Lecture Eight Portfolio Management. Standalone risk Portfolio risk Risk & return: CAPM/SML. 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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Lecture Eight
Portfolio Management
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.
Probability distribution
Firm X
Firm Y
Rate of
return (%)
70
0
15
100
Expected Rate of Return
Economy
Prob.
TBill
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 0.18.0 50.0 20.0 30.0 43.0
1.0
Will return the promised 8% regardless of the economy.
No, Tbills are still exposed to the risk of inflation.
However, not much unexpected inflation is likely to occur over a relatively short period.
^
k = expected rate of return.
^
kHT = (22%)0.1 + (2%)0.20
+ (20%)0.40 + (35%)0.20
+ (50%)0.1 = 17.4%.
^
k
HT
17.4%
Market
15.0
USR
13.8
Tbill
8.0
Coll.
1.7
HT appears to be the best, but is it really?
= Standard deviation.
.
(
)
(
)
2
2
é
ù
8.0

8.0
0
.
1
+
8.0

8.0
0
.
2
.5
ê
ú
(
)
(
)
2
2
s
=
+
8.0

8.0
0
.
4
+
8.0

8.0
0
.
2
ê
ú
T

bills
ê
ú
(
)
2
+
8
.
0 
8
.
0
0
.
1
ë
û
.
sTbills = 0.0%.
sColl=13.4%.
sUSR=18.8%.
sM=15.3%.
sHT = 20.0%.
Prob.
Tbill
USR
HT
0
8
13.8
17.4
Rate of Return (%)
Expected
Risk, s
Security
return
HT 17.4% 20.0%
Market 15.0 15.3
USR 13.8* 18.8*
Tbills 8.0 0.0
Coll. 1.7* 13.4*
*Seems misplaced.
Standardized measure of dispersion
about the expected value:
Std dev s
CV = = .
^
Mean
k
Shows risk per unit of return.
B
A
0
sA = sB , but A is riskier because larger
probability of losses.
s
= CVA > CVB.
^
k
Assume a twostock portfolio with $50,000 in HT and $50,000 in Collections.
^
Calculate kp and sp.
^
^
kp is a weighted average:
n
^
^
kp = Swikw.
i = 1
^
kp = 0.5(17.4%) + 0.5(1.7%) = 9.6%.
^
^
^
kp is between kHT and kCOLL.
Estimated Return
Economy
Prob.
HT
Coll.
Port.
Recession 0.1022.0% 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%.
1
/
2
2
(
)
é
ù
3.0

9.6
0
.
10
ê
ú
ê
ú
2
(
)
+
6
.
4 
9
.
6
0
.
20
ê
ú
ê
ú
2
(
)
s
=
+
10
.
0 
9
.
6
0
.
40
= 3.3%.
ê
ú
p
ê
ú
2
(
)
+
12
.
5 
9
.
6
0
.
20
ê
ú
ê
ú
ê
ú
2
(
)
+
15
.
0 
9
.
6
0
.
10
ë
û
3.3%
CVp = = 0.34.
9.6%
^
Stock W
Stock M
Portfolio WM
.
.
.
.
25
25
25
.
.
.
.
.
.
.
15
15
15
0
0
0
.
.
.
.
10
10
10
25
25
15
15
0
0
10
10
Stock M’
Portfolio MM’
Stock M
25
15
0
10
^
Prob.
Large
2
1
0
15
Even with large N, sp» 20%
sp (%)
Company Specific Risk
35
StandAlone Risk, sp
20
0
Market Risk
102030 40 2,000+
# Stocks in Portfolio
= +
risk risk risk
Market risk is that part of a security’s standalone risk that cannot be eliminated by diversification.
Firmspecific risk is that part of a security’s standalone risk which can be eliminated by proper diversification.
If you chose to hold a onestock portfolio and thus are exposed to more risk than diversified investors, would you be compensated for all
the risk you bear?
_
ki
Illustration of beta calculation:
Regression line:
ki = 2.59 + 1.44 kM
^
^
.
20
15
10
5
.
YearkMki
115% 18%
2 510
312 16
_
505101520
kM
5
10
.
Answer: Yes, if ri,m is negative. Then in a “beta graph” the regression line will slope downward.
_
b = 1.29
ki
HT
40
20
b = 0
TBills
_
kM
2002040
20
Coll.
b = 0.86
Expected Risk
Security Return (Beta)
HT 17.4% 1.29
Market 15.0 1.00
USR 13.8 0.68
Tbills 8.0 0.00
Coll. 1.7 0.86
Riskier securities have higher returns, so the rank order is OK.
SML: ki = kRF + (kM  kRF)bi .
^
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%.
kTbill= 8.0% + (7%)(0.00)= 8.0%.
kColl= 8.0% + (7%)(0.86)= 2.0%.
^
k
k
HT 17.4% 17.0% Undervalued:
k > k
Market 15.0 15.0 Fairly valued
USR 13.8 12.8 Undervalued:
k > k
Tbills 8.0 8.0 Fairly valued
Coll. 1.7 2.0 Overvalued:
k < k
^
^
^
SML: ki = 8% + (15%  8%) bi .
ki (%)
SML
.
HT
.
.
kM = 15
kRF = 8
USR
.
Tbills
.
Coll.
Risk, bi
1 0 1 2
bp= Weighted average
= 0.5(bHT) + 0.5(bColl)
= 0.5(1.29) + 0.5(0.86)
= 0.22.
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%.
Required Rate
of Return k (%)
D I = 3%
New SML
SML2
SML1
18
15
11
8
Original situation
00.51.01.52.0
If inflation did not changebut risk aversion increasedenough to cause the marketrisk premium to increase by3 percentage points, whatwould happen to the SML?
After increase
in risk aversion
Required Rate of Return (%)
SML2
kM = 18%
kM = 15%
SML1
18
15
D MRP = 3%
8
Original situation
Risk, bi
1.0
ki = kRF + (kM  kRF)b + ?