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Risk
RISK AND RETURN Risk is defined as the variation from the
expected return.
Risk is measured by the standard deviation of
M. Sadiqul Islam return (k).
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Return Risk of a Firm
Return is estimated as: Types of risk:
Amount Received - Amount Invested
1. Business Risk
Rate of Return
Amount Invested 2. Financial Risk
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Business Risk
Business Risk ROIC
Net Income to Common Stockholders After Tax Interest Payments
Capital
Business risk is the variation of return for the
main operation of the firm. If the firm does not have debt:
It is the riskiness of the firm’s stock if it Net Income to Common Stockholde rs
ROIC (zero debt) ROE U
uses no debt. Capital
In stand-alone sense, it is a function of the
uncertainty inherent in the projections of a Business risk of leverage free firm is
firm’s future return on invested capital measured by the standard deviation of its
(ROIC). ROE (ROE).
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Business Risk Business Risk
Business risk depends on:
a. Demand variability e. Ability to develop new products in a
b. Sales price variability timely cost effective manner.
c. Input cost variability f. Foreign risk exposure.
d. Ability to adjust output price for g. Operating leverage – the extent to
changes in input cost. which costs are fixed.
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Financial Risk Return on Stock
Financial risk is the additional risk Return on individual stock:
placed on the common stockholders for
(P1 - P0 ) D
the use of borrowed capital. Rate of Return
P0
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Return on Stock
Return on Stock
For example, X company’s common stock
was bought at Taka 20 and one year later, it
Expected rate of return:
was sold at Taka 24. Within this time, a
dividend of Taka 1 was received for the
stock. Expected rate of return k̂ P1k1 P2 k 2 ........ Pn k n
n
(24 - 20) 1 Pi k i
Rate of Return i 1
20
5
0.25 or 25%
20
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Risk Risk
n
Variance k2 Pi (k i k̂) 2 Coefficient of Variation is the relative
i 1 measure of risk.
n k
Standard Deviation k P (k i i k̂) 2 Coefficien t of Variation (CV)
i 1 k̂
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Risk and Return on Stock Risk and Return on Stock
Economic Probability Return Return
Expected Return (Stock A)
Condition Stock A Stock B
Recession 0.10 0.10 -0.05 = (0.10 x 0.10) + (0.20 x 0.15) + (0.40 x 0.20)
+ (0.20 x 0.25) + (0.10 x 0.30)
Weak 0.20 0.15 0.15 = 0.20 or 20%
Normal 0.40 0.20 0.26 Expected Return (Stock B)
= (0.10 x -0.05) + (0.20 x 0.15) + (0.40 x
Good 0.20 0.25 0.35 0.26) + (0.20 x 0.35) + (0.10 x 0.44)
Strong 0.10 0.30 0.44 = 0.243 or 24.30%
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Risk and Return on Stock Risk and Return on Stock
0.0548
CV (Stock A) 0.2739
Standard Deviation (Stock A) 0.20
{0.1(0.10 - 0.20) 2 0.2(0.15 - 0.20)2 0.4(0.20 - 0.20) 2 0.2(0.25 - 0.20)2 0.1(0.30 - 0.20)2 }
0.0548
CV (Stock B) = (0.128845 / 0.243) = 0.5302
Standard Deviation (Stock B)
= {0.10(-0.05-0.243)2 + 0.20(0.15-0.243)2 + 0.40(0.26-0.243)2 +
0.20(0.35-0.243)2 + 0.10(0.44-0.243)2}
= 0.128845
Stock B is more risky.
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Risk and Return on Portfolio
Risk and Return on Portfolio
Expected return on a portfolio is simply the
weighted average of the expected returns on Say, 50% Stock A and
the individual assets in the portfolio. The 50% Stock B,
weight is the fraction of the total portfolio k̂ p (0.50 x 0.20) (0.50 x 0.20)
invested in each asset. 0.20
k̂ p w 1 k̂ 1 w 2 k̂ 2 ............. w n k̂ n k̂ p (0.60 x 0.10) (0.4 x 0.15)
n
w i k̂ i 0.12
i 1
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Portfolio Risk Portfolio Risk
In the portfolio context, risk has two Systematic risk is the variation of return due to
the changes in the market.
components:
It happens mostly due to the changes in the
a. Systematic risk (market risk) economic condition or macro economic
b. Unsystematic risk (diversifiable risk). variables. For example, the variation due to
changes in the interest rate or fiscal
incentives.
Systematic risk is not diversifiable.
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Portfolio Risk Risk-Return Trade-off
Relationship between risk and return:
Unsystematic risk is the variation of return Higher the risk, higher the return.
due to the factors not related to the market.
It is caused by the micro level factors. For Risk Trade- Return
example, strikes, resignation of CEO, fire
off
etc.
It affects only one firm or industry. Positive relation between risk and return.
Unsystematic risk is diversifiable.
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Capital Asset Pricing Model
(CAPM) CAPM
CAPM is an asset pricing model which states
that securities would attain such a price that K
SML
is expected to produce a return equal to the
risk-free rate plus a premium for systematic
risk.
E (k ) k RF (k M k RF ) kRF
(kM – kRF) is the market risk premium.
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Risks of Fixed Income Securities
Risks of Fixed Income Securities
3. Purchasing power risk is the variation
Types of bond risk by source: of return due inflation in the economy.
1. Default risk is the variation of return 4. Foreign exchange risk is the variation
due to the non-payment of interest and of return due to the change in the
principal by the borrower. exchange rate.
2. Interest rate risk is the variation of 5. Call risk is the variation of return due
return due to the change in market to the redemption of bond prior to its
interest rate. maturity.
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