Total No
.
Typically I don’t believe in providing solutions immediately after exam as it creates more problem than solution especially for those of you find that your answers are different. But this time I am breaking the rule as I find lot of solutions and comments floating in the market are not up to the mark or even conceptually incorrect. I can’t believe that just a few conceptual and unseen questions can create that much problem. Don’t expect every exam like SFM Nov 10.This is not even 20% of SFM june09. Except question on APT, currency swap and utility (not because they are difficult but they are tested for the first time) everything else seems normal (copy paste as usual from past exam or RTP). My comments under each solution also discusses our coverage -CA Rajiv Singh
1.
(a)
Mr. Tamarind intends to invest in equity shares of a company the value of which depends upon various parameters as mentioned below: Factor
Beta
Expected value in %
Actual value in %
GNP
1.20
7.70
7.70
Inflation
1.75
5.50
7.00
Interest rate
1.30
7.75
9.00
Stock market index
1.70
10.00
12.00
Industrial production
1.00
7.00
7.50
If the risk free rate of interest be 9.25%, how much is the return of the share under Arbitrage Pricing Theory?
Solution: Student support comments This exam problem is based on the concept of APT. A practical question on APT has been tested for the first time. This question is simple but requires understanding of concepts. It is difficult for those who only cram formulae. Based on my discussion with students I find that most of you have wrongly picked expected value as factor return and that is a serious mistake. Remember class discussion and refer revision material where I have clearly mentioned that no method of calculation of factor risk premium is
5 Marks
. suggested by APT therefore it would be given in exam. Here it is given but you need to pick it up. The one practical way of estimating factor risk premium is by using concept of factor portfolio and this is not tested here. The other way would be to take difference between past data on the actual and forecast values of the factors. This is what is tested in this question. Now you see the solution below. How simple it is. Remember APT gives return on expected return basis. Therefore the expected return as per APT would be: =9.25%+(7.70-7.70)x1.2+(7-5.5)x1.75+(9-7.75)x1.30+ (12-10)x1.70+(7.5-7)x1=17.4%
(b)
The current market price of an equity share of Penchant Ltd is Rs. 420. Within a period of 3 months. The maximum and minimum price of it is expected to be Rs. 500 and Rs. 400 respectively. If the risk free rate of interest be 8% p.a. What should be the value of a "3 month's" CALL option under the 'Risk neutral' method at the strike rate of Rs. 450? Given 0.02
e
= 1.0202
Student support comments This exam problem is a simple application of Risk neutral method. To my surprise some of you have solved using portfolio replicating approach whereas the question is very specific about risk neutral method. Refer class notes we have discussed this method in detail and even basic questions done in class are sufficient enough to answer this question. For your understanding this problem is solved by both methods. Risk Neutral method .08x.25
Step I R= e
=1.0202
Step II u = 500/420=1.19 and d= 400/420=.952 (remember as per Cox Ross& Rubinstein u is estimated first and then the d is always 1/u. However this relationship is not correct if we take the forecast data given in the question. As usual I doubt ICAI would admit it. We have taken d based on price information given)
Step III probability of ‘up’ movement= 1.0202-.952/(1.19-.952)=.287 Probability of ‘down’ movement=1-.287=.713
Step III cu=50
cd=0
Step III call option value= (50x.287+ 0)/1.0202=14.06
5 Marks
.
Portfolio replicating method (remember this answer will not be accepted)
Step I delta=50-0/500-400=.50
Step II value of B(loan amount) We can get the value of B by either equating up value of stock with up value of option or down with down. .50x400-1.0202B=0 this gives value of B=196.04
Step III call option value= .5x420-196.04=13.96
(c)
A Mutual Fund is holding the following assets in Rs. Crore : Investments in diversified equity shares
90.00
Cash and Bank Balances
10.00 100.00
The Beta of the portfolio is 1.1. The index future is selling at 4300 level. The Fund Manager apprehends that the index will fall at the most by 10%. How many index futures he should short for perfect hedging so that the portfolio beta is reduced to 1.00? One index future consists of 50 units. Substantiate your answer assuming the Fund Manager's apprehension will materialize.
Solution Student support comments This exam problem is testing understanding of application of Index future contracts for hedging portfolio risk. The question has two parts. The first part asks to calculate number of future contracts to be sold to reduce portfolio beta and the second part asks to check hedging strategy if Index falls by 10%.We have done a detailed application of this concept. This question is exactly similar to ex 235 (for first part) and Ex227 for the second part under Module3. Part I Number of Future contracts required to be sold for reducing portfolio beta(assuming beta for future contract is equal to1)= (1-1.10)x 100 cores/(4300x50) = 465.12
5 Marks
. Hence 465 Index contracts need to be sold. However due to rounding off the hedge efficiency will be affected. Also remember that the above activity will not provide perfect hedge position. The sale of future contracts will ensure that portfolio beta is equal to 1.This means when Index changes by 10% the portfolio value should also change by 10% if we count overall position. Part II impact on overall portfolio position and fund position when Index Future falls by 10%
Assuming that hedge efficiency is calculated on the last date of the expiry of the contract date (on the last date future price is equal to spot price) the result is given below.
Loss on Portfolio position = 100 cores x (10x1.1 ) =11cores
Gain on future position= 465x50x (4300x10%)=1 Crore approx.
Net loss =10 crores. The objective of keeping beta equal to 1 is achieved because loss of Rs 11 on portfolio position is offset by Rs 1 Crore gain on Future. Hence net loss on portfolio is Rs 10 crores which we would have got had we maintained beta of the portfolio equal to 1 rather than 1.1. The future contract helped in achieving this objective without changing composition of the portfolio.
(d)
Mr. Tempest has the following portfolio of four shares: Name
Beta
Investment Rs. Lac.
Oxy Rin Ltd.
0.45
0.80
Boxed Ltd
0.35
1.50
Square Ltd
1.15
2.25
Ellipse Ltd
1.85
4.50
The risk free rate of return is 7% and the market rate of return is 14%. Required. (i) Determine the portfolio return. (ii) Calculate the portfolio Beta.
Solution Student support comments This exam problem is simply testing calculation knowledge in portfolio management. You won’t get a problem easier than that at CA final level.
5 Marks
. Refer Ex27 of Module 2 (ii) portfolio beta
Step I
O weight of the shares
B
.08 .17
S
E
.25 .50
step II portfolio beta = weighted average betas of individual assets =.45x.08+.35x.17+1.15x.25+1.85x.50=1.31 (i) Using SML equation we can get portfolio return =7%+(14%-7%)x1.31=16.17%
Typically I don’t believe in providing solutions immediately after exam as it creates more problem than solution especially for those of you find that your answers are different. But this time I am breaking the rule as I find lot of solutions and comments floating in the market are not up to the mark or even conceptually incorrect. I can’t believe that just a few conceptual and unseen questions can create that much problem. Don’t expect every exam like SFM Nov 10.This is not even 20% of SFM june09. Except question on APT, currency swap and utility (not because they are difficult but they are tested for the first time) everything else seems normal (copy paste as usual from past exam or RTP). My comments under each solution also discusses our coverage -CA Rajiv Singh
1.
(a)
Mr. Tamarind intends to invest in equity shares of a company the value of which depends upon various parameters as mentioned below: Factor
Beta
Expected value in %
Actual value in %
GNP
1.20
7.70
7.70
Inflation
1.75
5.50
7.00
Interest rate
1.30
7.75
9.00
Stock market index
1.70
10.00
12.00
Industrial production
1.00
7.00
7.50
If the risk free rate of interest be 9.25%, how much is the return of the share under Arbitrage Pricing Theory?
Solution: Student support comments This exam problem is based on the concept of APT. A practical question on APT has been tested for the first time. This question is simple but requires understanding of concepts. It is difficult for those who only cram formulae. Based on my discussion with students I find that most of you have wrongly picked expected value as factor return and that is a serious mistake. Remember class discussion and refer revision material where I have clearly mentioned that no method of calculation of factor risk premium is
5 Marks
. suggested by APT therefore it would be given in exam. Here it is given but you need to pick it up. The one practical way of estimating factor risk premium is by using concept of factor portfolio and this is not tested here. The other way would be to take difference between past data on the actual and forecast values of the factors. This is what is tested in this question. Now you see the solution below. How simple it is. Remember APT gives return on expected return basis. Therefore the expected return as per APT would be: =9.25%+(7.70-7.70)x1.2+(7-5.5)x1.75+(9-7.75)x1.30+ (12-10)x1.70+(7.5-7)x1=17.4%
(b)
The current market price of an equity share of Penchant Ltd is Rs. 420. Within a period of 3 months. The maximum and minimum price of it is expected to be Rs. 500 and Rs. 400 respectively. If the risk free rate of interest be 8% p.a. What should be the value of a "3 month's" CALL option under the 'Risk neutral' method at the strike rate of Rs. 450? Given 0.02
e
= 1.0202
Student support comments This exam problem is a simple application of Risk neutral method. To my surprise some of you have solved using portfolio replicating approach whereas the question is very specific about risk neutral method. Refer class notes we have discussed this method in detail and even basic questions done in class are sufficient enough to answer this question. For your understanding this problem is solved by both methods. Risk Neutral method .08x.25
Step I R= e
=1.0202
Step II u = 500/420=1.19 and d= 400/420=.952 (remember as per Cox Ross& Rubinstein u is estimated first and then the d is always 1/u. However this relationship is not correct if we take the forecast data given in the question. As usual I doubt ICAI would admit it. We have taken d based on price information given)
Step III probability of ‘up’ movement= 1.0202-.952/(1.19-.952)=.287 Probability of ‘down’ movement=1-.287=.713
Step III cu=50
cd=0
Step III call option value= (50x.287+ 0)/1.0202=14.06
5 Marks
.
Portfolio replicating method (remember this answer will not be accepted)
Step I delta=50-0/500-400=.50
Step II value of B(loan amount) We can get the value of B by either equating up value of stock with up value of option or down with down. .50x400-1.0202B=0 this gives value of B=196.04
Step III call option value= .5x420-196.04=13.96
(c)
A Mutual Fund is holding the following assets in Rs. Crore : Investments in diversified equity shares
90.00
Cash and Bank Balances
10.00 100.00
The Beta of the portfolio is 1.1. The index future is selling at 4300 level. The Fund Manager apprehends that the index will fall at the most by 10%. How many index futures he should short for perfect hedging so that the portfolio beta is reduced to 1.00? One index future consists of 50 units. Substantiate your answer assuming the Fund Manager's apprehension will materialize.
Solution Student support comments This exam problem is testing understanding of application of Index future contracts for hedging portfolio risk. The question has two parts. The first part asks to calculate number of future contracts to be sold to reduce portfolio beta and the second part asks to check hedging strategy if Index falls by 10%.We have done a detailed application of this concept. This question is exactly similar to ex 235 (for first part) and Ex227 for the second part under Module3. Part I Number of Future contracts required to be sold for reducing portfolio beta(assuming beta for future contract is equal to1)= (1-1.10)x 100 cores/(4300x50) = 465.12
5 Marks
. Hence 465 Index contracts need to be sold. However due to rounding off the hedge efficiency will be affected. Also remember that the above activity will not provide perfect hedge position. The sale of future contracts will ensure that portfolio beta is equal to 1.This means when Index changes by 10% the portfolio value should also change by 10% if we count overall position. Part II impact on overall portfolio position and fund position when Index Future falls by 10%
Assuming that hedge efficiency is calculated on the last date of the expiry of the contract date (on the last date future price is equal to spot price) the result is given below.
Loss on Portfolio position = 100 cores x (10x1.1 ) =11cores
Gain on future position= 465x50x (4300x10%)=1 Crore approx.
Net loss =10 crores. The objective of keeping beta equal to 1 is achieved because loss of Rs 11 on portfolio position is offset by Rs 1 Crore gain on Future. Hence net loss on portfolio is Rs 10 crores which we would have got had we maintained beta of the portfolio equal to 1 rather than 1.1. The future contract helped in achieving this objective without changing composition of the portfolio.
(d)
Mr. Tempest has the following portfolio of four shares: Name
Beta
Investment Rs. Lac.
Oxy Rin Ltd.
0.45
0.80
Boxed Ltd
0.35
1.50
Square Ltd
1.15
2.25
Ellipse Ltd
1.85
4.50
The risk free rate of return is 7% and the market rate of return is 14%. Required. (i) Determine the portfolio return. (ii) Calculate the portfolio Beta.
Solution Student support comments This exam problem is simply testing calculation knowledge in portfolio management. You won’t get a problem easier than that at CA final level.
5 Marks
. Refer Ex27 of Module 2 (ii) portfolio beta
Step I
O weight of the shares
B
.08 .17
S
E
.25 .50
step II portfolio beta = weighted average betas of individual assets =.45x.08+.35x.17+1.15x.25+1.85x.50=1.31 (i) Using SML equation we can get portfolio return =7%+(14%-7%)x1.31=16.17%
