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CFA Tier 2
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Gravity
Terms in this set (15)
Present value= PMT/r
Essentially dividing the payment by the required rate of return to find price willing to pay for it today
Describe the present vslue of a perpetuity formula
Nominal - assign observations to classes
Ordinal - order observations from smallest to largest
Interval - ordinal but ensure intervals are same
Ratio - as interval but ensure there is an absolute zero
Four types of measurement scale
Quartiles - 4
Quintiles - 5ths
Deciles- tenths
Percentiles- hundredths
Quantile types
3 square root (2
4
6) =3.634
Describe and calculate geometric mean for 2, 4 and 6
5/(1/2+1/3+1/5+1/7+1/60) =4.21
Harmonic mean calculate for 2,3,5,7,60
Average of squared deviations around the mean
So think find the mean x
Then take observations n
((N-x)^2 + .....) /n-1
Mean is 13
(15-13)^2 + (13-13)^2 + (17-13)^2 + (7-13)^2 / 4-1 = 18.67
Think variance helps look at volatility and the squaring removes the negatives to give a clearer picture on how much it deviates from the mean.
How do you calculate variance describe with numbers 15,13,16,7 and why does it matter?
CV = standard deviation/mean
The CV tells us risk per unit of mean return. Therefore lower is better
How do you calculate coefficient of variation (CV) and why does it matter?
Sum | (observation-mean) | / N
90-86= |4| = 4
75-86 = |-10| = 10
85-86= |-1|. = 1
100-86 =|14| = 14
80-86 = |-6|. = 6
35/5 =7
Better at measuring variability in non normal distributed numbers or very large outliers than standard deviation.
How do you calculate Mean Absolute Deviation (MAD) and why does it matter?
Calc 90,75,85,200,80
Find mean = 6
Sqrt ((3-6)^2)+ (12-6^2) + (9-6^2) + (4-6)^2) + (2-6)^2)/5)
=3.847
This assumes the numbers are the entire population of possible numbers where with sample it assumes it is just a sample by subtracting the bottom n by 1
How to calculate population standard deviation and why it's important? How does it differ from sample standard deviation?
Calc 3,12,9,4,2
Find mean = 6
Sqrt ((3-6)^2)+ (12-6^2) + (9-6^2) + (4-6)^2) + (2-6)^2)/5-1
=1.924
This assumes the numbers are the entire population of possible numbers where with sample it assumes it is just a sample by subtracting the bottom n by 1
How to calculate sample standard deviation and why it's important? How does it differ from population standard deviation?
Calc 3,12,9,4,2
Symmetrical distribution (normal) = mean=median= mode
Negatively skewed distribution (left) Mean<Median<mode :(
Positively skewed distribution (right)
Mode<median<mean :)
Describe the mean, median mode for
Symmetrical distribution (normal)
Negatively skewed distribution (left)
Positively skewed distribution (right)
Kurtosis creates shifts on distributions. Normal = 3
Positive- fat tails and higher peak is called leptokurtic
Negative is skinny tails less peaked is called platykurtic
What is kurtosis and what is negative vs positive called
P (AB) = P(A) * P(B|A) think this is probability of B given A happened.
This can be flipped for A given B or
Joint probability (bayes) P(B|A) = P(AB)/ P(A)
Describe this formula which can then be shifted around
P (AB) = P(A) * P(B|A)
1.645
90% = sample mean +/- 1.645
95% = sample mean +/- 1.96
99% = sample mean +/- 2.58
What are standard interval confidences for
90%
95%
99%
If n is at least 30 from a population the distribution of means of all of such samples will be normally distributed
The std is called the standard error.
This allows us to work with smaller data sets
Just remember 30 is magic number
Central limit theorem
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