value.
3.Decision tree analysis.
4.Standard model for a corresponding
financial option.
5
Analysis of a Real Option:
Example of a Basic Project

Initial cost = $70 million, Cost of Capital =
10%, risk-free rate = 6%, cash flows occur
for 3 years.
Demand
High
Average
Low
Probability
30%
40%
30%
Annual
cash flow
$45
$30
$15
6
Approach 1:
DCF Analysis (ignoring option)
E(CF) =.3($45)+.4($30)+.3($15)
= $30.
 PV of expected CFs = ($30/1.1) + ($30/1.12)
+ ($30/1/13)
= $74.61 million.
 Expected NPV = $74.61 - $70
= $4.61 million

7
Procedure 2:
Qualitative Assessment

The value of any real option increases if:



the underlying project is very risky
there is a long time before you must exercise the
option
This project is risky and has one year before
we must decide, so the option to wait is
probably valuable.
8
Procedure 3: Decision Tree Analysis
(Implement only if demand is not low.)
Cost
0
$0
Prob.
30%
40%
30%
1
NPV this
Future Cash Flows
2
3
4
Scenario
a
-$70
$45
$45
$45
$35.70
-$70
$30
$30
$30
$1.79
$0
$0
$0
$0
$0.00
Discount the cost of the project at the risk-free rate, since the cost is known.
Discount the operating cash flows at the cost of capital. Example: $35.70 = $70/1.06 + $45/1.12 + $45/1.13 + $45/1.13.
See FM12 Ch 13 Mini Case.xls for calculations later in this set of slides.
9
Project’s Expected NPV if Wait


E(NPV) =
[0.3($35.70)]+[0.4($1.79)] + [0.3 ($0)]
E(NPV) = $11.42
10
Procedure 4: Use the existing model
of a financial option.

The option to wait resembles a financial call
option-- we get to “buy” the project for $70
million in one year if value of project in one
year is greater than $70 million.

This is like a call option with a strike price
of $70 million and an expiration date of one
year.
11
Inputs to Black-Scholes Model for
Option to Wait





X = strike price = cost to implement project
= $70 million.
rRF = risk-free rate = 6%.
t = time to maturity = 1 year.
S (or P) = current stock price = $67.82 see
following spreadsheet.
σ2 = variance of stock return = 14.2% see
following spreadsheet.
12
Discounted Cash Flow Valuation and
Value-Based Management

Link to Real Options Valuation Excel file:

FM 12 Ch 13 Mini Case.xls
(Brigham & Ehrhardt file)
13
Relation between Financial Options
& Real Options
Corporate Project
Variable
Financial Call Option
Expenditures to
acquire asset
X
Exercise Price
PV of acquired asset
S
Stock Price
Time that decision
can be deferred
Riskiness of asset
t
Time to Expiration
s2
Variance of Return
Time value of money
r
Risk-free Rate
14
Calculating the NPV Quotient (NPVq)
PV ( Expected Net Cash Flows)
S
NPVq 

PV (CapitalExpenditures)
PV ( X )
_____ NPVq < 1.0____|____NPVq > 1.0_____
Negative NPV
Calls Out-of-Money
Positive NPV
Calls In-the-Money
15
Using Black-Scholes to Price
a Real Option

Identify 5 key Inputs to B-S OPM:








Initial Investment = X = $100
Current Asset’s Worth = S = $90
Asset’s Riskiness = s = 40%
Deferral Time = 3 years
Risk-free Rate = 5%
Note that current NPV = -10 but NPVq = 1.04
Using B-S OPM method, the Option’s worth =
.284 * $90 = +25.56 !!
Above analysis shows that this might be a promising
project in the future (the option to wait is valuable).
16
“Tomato Gardens” & Real Options
Cumul.
Variance
Out of the Money
(NPVq < 1.0)
Very Low Exercise Never
In the Money
(NPVq > 1.0)
Exercise Now
Low
Doubtful: NPV<0;
Wait if possible.
NPVq<1; & s2 is low. Otherwise, exercise
early.
High
Less Promising: NPV
< 0 and NPVq < 1;
but s2 is high.
Very Promising:
NPV < 0 but NPVq > 1
17
Real Option Implementation Issues

Need to Simplify Complex Projects.

Difficulties in Estimating Volatility (use
simulation, judgment, coefficient of variation)

Checking Model Validity (distributions,
decision trees).

Interpreting Results:
(sensitivity analysis is a must!)
18
Overview of Risk Governance Issues

1.
Key Risk Management Responsibilities of
Senior Managers / Board Members:
Board / Senior Management must approve firm’s risk
management policies and procedures.
2.
Ensure that operating team has requisite technical
skills to execute the firm’s policies and procedures.
3.
Evaluate the performance of the risk management
activity on a periodic basis.
4.
Maintain oversight of the risk management activity
(possibly with a board sub-committee).
19
Ways to Measure & Manage Risk

Value-at-Risk (VAR) has become a popular summary
measure of risk.

VAR is most useful when measuring market-based
risks of financial companies (less meaningful for
many non-financial companies).

Precursors to VAR (and still in use):




Maturity Gap
Duration and the Value of a 1 basis point change
Convexity plus Duration
Option-based Measures (delta, gamma, vega).
20
Why VAR has Become so Popular

VAR provides a succinct, dollar-based summary measure
of risk which allows management to aggregate risks.

Also, traditional risk measures had several weaknesses:





They could not be aggregated over different types of risk
factors/securities.
They do not measure capital at risk.
They do not facilitate top-down control of risk exposures.
VAR is easy for senior management to interpret: It
measures the maximum dollar amount the firm can lose
over a specified time horizon at a specified probability
level (e.g., the 1-day VAR with 99% confidence is $5M)
21
(See Spreadsheet)
Calculating VAR (Three Methods)…

Can calculate VAR via two types of simulation
methods and one analytic method.

Historical Simulation:
1.
2.
3.
4.
Identify Factors affecting market values of securities in the
portfolio
Simulate future values of these Factors using Historical
Data:
Use the simulated Factor values to estimate the value of
the portfolio several times (usually 1,000 or more times)
Create a histogram of the portfolio’s expected change in
value and identify the relevant probability level for the VAR
calculation (e.g., find the change in portfolio that occurs at
the lowest 1% of the distribution).
22
Calculating VAR (cont.)

Monte Carlo Simulation:


Follow the same steps as in the Historical Simulation
method except you use Monte Carlo techniques to obtain
the simulated Factor values (step 2 of the previous slide).
Analytic Variance-Covariance Method:

1.
2.
3.
4.
Can be simpler to estimate since you don’t need the entire
distribution of Factor values (summary measures will
suffice).
Specify Distributions and Payoff Profiles (e.g., normal and
linear).
Decompose Securities into Simpler Transactions/Buckets.
Estimate Variances/Covariances of “Standard Transactions”
Calculate VAR based on standard definition of variance.
23
Strengths / Weaknesses of the Three
VAR Methods

Historical Simulation does not assume specific
distributions for the securities and uses real-world
data but it requires pricing models for all
instruments and allows limited sensitivity analysis.

Monte Carlo Simulation makes it easier to do
sensitivity analysis but requires the analyst to
specify asset distributions as well as pricing models
(also, one step removed from real-world prices).

Analytic Method is intuitively simpler and does not
require any pricing models but it is not conducive to
sensitivity analysis and cannot handle non-linear
24
payoff profiles such as options.
Differences in VAR Estimates from
the Three Methods

Empirical Tests – to date, tests of the three methods
suggest that the approaches can yield similar results when:




Portfolio payoffs are linear.
95% confidence level is used.
There are not many large outliers in the historical data set.
Where Differences can Occur – biggest differences can
occur between the 2 simulation approaches and the
analytic method when:



Non-linear payoffs are a significant share of the portfolio and they
do not cancel out (e.g., long a large number of put options).
Large number of outliers in the historical data set.
99% or higher confidence level is used.
25
Choosing between the Methods

As in much of life, “It Depends!”

If the portfolio has linear (or weakly non-linear)
payoffs, then the Analytic method might be best.

If the portfolio has strongly non-linear payoffs, then
the two Simulation methods are better.

If stress-testing and sensitivity analysis are needed,
then Monte Carlo Simulation is the preferred method
(however, it can be very complex to remove all
possible arbitrage opportunities from the simulation).
26
Who Should Use VAR?

Firms that have their values determined primarily by
financial market risks should use VAR (e.g.,
Investment banks, Brokers/Dealers, as well as CB’s
and Insurance Co’s with active trading portfolios).

Firms that have their values determined by growth
opportunities or “growth options” probably should not
use VAR as their primary risk measure
(e.g., high tech or bio tech firms).

For firms with growth options, a VAR estimate is
typically not relevant because the real value of these
companies comes from non-traded assets where no-27
arbitrage arguments typically do not hold.
Implementing VAR

Parameter Selection:




Time Horizon (e.g., 1-day or 10-day VAR)
Confidence Level (usually 95% or 99%)
Variance-Covariance Data (unstable correlations vs. +1.0)
Other Important Issues:




Sensitivity Analysis (how sensitive is the VAR estimate to the
data set used in the analysis?)
Scenario Analysis (worst case vs. “standard” case)
Stress-testing (how does VAR change as the above
parameters change?)
Back-testing (how good have past VAR estimates been in
relation to actual portfolio changes?)
28