Quantitative Methods

[June 2013 CFA Level 1 Group]

Use this discussion thread to ask and discuss queries related to Quantitative Methods Topic.

[johncfa786]

Please can you solve q 19 of Reading 5 the curriculum gives a very long way to solve the question. 

thank you

[Subramanian L V]

Hi

As per the quiz uploaded in g drive in QT Q no 9 shouldn't the option A be 1st quartile is greatre than 1st quintile. As per the soln the 2nd quintile is given as the 20th percentile but as per my understanding on the vdos 2nd Quintile means the 40th percentile. Pls correct me if i am wrong.

[Lev Elgudin]

I think there was a typo in choice A. It probably should have said "1st quintile and 1st quartile".

Leo

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[Soban Memon]

[Arif Irfanullah]

Click here for the 2013 CFA Level I Quant quiz.

Feel free to share your comments and feedback.  

[Arif Irfanullah]

Leo is correct. There was a typo in question 9 of the quiz. We've fixed the typo in the latest version.

On Tuesday, February 12, 2013 9:18:32 PM UTC+5, June 2013 CFA Level 1 Group wrote:

[talha arif]

An investor wants to receive $1,000 at the beginning of each of the next ten years with the first payment starting today. If the investor can earn 10 percent interest, what must the investor put into the account today in order to receive this $1,000 cash flow stream?

A) $6,145.

B) $6,759.

C) $7,145.

 

This is an annuity due problem. There are several ways to solve this problem.

Method 1:

PV of first $1,000 = $1,000
PV of next 9 payments at 10% = 5,759.02
Sum of payments = $6,759.02

Method 2:

Put calculator in BGN mode.
N = 10; I = 10; PMT = -1,000; CPT → PV = 6,759.02
Note: make PMT negative to get a positive PV. Don’t forget to take your calculator out of BGN mode.

Method 3:

You can also find the present value of the ordinary annuity $6,144.57 and multiply by 1 + k to add one year of interest to each cash flow. $6,144.57 × 1.1 = $6,759.02.

[talha arif]

i cant find $6,759

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[talha arif]

The probabilities of earning a specified return from a portfolio are shown below:

Probability	Return
0.20	10%
0.20	20%
0.20	22%
0.20	15%
0.20	25%

What are the odds of earning at least 20%?

A) Three to two.

B) Two to three.

C) Three to five.

Odds are the number of successful possibilities to the number of unsuccessful possibilities:

P(E)/[1 − P(E)] or 0.6 / 0.4 or 3/2.

how to solve this dont get it.

[Arif Irfanullah]

If  you have quant questions please post by tomorrow (8 May).  On 9 May I'll create a video  and will try to address as many of your questions as possible. 

[Tariq Khoso]

hi there, i've a question. in the question below, shouldn't i do the following :

[ 0.4($60) + 0.6($55) ] * 0.45

the part highlighted in red is the part which i what i had done. i see the difference but i don't quite understand why we aren't supposed to multiply it with the probability of decrease in market.

thanks!

Tina O’Fahey, CFA, believes a stock’s price in the next quarter depends on two factors: the direction of the overall market and whether the company’s next earnings report is good or poor. The possible outcomes and some probabilities are illustrated in the tree diagram shown below:

Based on this tree diagram, the expected value of the stock if the market decreases is closest to:

A) $57.00.

B) $62.50.

C) $26.00.

Your answer: C was incorrect. The correct answer was A) $57.00.

The expected value if the overall market decreases is 0.4($60) + (1 – 0.4)($55) = $57.

[talha arif]

For assets A and B we know the following: E(R_A) = 0.10, E(R_B) = 0.10, Var(R_A) = 0.18, Var(R_B) = 0.36 and the correlation of the returns is 0.6. What is the variance of the return of a portfolio that is equally invested in the two assets?

A) 0.2114.

B) 0.1500.

C) 0.1102.

You are not given the covariance in this problem but instead you are given the correlation coefficient and the variances of assets A and B from which you can determine the covariance by Covariance = (correlation of A, B) × Standard Deviation of A) × (Standard Deviation of B).

Since it is an equally weighted portfolio, the solution is:
[( 0.5² ) × 0.18 ] + [(0.5²) × 0.36 ] + [ 2 × 0.5 × 0.5 × 0.6 × ( 0.18^0.5 ) × ( 0.36^0.5 )] 
= 0.045 + 0.09 + 0.0764 = 0.2114

Please explain from where this 0.5^2 is popping up from dont get this ugly question . HELLLLPPPP

[Soban Memon]

No prob with this q boy. 0.5^2 is as per the portfolio variance formula. weights are squared. 

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[haider iqbal]

So I came across this incredibly difficult question while doing Quant. I nearly cried after realizing that there is a chance that such a question might appear on the exam. Read the solution, cried some more, then read the final note and realized that there may still be hope.

Simone Mak is a television network advertising executive. One of her responsibilities is selling commercial spots for a successful weekly sitcom. If the average share of viewers for this season exceeds 8.5%, she can raise the advertising rates by 50% for the next season. The population of viewer shares is normally distributed. A sample of the past 18 episodes results in a mean share of 9.6% with a standard deviation of 10.0%. If Mak is willing to make a Type 1 error with a 5% probability, which of the following statements is most accurate?

A) With an unknown population variance and a small sample size, Mak cannot test a hypothesis based on her sample data.

B) Mak cannot charge a higher rate next season for advertising spots based on this sample.

C) The null hypothesis Mak needs to test is that the mean share of viewers is greater than 8.5%. Your answer: B was correct!  Mak cannot conclude with 95% confidence that the average share of viewers for the show this season exceeds 8.5 and thus she cannot charge a higher advertising rate next season. Hypothesis testing process: Step 1:  State the hypothesis. Null hypothesis: mean ≤ 8.5%; Alternative hypothesis: mean > 8.5% Step 2:  Select the appropriate test statistic. Use a t statistic because we have a normally distributed population with an unknown variance (we are given only the sample variance) and a small sample size (less than 30). If the population were not normally distributed, no test would be available to use with a small sample size. Step 3:  Specify the level of significance. The significance level is the probability of a Type I error, or 0.05. Step 4:  State the decision rule.  This is a one-tailed test. The critical value for this question will be the t-statistic that corresponds to a significance level of 0.05 and n-1 or 17 degrees of freedom. Using the t-table, we determine that we will reject the null hypothesis if the calculated test statistic is greater than the critical value of 1.74. Step 5:  Calculate the sample (test) statistic.  The test statistic = t = (9.6 – 8.5) / (10.0 / √ 18) = 0.479 (Note: Remember to use standard error in the denominator because we are testing a hypothesis about the population mean based on the mean of 18 observations.) Step 6: Make a decision. The calculated statistic is less than the critical value. Mak cannot conclude with 95% confidence that the mean share of viewers exceeds 8.5% and thus she cannot charge higher rates. Note: By eliminating the two incorrect choices, you can select the correct response to this question without performing the calculations.

[talha arif]

A group of investors wants to be sure to always earn at least a 5% rate of return on their investments. They are looking at an investment that has a normally distributed probability distribution with an expected rate of return of 10% and a standard deviation of 5%. The probability of meeting or exceeding the investors' desired return in any given year is closest to:

A) 84%.

B) 34%.

C) 98%.

Your answer: B was incorrect. The correct answer was A) 84%.

The mean is 10% and the standard deviation is 5%. You want to know the probability of a return 5% or better. 10% - 5% = 5% , so 5% is one standard deviation less than the mean. Thirty-four percent of the observations are between the mean and one standard deviation on the down side. Fifty percent of the observations are greater than the mean. So the probability of a return 5% or higher is 34% + 50% = 84%.

please can any one explain how to do such sort of questions

[haider iqbal]

Subramanian. I copied it. I am using Kaplan scheweser question bank its a computer application. Although I think what you can do is perhaps take a snapshot and upload it here not sure if that works with google groups but you can try.

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[Arif Irfanullah]

Click here to access the folder containing my video response and a couple of Quant quizzes.  Do the quizzes in an exam-like setting and post comments/feedback under this discussion thread.

[John Jacob]

Hi,

I've been working through quant problems, wanted a quick review for using the calculator (ti ba plus 2) I usually do it manually but using the calculator would save time for the following calculation

- when calculating std deviation mean for one variable using the 1-v mode, 2 variables (calculating the covariance correlation)

- when calculating one variable using statistics/probability  

Does anyone know of a video so i can go through it?

thanks!

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