CHAPTER 5 Risk and Rates of Return

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Principles of Business FinanceFin 510
Dr. Lawrence P. Shao Marshall University Spring
2002
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CHAPTER 5 Risk and Rates of Return

• Stand-alone risk
• Portfolio risk
• Risk return CAPM/SML

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What is investment risk?
Investment risk pertains to the probability of
earning less than the expected return. The
greater the chance of low or negative returns,
the riskier the investment.
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Annual Total Returns,1926-1996
Average Standard Return Deviation Distribution
Large-companystocks 12.7
20.3 Small-companystocks
17.7 34.1 Long-termcorporate bonds
6.0 8.7 Long-termgovernment
5.4 9.2 Intermediate-termgovernme
nt 5.4 5.8 U.S.
Treasurybills 3.8
3.3 Inflation 3.2
4.5
-90 0 90
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Investment Alternatives(Given in the problem)
Economy
Prob.
T-Bill
HT
Coll
USR
MP
Recession 0.1 8.0 -22.0 28.0
10.0 -13.0 Below avg. 0.2 8.0 -2.0 14.7
-10.0 1.0 Average 0.4 8.0 20.0 0.0 7.0
15.0 Above avg. 0.2 8.0 35.0 -10.0 45.0
29.0 Boom 0.1 8.0 50.0 -20.0 30.0 43.0 1.0
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Do T-bills promise a completelyrisk-free return?
No, T-bills are still exposed to the risk of
inflation. However, not much unexpected inflation
is likely to occur over a relatively short period.
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Do the returns of HT and Coll. move with or
counter to the economy?

• HT With. Positive correlation. Typical.
• Coll Countercyclical. Negative correlation.
  Unusual.

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Calculate the expected rate of return on each
alternative

k expected rate of return.

kHT (-22)0.1 (-2)0.20 (20)0.40
(35)0.20 (50)0.1 17.4.
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k
HT
17.4
Market
15.0
USR
13.8
T-bill
8.0
Coll.
1.7
HT appears to be the best, but is it really?
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Whats the standard deviationof returns for each
alternative?
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sT-bills 0.0.
sColl 13.4. sUSR 18.8. sM 15.3.
sHT 20.0.
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• Standard deviation (si) measures total, or
  stand-alone, risk.
• The larger the si , the lower the probability
  that actual returns will be close to the expected
  return.

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Expected Returns vs. Risk
Expected
Risk, s
Security
return
HT 17.4 20.0 Market 15.0 15.3 USR 13.8
18.8 T-bills 8.0 0.0 Coll. 1.7 13.4
Seems misplaced.
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Coefficient of Variation (CV)
Standardized measure of dispersion about the
expected value
Std dev s
CV .

Mean
k
Shows risk per unit of return.
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Portfolio Risk and Return
Assume a two-stock portfolio with 50,000 in HT
and 50,000 in Collections.

Calculate kp and sp.
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Portfolio Return, kp


kp is a weighted average
n


kp S wiki.
i 1

kp 0.5(17.4) 0.5(1.7) 9.6.



kp is between kHT and kCOLL.
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Alternative Method
Estimated Return
Economy
Prob.
HT
Coll.
Port.
Recession 0.10 -22.0 28.0 3.0 Below avg.
0.20 -2.0 14.7 6.4 Average 0.40 20.0 0.0
10.0 Above avg. 0.20 35.0 -10.0 12.5 Boom
0.10 50.0 -20.0 15.0

kp (3.0)0.10 (6.4)0.20 (10.0)0.40
(12.5)0.20 (15.0)0.10 9.6.
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3.3
CVp 0.34.
9.6
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• sp 3.3 is much lower than that of either stock
  (20 and 13.4).
• sp 3.3 is lower than average of HT and Coll
  16.7.
• \ Portfolio provides average k but lower risk.
• Reason negative correlation.

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General statements about risk

• Most stocks are positively correlated. rk,m
  0.65.
• s 35 for an average stock.
• Combining stocks generally lowers risk.

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Returns Distribution for Two Perfectly Negatively
Correlated Stocks (r -1.0) and for Portfolio WM
Stock W
Stock M
Portfolio WM
.
.
.
.
25
25
25
.
.
.
.
.
.
.
15
15
15
0
0
0
.
.
.
.
-10
-10
-10
22
sp ()
Company Specific Risk
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Stand-Alone Risk, sp
20 0
Market Risk
10 20 30 40 2,000
Stocks in Portfolio
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• As more stocks are added, each new stock has a
  smaller risk-reducing impact.
• sp falls very slowly after about 40 stocks are
  included. The lower limit for sp is about 20
  sM .

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Stand-alone Market Firm-specific

risk risk risk
Market risk is that part of a securitys
stand-alone risk that cannot be eliminated by
diversification. Firm-specific risk is that part
of a securitys stand-alone risk which can be
eliminated by proper diversification.
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Beta measures a stocks market risk. It shows a
stocks volatility relative to the market.

• Beta shows how risky a stock is if the stock is
  held in a well-diversified portfolio.

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How are betas calculated?

• Run a regression of past returns on Stock i
  versus returns on the market. Returns D/P g.
• The slope of the regression line is defined as
  the beta coefficient.

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Illustration of beta calculation
Regression line ki -2.59 1.44 kM


.
20 15 10 5
.
Year kM ki 1 15 18 2 -5 -10 3 12 16
_
-5 0 5 10 15 20
kM
-5 -10
.
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• If beta 1.0, average stock.
• If beta gt 1.0, stock riskier than average.
• If beta lt 1.0, stock less risky than average.
• Most stocks have betas in the range of 0.5 to 1.5.

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Expected Risk Security Return (Beta)
HT 17.4 1.29 Market 15.0 1.00 USR 13.8
0.68 T-bills 8.0 0.00 Coll. 1.7 -0.86
Riskier securities have higher returns, so the
rank order is OK.
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Use the SML to calculate therequired returns.
SML ki kRF (kM - kRF)bi .

• Assume kRF 8.
• Note that kM kM is 15. (Equil.)
• RPM kM - kRF 15 - 8 7.

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Required Rates of Return
kHT 8.0 (15.0 - 8.0)(1.29) 8.0
(7)(1.29) 8.0 9.0 17.0.
kM 8.0 (7)(1.00) 15.0. kUSR 8.0
(7)(0.68) 12.8. kT-bill 8.0
(7)(0.00) 8.0. kColl 8.0
(7)(-0.86) 2.0.
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Expected vs. Required Returns

k
k
HT 17.4 17.0 Undervalued k gt k Market
15.0 15.0 Fairly valued USR 13.8 12.8
Undervalued k gt k T-bills 8.0 8.0 Fairly
valued Coll. 1.7 2.0 Overvalued k lt k



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Calculate beta for a portfolio with 50 HT and
50 Collections
bp Weighted average 0.5(bHT) 0.5(bColl)
0.5(1.29) 0.5(-0.86) 0.22.
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The required return on the HT/Coll. portfolio is
kp Weighted average k 0.5(17)
0.5(2) 9.5. Or use SML kp kRF (kM -
kRF) bp 8.0 (15.0 - 8.0)(0.22)
8.0 7(0.22) 9.5.
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If investors raise inflation expectations by 3,
what would happen to the SML?
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Required Rate of Return k ()
D I 3
New SML
SML2
SML1
18 15 11 8
Original situation
0 0.5 1.0 1.5 Risk, bi
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If inflation did not changebut risk aversion
increasedenough to cause the marketrisk premium
to increase by3 percentage points, whatwould
happen to the SML?
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After increase in risk aversion
Required Rate of Return ()
SML2
kM 18 kM 15
SML1
18 15
D RPM 3
8
Original situation
Risk, bi
1.0
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• Investors seem to be concerned with both market
  risk and total risk. Therefore, the SML may not
  produce a correct estimate of ki
• ki kRF (kM - kRF)b ?