RETHINKING THE MARGIN OF SAFETY

HOW THINKING ABOUT RISKS CAN ADD VALUE TO A TIME HONORED METHOD FOR COMMON STOCK INVESTING

TABLE OF CONTENTS

Executive Summary ....................................................................................................................................................... 2

Model Assumptions ....................................................................................................................................................... 3

Factor Explanation ......................................................................................................................................................... 4

Factor Explanation (continued) ..................................................................................................................................... 5

RAMS In Action .............................................................................................................................................................. 6

Conclusion ..................................................................................................................................................................... 7

Matthew Scullen Page 2

EXECUTIVE SUMMARY

In his pivotal work "The Intelligent Investor", and his first work with David Dodd,

"Security Analysis: The Classic 1934 Edition", Benjamin Graham popularized the idea of

the margin of safety for finding the appropriate price at which to purchase an investment.

In simple terms, the margin of safety is the discount applied to the intrinsic value of a

security determined by an investor. A discount is required because of uncertainty; our

knowledge of the correct intrinsic value is only an estimate and is subject to forecasting

error. While Graham stresses the importance of having an adequate margin of safety,

there is no universal agreement or magic formula for quantifying what level discount is

required.

In many instances, a subjective discount is applied, rather than using a quantitative

approach which makes economic sense. Furthermore, there is no one size fits all margin

of safety that should be applied to every stock. Every security carries its own set of

unique risks. For example, applying a 30% margin of safety may be appropriate for a

company which sells non-discretionary consumer items. Shifting industries though to a

pharmaceutical drug manufacturer that depends on leverage and successful product

launches likely requires a larger margin of safety to properly account for the excess

relative risks. The paper here will outline a formula specific to each individual common

stock based upon five factors attributable to some type of risk.

Five Risk Factors:

1. Market Risk Factor

2. Leverage Risk Factor

3. Accounting Quality Risk Factor

4. Cash Flow Risk Factor

5. Growth Sensitivity Factor

The combination of these five factors are used to determine a Risk Adjusted Margin of

Safety (RAMS).

"A discount is

required because

of uncertainty;

our knowledge of

the correct

intrinsic value is

only an estimate

and is subject to

forecasting error."

Matthew Scullen Page 3

MODEL ASSUMPTIONS

Because the intrinsic value of a stock is not perfectly known investors require a

margin of safety to purchase the stock. The margin of safety can be estimated from

measureable market risks, specific business risks and forecasting risk.

The five factors used are assumed to be the most important risks to investors.

Each risk factor is given an equal weight.

Dividends offer realized returns from investment and therefore reduce the investors’

required margin of safety.

A non-dividend paying stock with factors equal to 1 have a purchase price of zero

with RAMS.

Any stock with factors that sum to greater than 1 indicate that the stock could be sold

short.

Risk/Return is not violated; to earn a higher expected return, stocks with larger risk

factors must be sought after and vice-versa.

"The margin of

safety can be

estimated from

measureable

market risks,

specific business

risks and

forecasting

risk."

"Risk/Return is

not violated; to

earn a higher

return, stocks

with larger risk

factors must be

sought after

and vice-

versa."

Matthew Scullen Page 4

FACTOR EXPLANATION

1) Market Risk Factor - βs

where βs is the Beta of the stock with the market.

All stock investors share what is known as systemic risk, or the risk of how much your

stock moves with the market. Beta is a scaled measure of correlation where a measure of

1 means the stock moves in perfect harmony with the market. If a stock has a Beta higher

than 1, than it will move larger variation relative to the market and vice-versa.

2) Leverage Risk Factor - D/E

where D/E is the Debt to Equity ratio.

The presence of large leverage is a risk factor to equity share holders. Creditors hold a

senior position relative to equity holders in the capital structure. Should an economic

crisis emerge, technology change, demand shift, etc., high levels of leverage could

expose a solvency crisis leaving equity owners exposed to steep losses. The D/E ratio

must be adjusted for off-balance sheet items like significant operating leases and special

purpose entities.

3) Accounting Quality Risk Factor - μ (n yr) Accrual Ratio (AR)

where the Accrual Ratio is ΔNOA/μNOA, where NOA is Net Operating Assets.

The Δ (change) in AR is over one year and the μ (average) is from beginning to

end of the period. The AQR used takes an average of the AR over the past n

years.

Use of aggressive accruals can be a signal that earnings are unsustainable if the cash flow

backing them never materializes. Because accruals from year to year can be volatile, an

average over a period of several years should be used. A persistently high accrual ratio

would be reflected in a high AQR.

Beta:" systemic

risk, or the risk

of how much

your stock

moves with the

market."

"leverage could

expose a

solvency crisis

leaving equity

owners exposed

to steep losses."

"Use of

aggressive

accruals can be

a signal that

earnings are

unsustainable"

Matthew Scullen Page 5

4) Cash Flow Risk Factor - (σ/μ) CF

where (σ/μ) CF is the Coefficient of Variation of Cash Flows over t years.

Any business with high variability in its cash flows can certainly be deemed riskier than

the business that has few surprises in the dispersion of its cash flows. Dispersion is

measured by the σ (standard deviation) and is divided by the μ (mean). The higher the

ratio the more volatility is present in the cash flows of the business.

5) Growth Sensitivity Factor - (σ/μ) g

where (σ/μ) g is Coefficient of Variation of Value from Δ g (growth) estimates.

Thorough analysts will consider a range of scenarios of growth and perform sensitivity

analysis by plugging in different growth assumptions into their forecasts. Often the

sensitivity of value to any particular growth assumption can be large. Dispersion is

measured by the σ (standard deviation) and is divided by the μ (mean). The higher the

ratio the more uncertainty is present in the valuation of the stock.

The five factors are each multiplied by 20% and to find the RAMS subtract the expected

dividend yield from the sum of the five factors:

RAMS = Σ factori – Div1/Ps

"Any business

with high

variability in its

cash flows can

certainly be

deemed riskier

than the

business that

has few

surprises in the

dispersion of its

cash flows."

"the sensitivity

of value to any

particular

growth

assumption

can be large."

Matthew Scullen Page 6

RAMS IN ACTION

A real world example is always helpful in creating a better understanding of an theory.

Company: Terra Nitrogen Company, L.P. 1 Symbol: TNH

Intrinsic value estimate2: $116 per share

Calculation of RAMS:

Factor

Type

Factor3 Weighted

Factor (F*20%)

Beta 0.70 0.14

D/E 0.00 0.00

AQR 0.12 0.02

CFRF 0.99 0.20

GSF 0.36 0.07

Dividend Yield -0.06

RAMS 0.38

The RAMS discount factor is 38%.

RAMS Purchase Price: $72.72 per share [$116 x (1 - .38)]

Decision:

Last Price (as of 6/9/11): $125.93 per share

The last price for TNH is above its intrinsic value estimate per share and far above the

purchase price indicated by using RAMS. Therefore the decision would be to sell shares

that are currently owned. A buy decision would be reached only if the last price were

equal to or less than the RAMS purchase price.

1 While writing this white paper the author did own shares in TNH and has since sold his interest.

2 Intrinsic value has been estimated using a free cash flow to equity discount forecast, available upon request.

3 Factor data was obtained through Reuters and from 2010 form 10-k data release by Terra Nitrogen Company, L.P.

"A buy decision

would only be

reached if the

last price were

equal or less

than the RAMS

purchase

price."

Matthew Scullen Page 7

CONCLUSION

RAMS can be a useful tool, especially for value investors who theoretically agree with

using a margin of safety, but find it difficult to practically implement due to the

subjectivity of finding the correct discount to apply.

Using RAMS also does not contradict other models or theories such as CAPM or APT,

which are used to determine required returns. Indeed, RAMS can be thought of as a

complementary tool to use in the valuation and portfolio management process.

Investors can approach the idea of RAMS flexibly. For instance, APT is not a model

because there is no cohesive rule for which factors should be included in the equation,

where CAPM explicitly assumes market risk is the only risk. While in my portrayal I

assume the five factors listed are the only relevant factors to include, I have not labeled

it a model.

If you are interested in contacting Matthew regarding this white paper please feel free

to email him at mscullen1@gmail.com and refer to the white paper in the subject line.

Dated 6/9/2011

Matthew Scullen is a

candidate in the CFA

program and has a

B.A. in Economics

from The Ohio State

University. He has

several years

experience working

for a financial service

firm with

approximately $50

million in AUM.