Free CFA Level 1 Practice Questions for December 2012 exam

Team DG and Knowledge Varsity is glad to announce that we will provide some free CFA Level 1 sample questions till November 29, 2012.

We had started a similar initiative for the June 2011 exam, please see link below June 2011 Question

Knowledge Varsity will be providing fresh set of CFA Level 1 sample questions.

How it will work?

1. Existing users should login and subscribe to this thread. Some users may be automatically subscribed (depending on your profile settings) and can skip this step.

2. New users can Register and then login to subscribe to this thread.

3. When you go to the Subscription page, make sure to choose "Daily/Weekly updates by email" option from the "Notification Type" dropdown. Then click "Add Subscription".

4. We will post a question and members can discuss the answer in this forum.

5. We will then post the solution and the next question.

All the best for your CFA Level 1 prep!

22-08-2012, 09:49 AM

ratankv

Question #1

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Today's Question (Questions and answers provided by Knowledge Varsity)

Q1. An investor, plan to retire at the age of 60. He expects to live till the age of 90. He is currently aged 25. He invests the first payment in the account today and invests for 35 years (that is total of 35 investment done). The retirement account earns 12% per annum. Assume that he would like to withdraw $30,000 per year starting from the point when he turns 60 for 30 years, find out the approximate amount he should deposit in his retirement account every year? Here assume, that the investor doesn't leave any money for their heirs.

22-08-2012, 11:17 AM

anita123

[QUOTE=ratankv;2947]================================================== ===============================================
Today's Question (Questions and answers provided by Knowledge Varsity)

Q1. An investor, plan to retire at the age of 60. He expects to live till the age of 90. He is currently aged 25. He invests the first payment in the account today and invests for 35 years (that is total of 35 investment done). The retirement account earns 12% per annum. Assume that he would like to withdraw $30,000 per year starting from the point when he turns 60 for 30 years, find out the approximate amount he should deposit in his retirement account every year? Here assume, that the investor doesn

23-08-2012, 01:16 AM

naveen

It will be A.

Thanks DG & Knowledge Varsity Team for helping & guiding us.

In these type of problems, we need to come up with a common point.
If we take the middle point as common point, that will be the best.
So, we can find out the PV of the cash inflows at T = 59; Using that, we can find out the PV at T=60; and then we can compute the PMT for the series of cash outflows. Let’s do step by step calculation
Step 1: Find out the PV at T = 59
Keep the calculator in the END mode, the 2nd series of cash flows from T=60 to T=89 looks like ordinary annuity and the PV will come one period before the first cash flow.
FV = 0; I/Y =12; N=30; PMT =$30,000; PV = ?
CPT-> PV => PV = $241,655.19
Step 2:Find out the PMT. Here you have to note that the FV of the investment would be equal to the present value that we have found out.
FV = PV59 = $241,655.19; PV = $0; N = 35; I/Y =12; PMT = ?
CPT -> PMT =>PMT = -$559.82
So, the investor needs to deposit $559.82 every year for 35 years, in order to get $30,000 every year when he retires.

24-08-2012, 10:44 AM

ratankv

Question #2

Today's Question (Questions and answers provided by Knowledge Varsity)
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Q2. A Firm's EPS was $5 in 2002, In year 2008 the EPS was $14. Find the compounded annual growth rate (CAGR) of the EPS.
A. 15.85 %
B. 18.7 %
C. Can

24-08-2012, 04:17 PM

Nidhi Taleja

Thank you Mr. Ratan for the video.
This is a very good initiative! :)

24-08-2012, 07:34 PM

Rohit Shehgal

Quote:

Originally Posted by ratankv

Today's Question (Questions and answers provided by Knowledge Varsity)
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Q2. A Firm's EPS was $5 in 2002, In year 2008 the EPS was $14. Find the compounded annual growth rate (CAGR) of the EPS.
A. 15.85 %
B. 18.7 %
C. Can’t be determined from the given options

We can use PV = -5, FV = 14 and calculate rate.
According to my calculation, CAGR = 15.8%
So answer is A.

25-08-2012, 01:14 AM

Shubhojit

@Ratan Sir:- Thanks for the new concept of video & detail explaination.... it's very helpful. I hv one query reg Q-1, what if we take common pt at one end ?? Then how to calculate ?

25-08-2012, 04:08 AM

ratankv

Hi Shubhojit,
You can take common point at the start/end/middle as per your convenience. However, the middle one is better, as it will require less computation steps.
Let's say that you are taking the common point in the end of the period (that is at T=90), then the following would be the steps
- Compute the FV of the $30,000 at the end of the period (T=90), this can be done by taking. N=30, I/Y=12, PV=0, PMT = +30,000, Compute FV, please note that the FV will come at T=89. You will have to multiply by 1.12 to get FV at 90.
FV(90) = FV(89) * 1.12
Now, next you will have to bring the FV at 90, to FV at 59. Find out how many periods are in between. 60 - 59 = 1 (and there is one period), so 90 - 59 = 31 => 31 periods are there.
therefore, FV(59) = FV(90)/1.12^31 = 241,655.519
Now, solve the PMT using the following (please note that we are still in end mode, so you need to visualise one period before 25, that is 24)
N = 35, I/Y= 12, PV =0, FV = FV(59) = 241,655.519, PMT = ?
The PMT value will come as 559.8238 which is the same as computed earlier.
If you, see here the number of calculation being done is more. Same would happen if you take the common point at the start also. So, it is advisable to make the middle as the common point.

Thanks
Ratan

Quote:

Originally Posted by Shubhojit

@Ratan Sir:- Thanks for the new concept of video & detail explaination.... it's very helpful. I hv one query reg Q-1, what if we take common pt at one end ?? Then how to calculate ?

25-08-2012, 12:30 PM

ratankv

1 Attachment(s)

Solution for Question # 2

Q2 Answer is B

Check the Video Solution Q#2 below:

Text Solution for Question #2 is below

CAGR is the rate at which the EPS has grown.
Please see the timeline below http://www.daulatguru.com/finance-fo...0&d=1345874193
Easily we can solve this with the financial calculator
So, the number of periods from 2002 to 2008 is equal to 6, therefore N = 6
The parameters of TVM are :
FV = -$14; PV = $5; PMT = 0; N=6; I/Y =?
CPT -> I/Y =>I/Y = 18.72%
So, the EPS has grown at an average rate of 18.72% for the 6 years.

Note that you will get option A as the answer when you mistakenly take n = 7, so ensure that you input correct data.
You will get error in your calculator, when you dont take PV and FV values having opposite sign.

Thanks
Ratan

Quote:

Originally Posted by ratankv

Today's Question (Questions and answers provided by Knowledge Varsity)
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Q2. A Firm's EPS was $5 in 2002, In year 2008 the EPS was $14. Find the compounded annual growth rate (CAGR) of the EPS.
A. 15.85 %
B. 18.7 %
C. Can’t be determined from the given options

25-08-2012, 12:36 PM

ratankv

Question #3

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Today's Question (Questions and answers provided by Knowledge Varsity)

Q3. An investor purchased one share of Goldman Sachs (NYSE:GS) at $100 at T = 0, he again purchased one more share of GS at $120 at T =1. He received total dividend of $2 at T= 1 and a dividend of $3 per share at T =2, the investor sold the shares at T=2 for a total consideration of $260 (or $130 per share). Find money weighted and time weighted return?
A. Money weighted = 14.4% ; Time weighted = 16.41%
B. Money weighted = 16.41% ; Time weighted = 14.4%
C. Money weighted = 14.4% ; Time weighted = 16.28%

@Ratan Sir:- Thanks a lot for explaining the concept. Right, the end pts takes long steps than middle one.

25-08-2012, 11:24 PM

Prabir Bansal

@Sir:- What are the basic applications of CAGR ?? Also, AMR (Arithmetic Mean Return) is the only tool to compare with CAGR or any other is also there..?? Plz explain.

Answer of Q3 shud be C.

26-08-2012, 08:11 PM

ratankv

Hi Prabir,

CAGR can be used to find out the average growth over a period of time, so essentially it gives an idea on the growth rate.
Arithmetic mean return should not be used to compute gorwth rate over multiple periods because it will give wrong answer.
Wait for sometime and I will be posting a question related to that concept also.

@Sir:- What are the basic applications of CAGR ?? Also, AMR (Arithmetic Mean Return) is the only tool to compare with CAGR or any other is also there..?? Plz explain.

Answer of Q3 shud be C.

26-08-2012, 08:14 PM

ratankv

Hi Rohit,

The number of period should be 6 and not 7.
Just think this way, we want to find out the growth in 1 year, you start with ending EPS of 2009 and ending EPS of 2010. So, here you have 2 EPS values, but the time period is 1.
So, in the problem we had 7 years, but the number of period was 6.
I hope it clarifies.

We can use PV = -5, FV = 14 and calculate rate.
According to my calculation, CAGR = 15.8%
So answer is A.

26-08-2012, 08:40 PM

ratankv

Solution for Question # 3

Q3 Answer is C

Check the Video Solution Q#3 below:

Text Solution for Question #3 is below

Important assumption : We assume that the dividend is paid just before the period ends. Money Weighted Return Calculation: Step 1 : We should identify the cash flows that are happening at the various intervals. As per our sign convention, money going out from investor should be treated as negative and money coming to an investor should be treated as positive. At T =0 : Purchase of 1st share was done => Cash outflow of $100 => CF0 = -$100 At T =1 : Purchase of 2nd share was done => Cash outflow of $120
Dividend is received => Cash Inflow of $2
Sum of these two results in cash outflow of $118 => CF1 = -$118 At T =2 : 2 shares are sold => Cash inflow of $260
Dividend is received => Cash Inflow of $3 * 2 = $6
Sum of these two results in cash inflow of $266 => CF1 = $266

Step 2: Plug the cash flow values in the financial calculator to compute the IRR (because MWR is nothing but IRR)
IRR = 14.438% or Money Weighted Return is 14.438%

Time Weighted return Calculation: Step 1: We should first find out the number of periods, here significant cash in-flow is happening at T=1 and cash outflow is happening at T=2. So we have one period from T=0 to T=1 and another period from T=1 to T=2

Step 2: Compute the portfolio value just before the significant cash inflow or outflow. For Period 1: Beginning Value = $100; Ending Value = $120; Dividend Received = $2 For Period 2: Beginning Value = $120 (for the 1st share) + $120 (amount that is invested) = $240
Ending Value = $260; Dividend Received = $6 (for 2 shares) Note: Many candidates have confusion regarding why the beginning value of the portfolio should be $240, why not it should be $220, the point here is that at the beginning of period 2, the first share could be sold for $120 and there is an investment of $120 more, hence the portfolio value is $240. Also we should consider the dividend in this period for both the shares.

Step 3:Find out the holding period return of the periods
For Period 1:HPR = (120 – 100 + 2)/100 = 22%
For Period 2: HPR = (260 – 240 + 6)/240 = 10.83%

Step 4: Find out the geometric mean return or TWR from the holding period returns
(1 + TWR)^2 = (1+ HPR1)*(1+ HPR2)
=>(1 + TWR)^2 = (1.22) * (1.1083) = 1.3522
=>(1 + TWR) = 1.1628 => TWR = 0.1628
Or Time Weighted return is 16.28%
Is it always the case that Time Weighted return is less than money weighted return? Please note that this is not the case and we got into this situation for this problem only.

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Today's Question (Questions and answers provided by Knowledge Varsity)

Q3. An investor purchased one share of Goldman Sachs (NYSE:GS) at $100 at T = 0, he again purchased one more share of GS at $120 at T =1. He received total dividend of $2 at T= 1 and a dividend of $3 per share at T =2, the investor sold the shares at T=2 for a total consideration of $260 (or $130 per share). Find money weighted and time weighted return?
A. Money weighted = 14.4% ; Time weighted = 16.41%
B. Money weighted = 16.41% ; Time weighted = 14.4%
C. Money weighted = 14.4% ; Time weighted = 16.28%

Q4. A T bill having 120 days to maturity is yielding 3.5% on bank discount basis, how much will be its money market yield?
A. 3.5%
B. 3.54%
C. 3.4%

27-08-2012, 12:53 AM

Shubhojit

@Sir:- It's thumb rule to assume that the dividend is paid just before the period ends or we can hv some other assumptions as well ?? Also, why Time wt return is always less than Money wt return ?? Kindly explain the concept.

Regards,
Shubhojit.

27-08-2012, 12:59 AM

mahesh

Answer of Q-4 should be A.

@Prabir:-

Some of the common CAGR applications are :
a) Calculating and communicating the average returns of investment funds
b) Demonstrating and comparing the performance of investment advisors
c) Comparing the historical returns of stocks with bonds or with a savings account
d) Forecasting future values based on the CAGR of a data series (you find future values by multiplying the last datum of the series by (1 + CAGR) as many times as years required). As every forecasting method, this method has a calculation error associated.
e) Analyzing and communicating the behavior, over a series of years, of different business measures such as sales, market share, costs, customer satisfaction, and performance.

Correct me, if I am wrong Ratan Sir.

28-08-2012, 12:39 AM

DG Mod

Q4 Answer B

Step 1: Assume the face value to be $100, we would like to find out the discount at which the T bill is trading

Step 2: Once discount is calculated, Find out the price at which the bond is trading
Price = F

28-08-2012, 11:47 PM

DG Mod

Q5 Answer A

First Step: Find the semi-annual yield
Semi-annual yield = (1+EAY)^(1/2)– 1
=> Semi-annual yield = (1.05)^0.5 – 1 = 2.4695%

Second Step: Multiply the semi-annual yield by 2 to get the BEY
=> BEY = 2 * 2.4695% = 4.939%

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Today's Question (Questions and answers provided by Knowledge Varsity)

Q6. Consider that you have made investment in a stock and it provided a return of 100% in the first year and -50% in the second year. How much is the return you have received from the stock?

First Step: Find the semi-annual yield
Semi-annual yield = (1+EAY)^(1/2)

30-08-2012, 12:57 AM

DG Mod

Q6 Answer B

Rather than getting into complication, let’s work from basic reasoning.

Let’s assume that you had invested $100 in the stock at T=0.
Since the first year return is 100%, the value of your stock will be $200 at T=1.

Now, in the 2nd year, the return is -50%, therefore the value of your stock will be $100 at T=2.
So, you started with $100 and have $100 in the end.

It implies that over the 2 years, the return is 0%, so it means that the average return should also be 0%.
Suppose, we use Arithmetic Mean return to explain the return over the 2 year period. The arithmetic mean return will be (100% + -50%)/2 = 25%
But, we see that the return is 0% over the 2 years. This implies that the Arithmetic mean return is not a correct measure to find the average stock return.

Now Let’s calculate the Geometric mean return over the 2 years.
R1 = 100% or 1; R2 = -0.5
=> (1+R1) = 2 and (1+R2) = 0.5
=> (1+ RG) = (2 * 0.5)^0.5 => (1+RG) = (1)^0.5 => (1+ RG) = 1
=> RG = 0 or 0%

So, the geometric mean return is 0%, which is the actual average return that we have calculated.

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Today's Question (Questions and answers provided by Knowledge Varsity)

Q7 Suppose you as an investor have invested in a Systematic Investment Plan of a mutual Fund. In a systematic investment plan, the investor has to make same amount of investment every month for some period. You are making contribution of $1000 every month in the fund for 3 months. The below table outlines the price of the fund at which you have made the investment. What is the average purchase price at which you bought the fund?

Will the answer be the arithmetic mean of the price for the 3 periods?
Let’s find the arithmetic mean, which will be ($100+$125+$80) = $305/3 = $101.67
Let’s try to build the following table, where we identify the number of units of the mutual fund that we have bought.

Time--------Investment-----------Price (NAV)-------------Number of Units T=0----------$1000-----------------$100--------------------=$1000/$100 = 10
T=1--------- $1000-----------------$125--------------------=$1000/$125 = 8
T=2----------$1000-----------------$80-------------------- =$1000/$80 = 12.5

So, the total investment is 3 * $1000 = $3000
Total Number of units that is bought is 10 + 8 + 12.5 = 30.5

We know that logically, the average purchase price should be equal to total investment divided by the total number of units
=> Average price = $3000 / 30.5 = $98.3606

So, it implies that the arithmetic mean is not the correct approach to find out the average purchase price in Dollar Cost Averaging method.

Now, what exactly we have calculated which we are saying as the correct answer?
We have calculated the harmonic mean of the purchase price, and that is the correct mean.
Let’s try to rewrite the Average Price Equation, which we have in the above

Now, $1000 will get cancelled in the numerator and the denominator

Or,

1/$100 + 1/$125 + 1/$80 = 3/(Average Price)

This is the formula of the Harmonic Mean, which is given in detail below

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Today's Question (Questions and answers provided by Knowledge Varsity)

Q8. Suppose you have 10 stocks in the portfolio, whose returns are given below. Find out the 4th quintile of the stock returns.
-5%, 4%, 3%, 10%, 2%, 8%, -10%, 7% , 12% and 18%

Consider the portfolio as population.
A. 11.6%
B. 10%
C.12%

Will the answer be the arithmetic mean of the price for the 3 periods?

01-09-2012, 12:47 AM

DG Mod

Q8 Answer A

First arrange the returns in ascending order
-10%, -5%, 2%, 3%, 4%, 7%, 8%, 10%, 12%, 18%

Now we need to find the position at which we will get the 4th quintile.
4th quintile is same as 80 percentile.
=> Ly = (10+1)80/100
=> Ly= 8.8

Therefore, the 4th quintile is 8.8th data from the left. Now 9th data is 12% and 8th data is 10%, this means that the value would be between 10% and 12%. What we can say is that the value will be 10% + 0.8 times the difference between 12% and 10%.

This is because for 1 unit, the difference is 12% minus 10% or 2%, therefore for 0.8 units, the difference will be 0.8 times 2%, this concept is Interpolation.
So the value will be = 8th Value + 0.8 * (9th Value – 8th Value)
=> 10% + 0.8 * (12% - 10%) => 10% + 0.8* 2% = 11.6%

So the 4th quintile is 11.6%, so we can say that 80% of the distribution is below 11.6%

IMPORTANT: We will apply interpolation only when the data set is population. When the data set is a sample, then interpolation should not be used. So, if we had mentioned that in this example, it was a sample then the interpolation would not have been used. The Ly value was 8.8, so we would just take the integer part of it, which in this case is 8, so the value would be the observation in the 8th position. Hence it would be 10%.

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Today's Question (Questions and answers provided by Knowledge Varsity)

Q9. Suppose you determine that the probability of Chennai Super Kings winning a match against Mumbai Indian is 0.6, then what would be the odds that Chennai Super Kings will win the match?
A. 2:3
B. 3:5
C. 3:2

For finding the odds for; without following the formula; we should think of odds for as
Probability the event will occur : Probability the event will NOT occur

=> Probability that Chennai will win : Probability that Chennai will lose
=> 0.6 : 0.4 Or 6:4 Or Simplifying it a bit, 3:2
=> So the odds that Chennai Super Kings will win the match is 3 : 2

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Today's Question (Questions and answers provided by Knowledge Varsity)

Q10. Last year, Reserve Bank of India was increasing the interest rates to contain the inflation. One of the major drawback of raising interest rate is that the chances that the economy will go into recession increases. However, it’s not the case that an economy can’t be in recession if the interest rates are decreased (see USA, even though the interest rates are decreased in US, the state of the economy is not good).

Coming to the question. Let’s say the probability that the Central Bank would increase the interest rate is 0.7 and the conditional probability of Recession happening when the interest rate is increased is 0.9. Also, the conditional probability that the recession will happen if the interest rate is decreased is 0.2.
Which of the following is the unconditional probability that the Recession will happen?

Unconditional probability of Recession = probability when interest rate increase and recession + probability when interest decrease and recession
= .63 + .06
= .69
so the answer according to me is A.

04-09-2012, 09:33 PM

ratankv

1 Attachment(s)

Solution to Question #10

Text Solution to Question #10
You will find that in book, there is notation to the unconditional probabilities. We will go through this problem by following those notations, and then try to solve the problem through the formula of the total probability. In the next step we will try to solve the problem using the TREE DIAGRAM. We advise the candidates to follow the tree diagram.

Probability of Increase in Interest Rate = P(I) = 0.7
Probability of decrease in Interest Rate = P(I’) = 1 – 0.7 = 0.3
Probability of Recession happening Given Interest Rate Increases = P(R|I) =0.9
Probability of Recession happening Given Interest Rate Decreases = P(R|I’) = 0.2
Probability of Recession NOT happening Given Interest Rate Increases = P(R’|I) = 1 - P(R|I) = 1 -0.9 = 0.1

Probability of Recession NOT happening Given Interest Rate Decreases = P(R’|I’) = 1- 0.2 = 0.8

The unconditional probability that the recession will happen is same as the total probability that the recession will happen.
As per the total probability formula, we can write
P(R) = P(R|I) * P(I) + P(R|I’) * P(I’)
=> P(R) = 0.9 *0.7 + 0.2 * 0.3 =0.63 +0.06 = 0.69

So, the unconditional probability that recession will happen is 0.69
The probabilities that you had seen earlier P(R│I) or P(R|I') were conditional probabilities, that is, they were dependent on whether the interest rate is increased or decreased. But the total probability is not depended on increase/decrease of interest rate, it doesn’t matter whether interest rate increases or decreases, if the interest rate increases, then the probability of recession will increase and if the interest rate decreases then the probability of recession will decreases, but overall the probability will be the same and hence un-conditional.
We can find the un-conditional probability of recession NOT happening – it will simply be 1 minus the un-conditional probability of Recession happening.

Let’s see, how we can solve this using Tree Diagram, You will find it intuitive http://www.daulatguru.com/finance-fo...1&d=1346770928
While constructing tree diagram, 1st STEP - We start with first the un-conditional probability, which we have here for the Interest rate. So the first branch will be for the interest rate increase and the other branch is for the interest rate NOT Increasing. 2nd STEP - Then we start with the conditional probabilities and draw branches for them. Throughout the process, we will keep in mind that the branches are Mutually exclusive and Collectively Exhaustive. 3rd STEP – We highlight the node is related to the respective probabilities. Here Node 1 and Node 3 are the nodes for Recession happening and Node 2 and Node 4 are the nodes for Recession NOT happening. 4th STEP - To find out the Total Probability of recession, we add up the value at the nodes were recession happens. Therefore Recession probability = 0.63 + 0.06 = 0.69

This is the way we will be drawing the TREE Diagram.
The Tree diagram will be very useful in solving Baye's Problems. We will be seeing a question on Baye's Very soon.

04-09-2012, 09:45 PM

ratankv

Question #11

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Today's Question (Questions and answers provided by Knowledge Varsity)

Q11. Your portfolio has 10 mutual funds, you met an investment advisor and he advised to hold 6 mutual funds and sell 4 mutual funds. In how many ways this can be achieved?
A. 5040
B. 210
C. 151200

04-09-2012, 09:46 PM

ratankv

Great!

Quote:

Originally Posted by bimupa

Unconditional probability of Recession = probability when interest rate increase and recession + probability when interest decrease and recession
= .63 + .06
= .69
so the answer according to me is A.

''@Sir:- It's thumb rule to assume that the dividend is paid just before the period ends or we can hv some other assumptions as well ?? Also, why Time wt return is always less than Money wt return ?? Kindly explain the concept.''

Regards,
Shubhojit

05-09-2012, 08:15 PM

ratankv

Hi Shubhojit,

Until and unless stated in the question regarding the dividend timing, you should assume that they are paid at the end of the period.
Note that the time weighted return can be more or less than the money weighted return, it will depend on how the returns are being generated in the portfolio.
A thumbrule MWR > TWR : If the amount of money in the portfolio is increasing and the periodic returns are increasing MWR < TWR : If the amount of money in the portfolio is increasing and the periodic returns are decreasing

@Sir:- It's thumb rule to assume that the dividend is paid just before the period ends or we can hv some other assumptions as well ?? Also, why Time wt return is always less than Money wt return ?? Kindly explain the concept.

Regards,
Shubhojit.

05-09-2012, 08:36 PM

ratankv

Solution to Question #11

Text Solution to Question #11 Ans B:
Here we are interested in selecting 6 funds out of the total of 10 funds, so this is a selection problem, which can be done in 10C6 ways.
This can be done in your financial calculator.
Press 10 (2nd) (+) (6) = 210
Please note that this doesn't involve arrangements its only selection problem.

Alternatively, we can directly use the labeling formula, because we are labeling 4 mutual funds as sell and 6 funds as hold.
=> the number of ways = 10!/(6! * 4!) = 210

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Today's Question (Questions and answers provided by Knowledge Varsity)

Q11. Your portfolio has 10 mutual funds, you met an investment advisor and he advised to hold 6 mutual funds and sell 4 mutual funds. In how many ways this can be achieved?
A. 5040
B. 210
C. 151200

05-09-2012, 08:40 PM

ratankv

Question #12

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Today's Question (Questions and answers provided by Knowledge Varsity)

This is continuation of the Question #10 - here we are covering the Baye's probability concept

Q12. Let

05-09-2012, 11:32 PM

Shubhojit

Thank you Ratan Sir. I am clear now.

05-09-2012, 11:33 PM

bimupa

If we see the above tree diagram Recession will happened when interest increase and when interest decrease will be given as Total P(R) = P(I)*P(R/I) + R(I)*P(R/I(bar))
=0.7*0.9 + 0.3*0.2 = 0.69
probability when interest increase and recession happen P(R) = P(I)*P(R/I) = 0.7*0.9 = 0.63
So updated probability of increase in interest rate = P(R)/Total P(R) = 0.63/0.69 = 0.91 ...According to me A is the answer.