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Pinnacle Academy
Chapter Tests [CT] Series
April 2015 Batch
201-202, Florence Classic, Besides Unnati Vidhyalay,
Jain Derasar Road, Ashapuri Society, Akota, Vadodara-20. ph: 98258 561 55
Solution of Test of
Portfolio Management
[SFM – CA Final]
Conducted on 31st October 2015
[Solution is at the end with marking for self-assessment]
Q1
(a)
Interpret following statements:
(i) Return from zero beta asset is 8 %.
(ii) Return of an asset having beta of 1 is 15 %.
(iii) Investor can borrow and lend at rate of 6 %.
(iv) Beta is 1.25
(b)
(4 Marks)
Answer the following:
i. For A Ltd. expected return is 16 %. Its beta is 0.8. Market return is 18% and risk-free
return is 5%. Is the share worth purchasing?
ii. For B Ltd. beta is 1.75 and it is priced in such a manner that it offers return of
12.75%. Market risk premium is 7% and risk free return is 4%. It is known that slope
of SML is 5. Is B Ltd. correctly priced?
iii. For C Ltd. expected return is 25%. Market portfolio offers return of 15%. An investor
requires return of 22%. What proportion of funds should be invested in C Ltd. and
market portfolio to achieve target return?
iv. D Ltd. and E Ltd. have risk (standard deviation) of 12% and 20% respectively. The
correlation coefficient between the two securities is 0.3. What proportion of funds
should be invested in D Ltd. and E Ltd. to ensure that portfolio risk is minimum?
(1 + 1 + 2 + 4 = 8 Marks)
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(c)
Following details are available for F Ltd. and market portfolio:
Scenario
pi
Return
F Ltd. Market
I
II
III
IV
V
0.1
0.2
0.4
0.2
0.1
20 %
30 %
40 %
50 %
60 %
25 %
15 %
50 %
15 %
25 %
Determine the following:
i.
ii.
iii.
iv.
v.
Risk of F Ltd. and of Market
Coefficient of Variation of F Ltd.
Covariance between returns of F Ltd. and Market
Correlation coefficient between returns of F Ltd. and Market
Ex-ante beta of F Ltd.
(10 Marks)
Q2
A presentation is required to be made to select foreign pension fund and hedge fund
managers on equity rebalancing strategies. Constant Mix strategy is to be followed.
Initial information is as under:
Portfolio Value:
Desired Equity Allocation:
Desired Bond Allocation:
$ 50 million
60%
40%
Consider following cases independent of each other:
i.
ii.
iii.
iv.
Equity stocks increase in value by 10%
Equity stocks decrease in value by 10%
Equity stocks increase in value by 100%
Equity stocks decrease in value by 50%
Demonstrate for each of the above scenarios the rebalancing between equity and
bonds to maintain the constant mix.
(8 Marks)
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Solution of Test of Portfolio Management
Conducted on 31st October 2015
Q1
(a)
(i) Risk free rate of return is 8 %.
(ii) Market return is 15 %.
(iii) Risk free rate of return is 6 %.
(iv) There shall be 1.25 % change in required return of security with every 1 %
change in market return in the direction of change in market return. Moreover, the
security is aggressive.
(1 Mark each i.e. 4 Marks in total)
(b)
i. CAPM required return = 5 + 0.8 [18 – 5] = 15.4 %. For A Ltd. expected return is 16%.
Thus, the given share is under-priced and worth purchasing.
(1 Mark)
ii. For B Ltd., CAPM required return = 4 + 1.75 [7] = 16.25 %. Now, slope of SML for B
Ltd. is: 16.25 – 4 / 1.75 = 7. But actual slope of SML is 5. Since, slope for B Ltd. is
different from that given, B Ltd. is not correctly priced.
(1 Mark)
iii. Portfolio Return = rc wc + rMP wMP
i.e. 22 = 25 wc + 15 (1 – wc)
i.e. 22 = 25wc + 15 – 15 wc
i.e. 22 – 15 = 10 wc
i.e. wc = 7/10 = 0.7
wMP = 1 – 0.7 = 0.3
Thus, one should invest 70% in C Ltd. and 30% in market portfolio to obtain desired
return of 22%.
(2 Marks)
iv. rDE = Cov (D,E) / σD σE
i.e. Cov (D,E) = rDE σD σE
i.e. Cov (D,E) = 12 (20) (0.3) = 72
W D = (20)2 – 72 / (12)2 + (20)2 – 2 (72) = 328 / 400 = 0.82 i.e. 82%
W E = 1 – 0.82 = 0.18 i.e. 18%
Thus, one should invest 82% in D Ltd. and 18% in E Ltd. to ensure that portfolio risk
is minimum.
(4 Marks)
(c)
Statistical Table:
F Ltd.
Market
pi
20
30
40
50
60
25
15
50
15
25
0.1 -20 -6 12
40
3.60
0.2 -10 -16 32
20
51.20
0.4 0
19
0
0 144.40
0.2 10 -16 -32
20
51.20
0.1 20 -6 -12
40
3.60
0 120 254.00
40
40
40
40
40
31
31
31
31
31
(5 Marks)
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i.
ii.
iii.
iv.
v.
σF = under-root of 120 = 10.95 %; σM = under-root of 254 = 15.94 %
Coefficient of Variation of F Ltd. = 10.95 / 40 = 0.2738
Cov (F, M) = 0 [from table]
rFM = Cov (F, M) / σF σM = 0 / (10.95) (15.94) = 0
Ex-ante beta of F Ltd. = 0 / 254 = 0
(5 Marks)
Q2
Rebalancing shall be as under –
(figures in millions)
Sr.
No.
Initial
Allocation
Change
in value
Rebalancing
Before
Action
After
(i)
Equity 30
Bonds 20
50
+ 10%
33 31.80 Sell
20 21.20
53 53.00
Equity of $ 1.2
(iI)
Equity 30
Bonds 20
50
- 10%
27
20
47
(iii)
Equity 30
Bonds 20
50
+ 100%
60
20
80
48 Sell
32
80
(iv)
Equity 30
Bonds 20
50
- 50%
15
20
35
21 Buy Equity of $ 6
14
35
28.2 Buy Equity of $ 1.2
18.8
47.0
Equity of $ 12
(2 Marks each i.e. 8 Marks in total)
CA. Ashish Lalaji
Solution is available on www.ashishlalaji.net
Solution prepared by
Common Mistakes Observed:
Question 1:
(a)
In (ii) market return is 15% was not interpreted. Instead interpretation for beta was
provided.
(b)
(i) Expected return of 16% was interpreted as required return due to which the
security turned out to be overpriced.
It is CAPM return, which is required return.
(ii) Slope of SML of B should be determined and compared with slope of SML
provided. Instead, the given slope was used to determine required return of B
leading to wrong conclusion.
(iv) Formula for optimal portfolio of two securities was not used
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(c)
Coefficient of variation (CV) was not calculated. It is SD / Return. Few of the
students mixed up CV with Co-variance.
Question 2:
Each case was independent. A few of the students did cumulative calculations and
hence lost marks.
Solution prepared by
CA. Ashish Lalaji
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