Quantifying the Value of Risk Management - Jan 2008

Strategic Capital Advisory
Management
Authors
© January 2008
This document has been approved and/or communicated by Merrill Lynch. The services described in this
document are provided by Merrill Lynch or by its subsidiaries and/or affiliated in accordance with
appropriate local legislation and regulation.
Quantifying the Value of
Risk Management
Jamie Ballingall
Merrill Lynch
+1 212 449 8792
jamie_ballingall@ml.com
Adrian Crockett
Head of Strategic Capital Advisory
Merrill Lynch
+1 212 449 9920
adrian_crockett@ml.com
David Denis
Professor of Finance
Burton Morgan Chair of Private Enterprise
Krannert School of Management
Purdue University
Eric Rattner
Merrill Lynch
+1 212 449 0884
eric_rattner@ml.com
January 2008
Corporate Risk

i Strategic Capital Advisory
Quantifying the Value of Risk Management
January2008
Acknowledgments
We would like to thank Michael Ondruska and Hans Tallis for their valuable comments. Of course, any
remaining errors are our own.

Strategic Capital Advisory ii
January2008
Executive Summary
In this paper we propose a new risk management framework that can
evaluate the cost-risk tradeoff of alternative risk management strategies.
Although there is ample theoretical support for risk management as an
activity, common risk management approaches suffer serious problems:
 Minimize Risk: Completely eliminating risk is expensive and
impractical
 Efficient Frontier: Can eliminate many poor risk management
strategies but rarely gives a definitive optimal
strategy
 Sharpe Ratio: Provides a cost-risk trade-off but the price of one
unit of risk is arbitrary
Based on a recent empirical study, we propose a new cost-risk measure which
directly values the impact of earnings per share and cash flow per share
volatility.
This new approach will enable corporate CFOs and treasurers to make more
robust risk management decisions and, critically, better defend those
decisions internally and to the broader market.

iii Strategic Capital Advisory
January2008
Contents
Table of Contents
Evaluating Risk Management Policies 1
Traditional Approaches to Policy Evaluation 3
Minimize Risk 3
Minimize Value-at-Risk (VaR) 3
Efficient Frontier 3
The Sharpe Ratio and Related Measures 5
Summary of Traditional Approaches 7
A New Approach 8
Introduction 8
Application of the New Approach 10
Relationship with the Sharpe Ratio 11
Drawbacks of the New Approach 12
Conclusion 13
Table of Figures
Figure 1—Summary of Impact of Cash Flow Volatility on Company Value 1
Figure 2— Desirable Properties of a Policy Evaluation Mechanism 2
Figure 3— EPS Risk-Reward for Various Funding Strategies 4
Figure 4— Efficient Funding Strategies 4
Figure 5— Using Sharpe Ratio to Find Optimal Strategy 6
Figure 6—No Traditional Approaches are Satisfactory 7
Figure 7—Sensitivity of Firm Value to Changes in Volatility 8
Figure 8—Valuing Risk Management Initiatives 10
Figure 8— Using the New Approach to Find Optimal Strategy 12
Figure 9—The New Approach Improves Upon Traditional Methods 13
Table of Examples
Example 1 – Efficient Frontier Analysis for FakeCo. 3
Example 2 – Can Risk/Return Ratios Help? 6
Example 3 – Collapsing the Efficient Frontier 11
Example 4 – Tying it All Together 12

Strategic Capital Advisory 1
January2008
Evaluating Risk Management Policies
In 1958 Modigliani and Miller advanced their famous value irrelevance theorem
which implied that, under perfect capital markets, neither capital structure nor
risk management policy impacts firm value. This provided a roadmap for future
researchers to examine the ways in which risk management could be value
relevant by examining how the effects of market imperfections are exacerbated
by volatility and uncertainty.
Well established arguments for the value relevance of risk management are
shown in Figure 1.
Figure 1—Summary of Impact of Cash Flow Volatility on Company Value
Factor
Highvolatility increases the probabilitythat a company will incur
costs associatedwithdistress—e.g., bankruptcy costs, lostsales, and
supplier problems
Consequence
Higher Expected
Costs of Financial
Distress
Highvolatility increases the probabilitythat a company will need
outside financing. Because external finance is costly, some profitable
projects may be bypassed
Foregone
Investment
Opportunities
Withprogressivetax schedules, highvolatility increasesexpected tax
payments
Higher Tax
Payments
Higher cashflow volatilityincreases the probability that earnings will
fall short of market expectations,leading to stockprice drop
Greater Probability
of Missed Earnings
Targets
However, less research has been conducted on quantifying how much value is
created by managing risk or on how to evaluate two risk management policies
and choose the ―best‖. In practice, most companies actively engage in risk
management, but with only subjective evaluation of the costs and benefits of this
activity.1
In this paper, we examine traditional approaches to risk management policy
evaluation, note their practical and theoretical drawbacks, and then propose a
new evaluation measure which we believe overcomes many of these drawbacks.2
We call a mechanism for evaluating a risk management policy a measure.
Figure 2 lays out the desirable properties of an ideal risk management measure.
1 This subjective evaluation may have a quantitative element. E.g., “We have reduced the standard deviation of our interest
expense from USD 100m to USD 75m, at a cost of USD 10m.” However, deciding if such a change is beneficial to the
company overall still requires a subjective judgment.
2 See our paper “Does Risk Management Create Value?” for a detailed discussion of the study from which the framework
presented in this paper is developed.
Qualitative arguments for
the value of risk
management are well
established and accepted…
…but less emphasis has been
placed on quantifying the
value of risk management

2 Strategic Capital Advisory
January2008
Figure 2— Desirable Properties of a Policy Evaluation Mechanism3
Definitive
Risk-Aware
Earnings-Aware3
Non-Arbitrary
Universal
Forany two risk management policies, alwaysprovide a clear
indicationof whichis preferable and by how much
Recognize the desirability of reduced risk
Recognize the desirability of increased earnings
Make risk-earnings trade off ina way that is broadly inline with
investorpreferences
Be applicable to operational and financial risks and to the entire firm
orany sub-unit of the firm
3 Risk management policies are often represented in terms of cost versus risk. In this paper, we use the broader concept of
earnings versus risk, since any cost impact can be translated into an earnings impact. Hence we are seeking to maximize
earnings and minimize risk.

January2008
Traditional Approaches to Policy Evaluation
Minimize Risk
A firm could simply choose whichever policy gives the lowest risk as measured
by the standard deviation of earnings or some other dispersion metric. This is
sometimes valid at the sub-unit level if a risk has already been identified as
highly toxic. However, it is neither earnings-aware nor universal. If applied to
the entire firm it would suggest selling all operating assets and investing the
funds in risk-free securities, such as government bonds.
Minimize Value-at-Risk (VaR)
A firm could chose the policy with that gives the lowest VaR of earnings. This is,
at least, earnings-aware because moving the distribution to the right will reduce
VaR. However, the choice of level (e.g., 95%, 99%, etc.) and base makes this
approach arbitrary.4
Efficient Frontier
A very common approach, borrowed from portfolio management, is the
―efficient frontier‖. Here the risk and earnings5 of different policies are plotted on
a scatter diagram. A policy is deemed efficient only if there is no other policy
with the same risk and higher earnings or the same earnings and lower risk.
Example 1 provides an example of how this method is used in practice.
Example 1 – Efficient Frontier Analysis for FakeCo.
FakeCo. is a manufacturing firm based in the United States but with some
operations in the EuroZone. Currently, all FakeCo.’s debt is fixed rate and USD
denominated. The new CFO asks the firm’s treasurer to determine the firm’s
optimal currency mix and fixed-floating mix of debt.
First, the treasurer’s staff conducts a correlation analysis and determines that
USD operating income is positively correlated to USD interest rates and EUR
operating income is positively correlated to EUR interest rates. Additionally,
USD and EUR operating incomes are correlated and USD and EUR interest rates
are correlated, building out a full correlation matrix of the main drivers in this
analysis.
The Treasury team then runs a Monte-Carlo simulation of earnings per share for
different financial policies. Specifically, they vary three variables from 0% to
100%, in steps of 5%:
 Proportion of debt in EUR
 Proportion of USD debt that is floating rate
 Proportion of EUR debt that is floating rate
This gives a total of 213 ≈ 9,300 possible risk management policies under
consideration – which the Treasury team considers representative of the policies
they might implement. Figure 3 depicts the expected EPS and the EPS risk of the
policies examined.
4 A comprehensive discussion of the shortcomings of VaR is beyond the scope of this paper. Please see Beder, Tanya Styblo,
1995, VaR: Seductive but Dangerous, Financial Analysts Journal.
5 Or equivalently, for this efficient frontier discussion, cash flows.
Although the efficient
frontier approach is
commonly used by
practitioners, there are a
number of difficulties with
this method, making it
inappropriate for optimizing
the tradeoff between
different risk management
policies

January2008
Figure 3— EPS Risk-Reward for Various Funding Strategies
1.00
1.05
1.10
1.15
1.20
0.10 0.12 0.14 0.16 0.18 0.20
ExpectedEPS($)
EPS Risk ($)
Most Desirable
Risk/Return Tradeoff
Least Desirable
Risk/Return Tradeoff
The Treasury team can now eliminate inefficient policies as shown in Figure 4.
Figure 4— Efficient Funding Strategies6
1.00
1.05
1.10
1.15
1.20
0.10 0.12 0.14 0.16 0.18 0.20
ExpectedEPS($)
EPS Risk ($)
Inefficient Portfolios
6 The curvature of the line connecting the efficient portfolios is predominantly driven by the respective positive correlations
between operations in the United States and the EuroZone and USD and EUR interest rates.
Inefficient portfolios may be
easy to identify, but there are
still a number of efficient
portfolios remaining, all of
which are considered
―optimal‖ from a risk-return
perspective

January2008
The Treasurer now has 40 policies, all of which are ―optimal‖ using the efficient
frontier measure. Unfortunately, these policies cover a wide range of
possibilities, including:
Strategy
USD Fixed
Rate Debt
USD Floating
Rate Debt
EUR Fixed
Rate Debt
EUR Floating
Rate Debt
Min. Risk 0% 0% 100% 0%
Low Risk 0% 0% 85% 15%
High EPS 0% 50% 0% 50%
Max. EPS 0% 100% 0% 0%
The efficient frontier approach is valuable in so far as it can identify poor risk
management policies. However, it rarely gives a definitive answer since it does
not provide a measure of the value of one policy versus another.
The Sharpe Ratio and Related Measures
Another concept borrowed from asset management is the Sharpe ratio, which is
defined as:
)var
)E
f
f
R(R
R(R
S



where R = Return on the portfolio
Rf = Risk-free rate
When applied to corporate policies, the risk-free rate is often omitted and the
Sharpe ratio simply becomes the expected earnings divided by the standard
deviation of earnings. Example 2 illustrates how the Sharpe Ratio is commonly
used in risk management policy determination.

January2008
Example 2 – Can Risk/Return Ratios Help?
Continuing from Example 1, the Treasurer recalls the Sharpe ratio and is initially
optimistic that it resolves her dilemma. It can be applied to each risk
management policy and one policy will be the ―best‖. Equivalently, she can
draw equipreference or indifference lines that represent earnings-risk
combinations with the same Sharpe ratios. The point at which the first
equipreference line touches the efficient frontier is the optimal point.
Figure 5— Using Sharpe Ratio to Find Optimal Strategy
1.00
1.05
1.10
1.15
1.20
0.10 0.12 0.14 0.16 0.18 0.20
ExpectedEPS($)
EPS Risk ($)
Equipreference
Lines
Optimal
Strategy
On reflection, however, she realizes that she would be unwilling to stand in
front of the Board of Directors and defend her choice. Her concern is that this
methodology implicitly assumes that a 1% reduction in risk is as desirable as a
1% increase in earnings. Fundamentally, she isn’t sure that this risk-return
tradeoff is the same as the tradeoff that is priced in the marketplace.
Thus, the Sharpe Ratio fixes the main problem with the efficient frontier—it is at
least definitive. However, the price of a unit of risk is entirely arbitrary.
Although there are many variants of the Sharpe ratio, such as the Sortino ratio7,
they are all arbitrary in their assignment of the cost of a unit of risk.
7 The Sortino ratio uses a target rate in place of the risk free rate and the downside semi-variance instead of the variance.
Although the Sharpe Ratio
gives a unique optimal
policy, there is no reason to
believe that the risk-return
tradeoff assigned by the
Sharpe ratio has any
connection to that priced in
the marketplace

January2008
Summary of Traditional Approaches
To put the relative attractiveness of each of the traditional evaluation approaches
in perspective, Figure 6 evaluates them against the desirable properties of a
policy evaluation mechanism outlined in Figure 2.
Figure 6—No Traditional Approaches are Satisfactory
Definitive Risk-Aware
Earnings-
Aware
Non-
Arbitrary
Universal
MinimizeRisk
MinimizeVaR
Efficient Frontier
Sharpe Ratio

 
 








 


½
½
½
As the above table demonstrates, unfortunately none of these traditional
approaches provides a satisfactory framework for making fully informed
decisions on risk management strategy.

January2008
A New Approach
Introduction
The largest drawback with existing measures is the arbitrary price associated
with each unit of risk. To overcome this, we conducted a study of the impact of
EPS volatility on valuation. To determine whether shareholders considered cash
flow only, or whether they place incremental informational value of earnings, we
also considered the volatility of cash flow per share (CFPS).
We found that, even after controlling for other determinants of value, such as
firm size and profitability, EPS and CFPS volatility negatively impact firm
valuation.8 The sensitivity of Market-to-Book (M-B) ratio to changes in the
volatility of earnings and cash flow are detailed below in Figure 7.
Figure 7—Sensitivity of Firm Value to Changes in Volatility
1.6%
3.5%
5.6%
8.1%
11.2%
0.6%
1.3%
2.1%
3.0%
4.0%
0%
3%
6%
9%
12%
15%
10% 20% 30% 40% 50%
% Increase in
M-B Ratio
% Reduction in Volatility
Earningsvolatility Cash flow volatility
2.2%
4.8%
11.3%
7.8%
15.7%
Mathematically, the results of our study can be summarized as:
   cEc
B
M
 log.log.log 





05701530
where assetsofvaluemarketM
assetsofbook valueB
constantspecific-firmAc 9
shareperearningsquarterlyofVolatilityE
shareperflowcashquarterlyofVolatilityc
8 The full results are published in our recent paper “Does Risk Management Create Value?”
9 This constant is a function of several firm characteristics. Therefore, care should be taken to ensure this methodology is only
applied to policy changes that do not significantly impact these characteristics.
Both independently and
together, changes in EPS
volatility and changes in
CFPS volatility are associated
with changes in
M-B ratio
(1)

January2008
A rearrangement leads to a formula for firm value in terms of book value of
assets, earnings volatility and cash flow volatility
05701530 .. 
 CEBkM 
where )exp(ck 
The constant c, and hence k, can be estimated in one of two ways. Either, using
the full regression equation presented in our previous paper or by reversing out
the constant using current or historical values for M, B, E and C :
05701530 ..
CE
B
M
k  
Once we’ve estimated the constant, it is now possible to rearrange the results in
order to present them solely in terms of the proportional change in EPS and
CFPS volatility and not on the absolute starting level of M-B or volatility.
05701530 .. 


















Base
New
Base
New
C
C
E
E
Base
Base
New
New
B
M
B
M




Given these results, in practice we can estimate the expected value of any risk
management policy by following by:
(1) Calculating the firm-specific constant (k = exp(c))
(2) Calculating expected book value of assets (B) under the policy based on
expected earnings10
(3) Calculating the volatility of EPS ( E ) under the policy
(4) Calculating the volatility of CFPS ( C ) under the policy
(5) Evaluating the new implied market value of assets (M) calculated with
Equation 2
(6) Determining the implied market value of equity by subtracting the
market value of debt
These steps are presented diagrammatically in Figure 8 below.
10 Calculation of expected book value of assets requires an estimation of the policy’s effect on net earnings and therefore book
value of equity/assets (where book value of assets = book value of liabilities + book value of equity).
(2)
(3)
(4)

January2008
Figure 8—Valuing Risk Management Initiatives
Net Income
Book Value of
Assets
B
Earnings per
ShareVolatility
E
Cash Flow per
ShareVolatility
C
Firm-Specific
Factors
c
Implied Market
Value of Assets
M
Implied M/B Ratio
Implied Share Price
After going through the six steps for every strategy under examination, the
optimal policy can be determined by comparing the respective share price
implications.
Application of the New Approach
Under the new approach, we can trace the implications of any risk management
policy down into forecast earnings and cash flows and the volatility thereof.
Then, we can use forecasted earnings to determine the consequences for book
value of assets and equity and easily apply the framework to work out the
expected change in value if the policy were implemented.
The new approach folds the
tradeoff between cost and
risk of various strategies into
one critical number, the
impact on share price and
allows for much more clarity
in setting optimal risk
management policy

January2008
Example 3 – Collapsing the Efficient Frontier
Continuing from Example 1, the Treasury team applies Equation (2) to each of
the roughly 9,300 risk management policies under consideration.11 They then put
the policies in order and find a single policy which is preferable to all others.
Strategy
Implied
Stock
Price
USD
Fixed Rate
Debt
USD
Floating
Rate Debt
EUR
Fixed Rate
Debt
EUR
Floating
Rate Debt
Optimal $20.00 0% 0% 85% 15%
Next Best $19.99 0% 0% 80% 20%
Max. EPS $19.37 0% 100% 0% 0%
Min. Risk $19.98 0% 0% 100% 0%
Current $18.99 100% 0% 0% 0%
The Treasurer can then confidently make the following statements:
 The optimal policy is 85% EUR denominated fixed rate debt and 15%
EUR denominated floating rate debt
 The next best policy is very similar to the optimal policy
 The firm is destroying $1.01 ($20.00 - $18.99) per share of theoretical
shareholder value by not being at the optimal fixed floating and currency
mix
Relationship with the Sharpe Ratio
Although more complex in form than the Sharpe ratio, our new equation can
nevertheless be used to draw equipreference lines on an efficient-frontier
diagram. This is easiest if the equation is rearranged into12:









S
B
E
kS
M
E Base
BaseCE
05701530 ..

where shareperearningsE
goutstandinsharesS
11 Having already computed the efficient frontier they could apply equation (2) only to those points on the frontier. However,
because the equation is fast to compute, we typically apply it to every policy.
12 Assuming that SESEBB BaseBase 
Under this method, the exact
dollar value of a particular
risk management policy can
be easily calculated
(5)

January2008
Example 4 – Tying it All Together
Satisfied with the Treasurer’s recommendation, the CFO asks her help in
preparing a presentation to the Board of Directors. To help visualize the possible
policies and see the optimal policy, the Treasurer draws equipreference lines on
the efficient frontier diagram.
Figure 8— Using the New Approach to Find Optimal Strategy
1.00
1.05
1.10
1.15
1.20
0.10 0.12 0.14 0.16 0.18 0.20
ExpectedEPS($)
EPS Risk ($)
Optimal
Strategy
The optimal strategy is then where the lowest equipreference line touches the
efficient frontier.
Drawbacks of the New Approach
The new risk measure we propose meets most of our criteria for the ideal
measure. However, it is not fully universal. It cannot be applied to sub-units in
isolation. The user must always consider the impact of the policy on the overall
earnings and balance sheet of the firm, which requires an estimate of the
correlation of the risk under consideration and the broader risks of the firm.
Nevertheless, the measure can be used in the examination of any policy and
relate to both financial and operational risk.

January2008
Conclusion
Most existing measures have significant practical and theoretical drawbacks. We
believe that the market-based risk-return trade-off we propose will provide
CFOs and Treasurers with a clear, pragmatic and defensible measure of the costs
and benefits of risk management activities.
Figure 9—The New Approach Improves Upon Traditional Methods
Definitive Risk-Aware
Earnings-
Aware
Non-
Arbitrary
Universal
MinimizeRisk
MinimizeVaR
Efficient Frontier
Sharpe Ratio
EPS & CFS
Volatility

 
 






 




 


½
½
½
½

January2008
This Page is Left Intentionally Blank

January2008
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Management
Authors
© January 2008
This document has been approved and/or communicated by Merrill Lynch. The services described in this
document are provided by Merrill Lynch or by its subsidiaries and/or affiliated in accordance with
appropriate local legislation and regulation.
Quantifying the Value of
Risk Management
Jamie Ballingall
Merrill Lynch
+1 212 449 8792
jamie_ballingall@ml.com
Adrian Crockett
Head of Strategic Capital Advisory
Merrill Lynch
+1 212 449 9920
adrian_crockett@ml.com
David Denis
Professor of Finance
Burton Morgan Chair of Private Enterprise
Krannert School of Management
Purdue University
Eric Rattner
Merrill Lynch
+1 212 449 0884
eric_rattner@ml.com
January 2008
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