p = 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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^kp is between ^kHT and ^kCOLL.
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Alternative Method
6 - 20
Economy Prob.
Recession 0.10
Below avg. 0.20
6 -1
CHAPTER 6
Risk and Rates of Return
Stand-alone risk Portfolio risk Risk & return: CAPM/SML
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6 -2
Risk,
20.0% 15.3 18.8*
0.0 13.4*
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6 - 16
Coefficient of Variation (CV)
Standardized measure of dispersion about the expected value:
Std dev
HT: Moves with the economy, and has a positive correlation. This is typical.
Coll: Is countercyclical of the economy, and has a negative correlation. This is unusual.
6 - 15
Expected Returns vs. Risk
Security
HT Market USR T-bills Coll.
Expected return
17.4% 15.0 13.8* 8.0 1.7*
*Seems misplaced.
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6 -9
Calculate the expected rate of return on each alternative:
k^ = expected rate of return.
n
kˆ = k Pi i. i=1
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6 - 23
General statements about risk
Most stocks are positively correlated. rk,m 0.65.
35% for an average stock.
Combining stocks generally lowers risk.
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Prob. T-bill
USR HT
6 - 13
0 8 13.8 17.4 Rate of Return (%)
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6 - 14
Standard deviation (i) measures total, or stand-alone, risk.
^k = CVA > CVB.
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6 - 18
Portfolio Risk and Return
Assume a two-stock portfolio with $50,000 in HT and $50,000 in Collections.
Inflation
3.2
4.5
0 3.2%
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6 -5
Investment Alternatives
(Given in the problem)
Economy Prob. T-Bill HT Coll USR MP
+
(8.0
–
8.0)20.2
1/2
T-bills = + (8.0 – 8.0)20.4 + (8.0 – 8.0)20.2
+
(8.0
–
8.0)20.1
T-bills = 0.0%. HT = 20.0%.
Coll = 13.4%. USR = 18.8%.
M = 15.3%.
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^k 17.4% 15.0 13.8 8.0 1.7
HT appears to be the best, but is it really?
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6 - 11
What’s the standard deviation of returns for each alternative?
Boom
0.1 8.0 50.0 -20.0 30.0 43.0
1.0
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6 -6
Why is the T-bill return independent of the economy?
Will return the promised 8% regardless of the economy.
CV = Mean = ^k .
Shows risk per unit of return.
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6 - 17
A
B
0
A = B , but A is riskier because larger
probability of losses.
However, not much unexpected inflation is likely to occur over a relatively short period.
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6 -8
Do the returns of HT and Coll. move with or counter to the economy?
^kHT = (-22%)0.1 + (-2%)0.20 + (20%)0.40 + (35%)0.20
+ (50%)0.1 = 17.4%.
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6 - 10
HT Market USR T-bill Coll.
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6 - 21
(3.0 – 9.6)20.10
+ (6.4 – 9.6)20.20
p = + (10.0 – 9.6)20.40
+ (12.5 – 9.6)20.20
+
(15.0
–
What is investment risk?
Investment risk pertains to the probability of actually earning a low or negative return.
The greater the chance of low or negative returns, the riskier the investment.
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6 -4
Annual Total Returns,1926-1998
Average Standard Return Deviation
Distribution
Small-company
stocks
17.4%
Large-company
stocks
13.2
33.8% 20.3
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6 -3
Probability distribution
Firm X
Firm Y
-70
0
15
Rate of 100 return (%)
Expected Rate of Return
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9.6)20.10
1/ 2
= 3.3%.
CVp =