PRACTICE 2 A stock market advisory service offers three investments portfolios f
ID: 3298592 • Letter: P
Question
PRACTICE 2 A stock market advisory service offers three investments portfolios for one of its customers. All portfolios have the same investment cost. Portfolio A contains speculative stocks, which aim for capital gain through price appreciation. Portfolio B is made up of stocks of stable companies that pay good dividends overt the long run Portfolio C comprises stocks with a moderate potential for growth and a moderate yield of dividends. The customer has enough money to invest in only one of these three portfolios for a period of one year. The net return on investments will depend on whether the economy during the period will be in a stage of inflation, recession, or depression. The net potential gains or losses are calculated as follows STATES OF NATURE Portfolio A Portfolio B Portfolio C Inflatiorn S 100 S 50 S 70 Recession S 50 S 45 S 40 Depression S- 60 S 40 ALTERNATIVES 1. What would be the decision according to (1) Maximax (optimism); (2) Maximin (pessimism) (3) Equal Likelihood; (4) Minimizing Regret, and, (5) Realism where = .6? Be sure to show work and indicate the recommended alternative each time 2. Consider the objective probabilities for inflation, recession and depression are 70%, 20%, and 10%. respectively. Which portfolio should now the customer choose by applying the method of coefficient of variation? (NB. Remember to find x and ) 3. What is the probability of making a profit of at least $40 for each alternative? N.B. Use the Z-Table.) Which alternative is preferred under this requirement?Explanation / Answer
PORTFOLIO A:
CALCULATION OF MEAN RETURN:
Expected Return=SUM(Probability of return* Return)
Probability of Inflation =70%=0.7, Return=$100
Probability of Recession =20%=0.2, Return=$50
Probability of Depression =10%=0.1, Return= $ -60
Expected return=0.7*100+0.2*50-0.1*60=$74
Mean Return=74
CALCULATION OF STANDARD DEVIATION:
Variance=SUM OF(((Return-mean return)^2)*Probability of return)
Standard Deviation=Square Root of Variance.
Calculation of Standard Deviation of Portfolio A is given below
A
B
C=B-74
D=C^2
E=D*A
Scenario
Probability
Return
Deviation of return
Deviation of return
Deviation Squared*
from mean
Squared
Probability
Inflation
0.7
$100
$26
$676
$473.20
Recession
0.2
$50
($24)
$576
$115.20
Depression
0.1
($60)
($134)
$17,956
$1,795.60
TOTAL
$2,384.00
STANDARD DEVIATION
48.8262225
Coefficient of Variation=Standard Deviation/Mean=48.83/74=0.6598=65.98%
PORTFOLIO B:
CALCULATION OF MEAN RETURN:
Expected Return=SUM(Probability of return* Return)
Probability of Inflation =70%=0.7, Return=$50
Probability of Recession =20%=0.2, Return=$45
Probability of Depression =10%=0.1, Return= $ 40
Expected return=0.7*50+0.2*45+0.1*40=48
Mean Return=48
CALCULATION OF STANDARD DEVIATION:
Variance=SUM OF(((Return-mean return)^2)*Probability of return)
Standard Deviation=Square Root of Variance.
Calculation of Standard Deviation of Portfolio B is given below
A
B
C=B-48
D=C^2
E=D*A
Scenario
Probability
Return
Deviation of return
Deviation of return
Deviation Squared*
from mean
Squared
Probability
Inflation
0.7
$50
$2
$4
$2.80
Recession
0.2
$45
($3)
$9
$1.80
Depression
0.1
$40
($8)
$64
$6.40
TOTAL
$11.00
STANDARD DEVIATION
3.31662479
Coefficient of Variation=Standard Deviation/Mean=3.32/48=0.0691=6.91%
PORTFOLIO C:
CALCULATION OF MEAN RETURN:
Expected Return=SUM(Probability of return* Return)
Probability of Inflation =70%=0.7, Return=$70
Probability of Recession =20%=0.2, Return=$40
Probability of Depression =10%=0.1, Return= $ -10
Expected return=0.7*70+0.2*40+0.1*(-10)=$56
Mean Return=56
CALCULATION OF STANDARD DEVIATION:
Variance=SUM OF(((Return-mean return)^2)*Probability of return)
Standard Deviation=Square Root of Variance.
Calculation of Standard Deviation of Portfolio C is given below
A
B
C=B-56
D=C^2
E=D*A
Scenario
Probability
Return
Deviation of return
Deviation of return
Deviation Squared*
from mean
Squared
Probability
Inflation
0.7
$70
$14
$196
$137.20
Recession
0.2
$40
($16)
$256
$51.20
Depression
0.1
($10)
($66)
$4,356
$435.60
TOTAL
$624.00
STANDARD DEVIATION
24.979992
Coefficient of Variation=Standard Deviation/Mean=24.98/56=0.4461=44.61%
CONCLUSION :
Portfolio
Coefficient of
Variation
A
65.98%
B
6.91%
C
44.61%
BY APPLYING THE METHOD OF COEFFICIENT OF VARIATION, THE CUSTOMER SHOULD CHOOSE PORTFOLIO B
3.CALCULATION OF PROBABILITY OF MAKING AT LEAST $ 40 PROFIT
Alternative A
Mean=$74
Standard deviation=Sa=48.83
Minimum Return required=$40
Deviation from Mean=(40-74)=-34
In terms of standard deviation -34=-(34/48.83)*Sa=-0.6963Sa
USING STANDARD NORMAL TABLE:
D=-0.70,N(d)=0.2420
This means the probability of return less than $40=0.2420
Probability of return of at least $40=(1-0.2420)=0.7580=75.80%
Alternative B
Mean=$48
Standard deviation=Sa=3.32
Minimum Return required=$40
Deviation from Mean=(40-48)=-8
In terms of standard deviation -8=-(8/3.32)*Sa=-2.41Sa
USING STANDARD NORMAL TABLE:
D=-2.41,N(d)=0.0082
This means the probability of return less than $40=0.0082
Probability of return of at least $40=(1-0.0082)=0.9918=99.18%
Alternative C
Mean=$56
Standard deviation=Sa=24.98
Minimum Return required=$40
Deviation from Mean=(40-56)=-16
In terms of standard deviation -16=-(16/24.98)*Sa=-0.64Sa
USING STANDARD NORMAL TABLE:
D=-0.64,N(d)=0.2611
This means the probability of return less than $40=0.2611
Probability of return of at least $40=(1-0.2611)=0.7389=73.89%
PROBABILITY OF AT LEAST $ 40 PROFIT:
Portfolio
Probability
A
75.80%
B
99.18%
C
73.89%
A
B
C=B-74
D=C^2
E=D*A
Scenario
Probability
Return
Deviation of return
Deviation of return
Deviation Squared*
from mean
Squared
Probability
Inflation
0.7
$100
$26
$676
$473.20
Recession
0.2
$50
($24)
$576
$115.20
Depression
0.1
($60)
($134)
$17,956
$1,795.60
TOTAL
$2,384.00
STANDARD DEVIATION
48.8262225
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