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.
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.
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
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.
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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
Dear Ratan Sir,
Kindly clear my doubt reg Solution of Q3 at http://www.daulatguru.com/finance-fo...012-exam/page2
''@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
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
Hope this helps.
Ratan Gupta
Director, Knowledge Varsity
www.KnowledgeVarsity.com
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
Regards,
Ratan Gupta
Director, Knowledge Varsity
www.KnowledgeVarsity.com
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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
Thank you Ratan Sir. I am clear now.
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.
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