management of risk module 3

8/13/2019 Management of Risk Module 3

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Module 3

Risk Adjusted Value

Dr. Sankersan Sarkar


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Some Questions

Value of What?

Why do we require Risk Adjusted

Value?

What do we mean by the term

Asset?

How do we assess value?


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Contents

DCF value of an asset

DCF Value using risk adjusted discount rates

DCF Value using certainty equivalent cash flows

Risk adjusted discount rates versus certainty

equivalent cash flows

Hybrid Models

DCF Risk adjustment: merits and demerits

Post-valuation risk adjustment Relative valuation approaches

DCF versus relative valuation

Risk adjustment in practice


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Value of an asset is a function of the expected cash

flows generated by the asset and is considered to be

equal to the present value of the expected cash flows

generated by the asset.

Assets with predictable cash flows are likely to havehigher value than assets with unpredictable or

volatile (hence risky) cash flows


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Value of a risk-free asset should be the present

value of the cash flows from it discounted at therisk-free rate

If cash flows from the asset are likely to be

affected by risk then the impact of risk can befactored into valuation either by adjusting thecash flows or by adjusting the discount rate.

Thus a risky asset can be valued in either of thefollowing ways:

Using risk adjusted discount rates

Using adjusted cash flows


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DCF Value using risk adjusted discount

rates

A higher discount rate is used to discount the expectedcash flows arising out of more risky assets and lowerdiscount rate for the less risky assets

Where

n=life of the asset in number of years E(CFt)=expected cash flow from the asset in the year t

r =risk adjusted discount rate applicable to the asset.

How to decide the correct discount rate?


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Correct Risk Adjusted Discount Rate

1. Risk-Return Models

2. Implied Discount Rates


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Risk adjusted discount rates: Risk Return Models

The answer to the previous question can be provided by the use of

risk return models e.g. CAPM, APM and Multifactor models

According to CAPM:

Expected rate of return = Risk-free rate + Beta x Market risk

premium

Where

Risk-free rate is the market rate of interest on govt.

securities

The market risk premium (also called equity risk premium) isthe excess return expected on the market index over the

risk-free rate = RMRF

Beta is the risk parameter that is specific to the asset


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1. Risk-free rate of return: Yield on T-bills

Yield on long term G-secs

2. Market risk premium: RMRF

Historical premiums OR

Prospective premiums

3. Beta:

Historical beta OR

Bottom up beta


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The APM and the multi-factor models are

extensions of the CAPM Risk free rate would remain the same but risk

premium and betas have to be calculated for eachrisk factor

Each beta measures the exposure of the asset tothe underlying risk factor

Each beta can be historical/bottom up estimate

In APM the factors are unspecified market riskfactors while in Multi-factor models, these arespecified macroeconomic factors

Proxy models use firm specific factors as proxies

for risk


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Caveats:

CAPM is simple but makes restrictiveassumptions viz. quadratic utilityfunction, normally distributed returns

All risk-return models (CAPM & others)assume that investors maintain welldiversified portfoliosso the relevantmeasure of risk is not the total risk butthe risk added on to a diversifiedportfolio by including the asset (Beta)


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Risk adjusted discount rates: Implied Discount Rates

Implied discount rate can be calculated on the basis of the following

relationship:

The implied discount rate does not require any assumptions on theinvestor utility and the return distributions as made in the risk-

return models. However it suffers from the following limitations

due to which it has not been popular:

1. It cannot be applied in case of non-traded assets because it can beapplied only if the asset is traded and has a market price.

2. Further even if the asset has a market price it assumes that the

asset is correctly priced. However due to market imperfections an

asset may not always be correctly priced.

rateGrowthRateDiscountadjustedRisk

yearnextflowcashExpectedValueMarket


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Risk adjusted discount rates: Implied Discount Rates

Two techniques to get around the second problem:

1. Calculate the implied discount rate for everyasset belonging to same risk class at a specificpoint of time and average them out. Assumption:

All assets belonging to the same risk class havethe same risk and the average risk adjustedreturn should be applicable to all of them.

2. Calculate the implied discount rate for the same

asset in several consecutive years over a longperiod of time and average them. Assumption:Risk adjusted discount rate does not change overtime & averaging over several consecutive years

is the best estimate.


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Examples

1. The current level of S&P 500 index is 900,

the expected dividend yield for the next

period is 3 percent approx. the long term

expected growth rate in dividends is 6percent. Calculate the implied rate of

return required on the market & implied

market risk premium. Use this informationto calculate the required rate of return for

a stock having a beta of 1.20.


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Examples

2. The S&P 500 index on January 1 of 2011 was at

1248 approx. The dividend yield on the index in the

previous year was 3.34 percent approx. The market

in general expects that the earnings & dividends of

the companies in the index will grow at 8 percentfor next five years followed by a constant growth

rate of 4.39 percent thereafter. The yield on 10 year

govt. bonds was 4.39 percent as on Jan 1, 2011.

Calculate the implied rate of return required on the

market and the implied market risk premium. Use

this information to calculate the required rate of

return for a stock with beta 1.50.


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Examples

3. A commercial property is likely to generate

cash flow of Rs. 3.20 lakh next year. The cash

flows from the assets are growing at a long

term rate of 6% and the asset has a market

value of Rs. 88 lakh at present. Calculate theimplied discount rate for the asset.

4. Over a 7 year period the Sensex has grown

from 5000 to 15000. During the same periodyield on 10 year govt. bonds have averaged 9%.

Calculate the historical rate of return on the

market and the historical risk premium.


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Risk adjusted discount rates: General Issues

A. Single period models and multi-period cash flows

Most of the models discussed earlier are single periodmodels while the cash flows are generated over multipleperiods in future, but the same risk adjusted discount rateis used for all future periods

Underlying assumption: systematic risk & market riskpremium will not change over time

This assumption is violated when an asset has potential forgrowtha. systematic risk under growth conditions tendsto be more than that in the absence of growth; b.

systematic risk under growth conditions tends to changeover time

Thus systematic risks & growth potentials may change overtime and so risk adjusted discount rates should be changed

for each consecutive year. Que: By how much?

k d d d l


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B. Composite discount rate versus item-specific

discount rate Expected cash flows used in the DCF models are

the net of expected cash inflows & outflows in

different years; moreover inflows/outflows will

consist of several components

If the inflows & outflows or the different

components of cash flows have different

exposures to systematic risk factors using the

same risk adjusted discount rate for discounting

all components of cash flows is not appropriate,

even in any particular period


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C. Negative versus positive cash flows

The same discount rates would affect thenegative cash flows differently vis--vis thepositive cash flows due to the discounting effect

Due to the discounting effect the Negative cashflows will be smaller in negative terms

The higher the discount rate the lower will be

the magnitude of the present value of thenegative cash flows

This may increase the NPV of the asset


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C. Negative versus positive cash flows

Some experts suggest using a lower discount ratefor negative cash flows & higher rate for positivecash flows

Using different discount rates for differentcomponents during the same periods will beinternally inconsistent

Using lower discount rate for the negative cash

flows will be reasonable only if they are morepredictable & stable than the positive cash flows;not just because they are negative


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DCF Value Using Certainty Equivalent Cash Flows

An alternative technique is to adjust the expected cash

flows for risk Expected cash flows which are uncertain due to the

influence of risk are adjusted to derive cash flows whichare certain to occur (and hence free from risk)

These adjusted cash flows are called certaintyequivalent cash flows

Certainty equivalent cash flows may be considered to

be risk-free guaranteed cash flows that are equivalentto the uncertain expected cash flows under risk.

How do we estimate the Certainty Equivalent Cash flows?


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Estimation of Certainty Equivalent

Cash Flows

Three approaches:

A. Utility based approach

B. Risk-return model based approach

C. Cash flow Haircuts


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Certainty Equivalent Cash Flows (CECF)

A. Utility based approach:

Because certainty equivalent is a risk-free cash flow that iscertain to occur & it provides the same utility as theexpected utility of the risky outcomes it is a function of therisk aversion of the decision makers

The greater the risk aversion the lower the CECF & viceversa

Issues:

However risk aversion differs from individual to individual(or firm to firm)

Utility functions may be different for different individuals

Hence same investment may have different set of CECF for

different investors


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CECF

A. Utility based approach

How do we derive a utility model foran individual / firm?

Because the utility function is a

mathematical function, CECF derivedon the basis of such functions may turnout to be negative for positive riskycash flows for extremely risk averseindividuals

Many utility functions have failed toexplain individual / firm behaviour in

practice


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CECF

B. Risk-Return Model based approach:

This approach uses the risk premium embedded in the risk

adjusted discount rate derived from the risk-return models

to calculate the CECF

For any year the compounded value of the risk premium isused to discount the uncertain cash flow in order to derive

the CECF for that yearhence the risk premium is also

called Compounded Risk Premium


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CECF

A. Risk-Return Model based approach: For any year t the CECF can be calculated

as:

Where:CECFt= Certainty Equivalent Cash Flow for

year t

t= Certainty equivalent coefficient foryear t=

)E(CFCECF ttt

t

t

f

r)(1

)r1(


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CECF

t= Certainty equivalent coefficient for year t

= =

Risk premium embedded in the risk adjusted discount rate =

t

t

tr)(1)r(1

f

tf

t

)r(1

r)1(

1

tPremium)Risk1(

1

1-

)r(1

r)1(

f

CECF


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CECF

The effects of this type of adjustment are

Uncertainty increases with futurity

Hence Uncertainty has a compounding

effect over time; so the cash flows that arefurther into the future will have lower

certainty equivalents than the earlier cash

flows The more uncertain cash flows have lower

certainty equivalents.


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DCF Value Using Certainty Equivalent

Cash Flows

(C) Trimming the Cash FlowsCash Flow

Haircuts

Reduction of the uncertain cash flows by

subjective judgment instead of adjusting thediscount rate

But reduction of cash flows may be subjective

based on individual perception e.g. more riskaverse investor would reduce the cash flows more

as compared to less risk averse investor


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Risk Adjusted Discount Rate Versus

Certainty Equivalent Cash Flows

Adjusting the cash flow by the certainty equivalent, and then

discounting the resulting cash flow by the risk-free rate is equivalent

to discounting the uncertain cash flow by a risk adjusted discount rate

However in some situations the two approaches will result in different

outcomes

When risk premiums change over time, certainty equivalent

approach is better to use.

Both approaches will give different outcomes , when certainty

equivalents are derived through subjective judgments while riskadjusted rate is derived through risk return models.

Negative cash flows are treated differently by the two approaches


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Hybrid Models

Risk-Return based approach & CE approach have

their own comparative merits It is easier to estimate the parameters of risk-

return models and so adjust the risk baseddiscount rate for some market-wide risk factors

Eg. Interest rate volatility, purchasing power risk,economic cycles & variations in economic growth

The above risk factors tend to operate in a

continuous manner and affect the investmentreturns on a continuous basis

For such risks it is easier to adjust the discount

rate instead of cash flows


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Hybrid Models

There are other types of market riskssudden political

changes, changes in govt. policies, economicdisruptions etc.

Further there can be market risk factors that can be

contingent upon occurrence of definite eventssudden price rise / fall due to sudden disturbances in

supply-demand balance

These are discontinuous market risk factors; they occur

less frequently but can have a great impact on value

It is generally easier to adjust the expected cash flows

for such risks if the cost of protection is known


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Hybrid Models

Continuous market risk factors: volatility ofinterest rates, economic cycles & inflation

Discontinuous market risk factors:economic policy changes or political risks(change in govt. or others)

Contingent market risk factors: suddenincrease/decrease in commodity pricestriggered by certain conditions

Firm-specific risks: IR problems, Technology

risks, Competition risk


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Hybrid Models

Different types of risk factors can be more

conveniently adjusted in differentcomponents of the fundamental valuation

model

Adjustment for continuous market risk factors

can be conveniently done in discount rate

Adjustment for discontinuous market riskfactors & contingent risk factors can be

conveniently done in cash flows

Firm specific risks may be treated selectively


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Hybrid Models: Caution

Adjusting both cash flows and discount ratesubjectively can lead to double adjustment for the

same risk factors

To prevent this a 2-step procedure should befollowed:

1. Classify the risks that an investment / asset /

project faces2. State explicitly how the risks will be adjusted for


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Example: Damodaran

Table 5.2 (p 113), Table 5.3 (p 114), Table 5.4

(p 115), Table 5.5 (p 116)


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DCF Risk Adjustment: Merits & Demerits

Use of risk return models for risk adjustment is

more standardized, transparent, understandablefor those who might examine the valuationmethodology & are flexible to changes.

Further they are explicit about the risks adjustedfor & the risks that are not

However these models are based on assumptionson how the investors & markets behave but the

reality may be quite different

The correct impact of risks may not be capturedwholly in the discount rate and cash flows

l k d


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Post-Valuation Risk Adjustment

An approach to risk assessment and adjustment is

to find out the value of a risky asset / investment/project as if there were no risk involved and then

to adjust the risk-free value for the risk involved

Adjustments may be: Discounts / Premiums

Common practice: Some risks adjusted in discount

rate, others adjusted post-valuation

2 steps:

1. Calculate the risk-free value: Base case value

2. Adjust the base case value for the risks

l k d


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Justification for Post-Valuation Adjustment

Downside Impact: Someassets/investments may not be veryactively traded and hence involve anilliquidity risk; such risks can not beadjusted in discount rates

Upside Impact: Similarly premiums may beapplied in the post-valuation adjustment if

there are concerns that the expected cashflows do not fully reflect the potential forupside benefits in some risky investments

l i i k dj


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Adjustment for Downside Risks:

Most common downside risk: Illiquidity

May be associated with following assets:

a. Stocks of closely held cos.

b. Real estate

c. Precious metalsbullion / jewelry

d. Antiquee. Fine art

f. Stamps

g. Private businesses/cos.

P V l i Ri k Adj


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Adjustment for Downside Risks: Illiquidity Risk

It may be measured through the implicit/explicitcosts associated with liquidation of assets

For publicly held stocks of listed cos. following are

the liquidation costs: commission or brokerage to the broker

Bid-ask spread of the broker

Price impact of the stock when buy or sellorder is placed by the investor - depends onthe nature of stock & type of investor

Opportunity costtiming & need to wait

D id Ri k Illi idi Ri k


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Downside RiskIlliquidity Risk

These costs will vary based on the characteristics of

the assets The costs associated with liquidation of stocks of

closely held companies (e.g. private limited

companies and unlisted public limited companies) or

real assets are much higher than those for publicly

traded stocks (widely held cos.)

Real assets include gold, real estate, fine art, stamps,

antiques etc Transaction costs are least for assets such as gold &

silver because they are traded in standardised units

D id Ri k Illi idi Ri k


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Commissions payable on realestate depend on:

a. Type of real estateresidential

or commercialb. Value of the propertyc. Location & local conditions

Commissions will be far in excessof that payable on financialassets

D id Ri k Illi idit Ri k


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For assets such as fine art the

commissions may be as high as 15-20

percent of the value because:

Fewer intermediaries Fine art (& Real estate) are not

standardised items

Experts are involved in valuation, &they charge significant fee thus raising

the transaction costs

D id Ri k Illi idit Ri k


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The transaction costs involved in buying

& selling of private businesses tend tobe very high

Depend upon the size of business,

quality of assets, nature of liabilities &profitability

There is no organised market forbuy/sell of business entities whichentails further costs for searching thebuyer or seller

Do nside Risk Illiq idit Risk


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Hence investors in private equity

and venture capitalists have to

provide for illiquidity of their

investments while assessing thevalue of such investments.

So transaction costs of illiquid assets

can be substantial and are higher

than those for the liquid assets.

lli idi i k i i l id


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Illiquidity RiskEmpirical Evidences

Bond market:Liquidity matters for all types of

bonds but it matters more for risky

bonds than for safer bonds

Liquidity differs across bonds issued

by different entities and also acrossdifferent bonds issued by same issuer


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Illi idi Ri k E i i l E id


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Illiquidity RiskEmpirical Evidences

Venture Capital & Private Equity (PE) Investors provide funding & want a share in ownership

of these businesses.

These investments are highly risky and mostly illiquid

Hence investors discount more on worth of the business

Thus the higher the discount, the lower the intrinsic

value & the larger the proportion of ownership claimed

for the amount of funding provided An estimate of the amount of illiquidity discount:

difference between the returns earned by PE investors &

those who invest in listed cos.

Illi idi Di C P i


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Illiquidity DiscountCommon Practice

Fixed illiquidity discount for valuation ofPE Or

Range of discount with the exact

amount of discount in that range being

determined by the subjective judgment

of the analyst

Other Types of Discount


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Other Types of Discount

Companies belonging to regulated industries are

exposed to unfavourable regulatory changes Those that are subject to possible litigations will

be discounted by the analysts during the

valuation exercise Adjustments for such risks are typically in the

form of post-valuation discounts because thesame are generally difficult to be incorporated in

the discount rate

Extent of discount reflects the analysts own riskaversion

Post Valuation Risk Adjustment: Premiums


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Post-Valuation Risk Adjustment: Premiums

This is particularly important in the contextof corporate restructuring

Adjustment for Upside Risks:

Control premium

Synergy Premium

Adjustment for Upside Risks


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Control premium:

The potential value that can be created if acompetent & effective management replaces

existing incompetent management, & controls

the firm Adjusting for the control premium: Adding a

premium to the existing value of the firm (status

quo value)

Assumption: functioning of the incumbent

management team is not optimal & can be

improved upon by a better management team.



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Synergy premium:

Synergy refers to the scope for

additional value creation by a

combination of several firms that leadsto new opportunities otherwise not

available to the firms operating

independently

Operating synergies & Financial

synergies



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Synergy premium

Operating synergies: Additional value creation fromthe operations of the combined firm & includes

factors: economies of scale, better bargaining power

vis--vis suppliers & customers and higher growthpotential; generally reflected in increased expected

cash flows after combination

Financial synergies: Additional value that can be

created as a result of tax benefits, diversification of

risk, higher debt capacity & returns generated by the

use of excess cash; generally reflected either in the

form of increased cash flows or lower discount rate

Limitations of Post Valuation Adjustments


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Limitations of Post-Valuation Adjustments

Double counting: These risks (downside/upside)

can be double counted, if the analyst has already

taken them into consideration while estimating

the discount rates and cash flows

Basis of adjustment: Difficulty to arrive at the

amount of the premiums or discounts that is to be

used and the basis for the same

Bias: Individual biases can creep into valuation

process due to the subjectivity of the technique

Relati e Val ation Approach


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Relative Valuation Approach

Does not assume a DCF framework Very popular approach owing to its

apparent simplicity Assets are valued on the basis of how

the market values similar assets

Widely used in capital markets; can be

applied in other markets as well

Relati e Val ation Basis


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Relative Valuation: Basis

Value of an asset is arrived at from thevalue of 'comparable' assets, and this

process is standardized by using a

common variable Rests on two basic components:

a. Concept of comparable assetsb. Standardized price

Relative Valuation Basis


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a. Comparable/similar assets: Assets similar in terms of cash

flows, risk and growth potential In corporate valuation it is

assumed that other cos. in the

same line of business as the one

being valued are comparable cos.



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b. Standardized price:

A standardized price is calculated by dividing

the market price by some quantity that can

be logically related to that value; multiplescan be compared across comparable

companies

Commonly used multiples in valuation ofequity shares: Price/Earnings multiple,

Price/Book value multiple, Price/Revenues

multiple



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This approach may be used in real asset valuation

because it is easy to find out similar or identicalassets

For valuation of stocks of listed cos. this approachhas following limitations:

a. Non-availability of similar stocksevery co. isunique in itself; so definition of comparable assetsis extended to include companies that are different

from the one under considerationb. Different multiples calculated with respect to

different bases can result in different assessmentfor the same company

R l i V l i Ri k Adj


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Relative Valuation: Risk Adjustment

Risk adjustment process is very

unsophisticated

Based on strong assumptions

Adjustments are implicit &

subjective

R l i V l i Ri k Adj I


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Relative Valuation: Risk Adjustment Issues

Sector Comparison

Size / Market cap

Ratio-based comparisons

Statistical approach



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Sector Comparison:

Assumption: All firms in the same industry

(FMCG, Technology) are in equivalent risk class;

hence their P/E multiples are comparable

As risk characteristics of firms in a sector tend to

diverge increasingly this approach will give

misleading estimates of firm value

Thus firms with higher risks may be overvalued

and those with lower risks may be undervalued



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Firm Size:

Generally firm size is estimated in terms of revenues

or market cap

If there are many firms within the same sector then

generally analysts compare firms of similar size

Assumption: Riskiness differs across firms of

different sizes; firms of different size should be

priced at different multiples of book value, earnings

and revenues



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Statistical approach:

Regressing the P/E Multiples against

some measure of risks e.g. Beta,

market capitalization, S.D. of earnings

or stock price etc.

This approach could be used to findout whether valuation multiples

differ for riskier cos & safer cos

DCF Valuation Versus Relative Valuation


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DCF Valuation Versus Relative Valuation

Risk adjustment in DCF approach is explicit

and systematic whereas it is ad hoc andarbitrary in the relative valuation approach

Risk adjustment in DCF is more time and dataintensive whereas relative valuation is lesstime consuming and requires less data

DCF approach is less dependent on marketefficiency while relative valuation critically

depends on the assumption that market isefficient & prices the assets correctly (hencevalue multiples are a good measure of theequity value of a firm).

Risk Adjustment in Practice


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Risk Adjustment in Practice

Common practice is to make multiple

adjustments using the four major

approaches discussed so far.

But it may become difficult to review andrevise the risk adjustment due to various

approaches used

There is a possibility of multiple adjustmentsfor the same risk being done in the value

estimate

management of risk module 3

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