
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
3.5 % = (D/100) * (360/120) => 3.5% = (D/100) * 3
=> D = 3.5% * 100 / 3 = $1.1667
Step 2: Once discount is calculated, Find out the price at which the bond is trading
Price = F

Q5 Answer A
First Step: Find the semiannual yield
Semiannual yield = (1+EAY)^(1/2)– 1
=> Semiannual yield = (1.05)^0.5 – 1 = 2.4695%
Second Step: Multiply the semiannual yield by 2 to get the BEY
=> BEY = 2 * 2.4695% = 4.939%
==================================================
===============================================
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?
A. 25%
B. 0%
C. Cant be determined
==================================================
===============================================

Q5 Answer A
First Step: Find the semiannual yield
Semiannual yield = (1+EAY)^(1/2)

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.
==================================================
===============================================
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?
Time Investment Price
T=0 $1000 $100
T=1 $1000 $125
T=2 $1000 $80
A. $101.67
B.$100
C. $98.36
==================================================
===============================================


Q7 Answer C
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.
TimeInvestmentPrice (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
N/(Harmonic Mean) = 1/X1 + 1/X2 + ................ + 1/XN
==================================================
===============================================
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%
==================================================
===============================================

Question 8 Ans
Q7 Answer C
Will the answer be the arithmetic mean of the price for the 3 periods?

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%.
==================================================
===============================================
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
==================================================
===============================================


Q9 Answer C
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
==================================================
===============================================
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?
A. 0.69
B. 0.9
C.0.2
==================================================
===============================================