# Quant: Concept Checkers - Statistical Concepts

Today is a quant day, so here it goes. 1) For a frequency distribution interval, is the bottom or top value of the interval inclusive in the set? 2) When will the geometric and arithmetic means be the same? 3) Which is better for backward looking data. Geometric or arithmetic avg? 4) If you have 100 observations, what is the location value of the 75% percentile? 5) If the 50% percentile is located at the 12.75 observation point, and the 12th observation has a value of 14.3 and the 13th has a value of 15, then what is the value of the 50% percentile? 6) Which is correct. The a) sum or b) product of the deviations from the mean will equal zero? 7) If the downside semi-variance of a sample is less than the variance of the total sample, does the total sample variance understate or overstate downside risk? 8) True or false: The coefficient of variation uses variance as the numerator value? 9) True of false: The sharpe ratio indicates how much risk you take on with each additional unit of return? 10) What might you need to be careful of when evaluating the sharpe ratio when the risk free rate is extremely high? 11) If a distribution is positively skewed, which direction does the tail extend? 12) If a distribution is negatively skewed, is it true that the mean > median > mode? 13) If a distribution has kurtosis of 3, is it lepto/meso/playt-kurtotic? 14) True or false, a distribution with excess kurtosis of 4 will be leptokurtotic, will have a more peaked distribution than the normal distribution, and will have thinner tails at the extremes. 15) Bonus: True or false, investors prefer normally distributed returns rather than positively skewed returns because it provides a more predictable outcome?

Answers will be posted in a few minutes.

1. For a frequency distribution interval, is the bottom or top value of the interval inclusive in the set? bottom 2) When will the geometric and arithmetic means be the same? when all the return rates are equal 3) Which is better for backward looking data. Geometric or arithmetic avg? geometric 4) If you have 100 observations, what is the location value of the 75% percentile? don’t know edit: misread the question, it will be (101)*0.75 = 75.75 5) If the 50% percentile is located at the 12.75 observation point, and the 12th observation has a value of 14.3 and the 13th has a value of 15, then what is the value of the 50% percentile? 14.3 + (15-14.3)*0.75 = 14.825 6) Which is correct. The a) sum or b) product of the deviations from the mean will equal zero? sum 7) If the downside semi-variance of a sample is less than the variance of the total sample, does the total sample variance understate or overstate downside risk? understate 8) True or false: The coefficient of variation uses variance as the numerator value? false, sd/mean 9) True of false: The sharpe ratio indicates how much risk you take on with each additional unit of return? yes, excess return per unit of risk 10) What might you need to be careful of when evaluating the sharpe ratio when the risk free rate is extremely high? hmm, don’t know… negative sharpe ratio? inflation? 11) If a distribution is positively skewed, which direction does the tail extend? more extreme observations on the right 12) If a distribution is negatively skewed, is it true that the mean > median > mode? true 13) If a distribution has kurtosis of 3, is it lepto/meso/playt-kurtotic? no excess kurtotis = mesokurtic 14) True or false, a distribution with excess kurtosis of 4 will be leptokurtotic, will have a more peaked distribution than the normal distribution, and will have thinner tails at the extremes. false, leptokurtic = more peak, fat tails 15) Bonus: True or false, investors prefer normally distributed returns rather than positively skewed returns because it provides a more predictable outcome? false, makes no sense!
1. For a frequency distribution interval, is the bottom or top value of the interval inclusive in the set? - For every interval, the bottom value is inclusive in the set. The top value is not inclusive. The only exception is the final, greater interval where the top value is also inclusive. 2) When will the geometric and arithmetic means be the same? - If there is not variance in the values being average, geometric and arithmetic means will be identical. Their values become increasingly distinct as variance in values grows larger (e.g. more outliers) 3) Which is better for backward looking data. Geometric or arithmetic avg? - The geometric average is preferred for averaging historic return data. Arithmetic is considered the superior forward looking measure. 4) If you have 100 observations, what is the location value of the 75% percentile? - The answer is not simply the 75th observation. You need to be aware of the difference between observations and intervals. The value of the location at the 75% in actually (n+1)*.75… in this case (100+1) * .75 —> 75.75 5) If the 50% percentile is located at the 12.75 observation point, and the 12th observation has a value of 14.3 and the 13th has a value of 15, then what is the value of the 50% percentile? - You need to extrapolate the value. Take the top value minus bottom value and multiply by the percentage of the interval that your location value falls in. In this case it’s (15-14.3)*.75 --> .525. This value is added to the lower interval value. So, the value is 14.3+.525 —> 14.825 6) Which is correct. The a) sum or b) product of the deviations from the mean will equal zero? - The sum 7) If the downside semi-variance of a sample is less than the variance of the total sample, does the total sample variance understate or overstate downside risk? - If downside semivariance is less than total variance, then using the total variance as a measure of risk is overstating downside risk. 8) True or false: The coefficient of variation uses variance as the numerator value? - False: While ‘variation’ may seem like it is using variance, the numerator uses the standard deviation value. Hint: most equations used in statistics use standard deviation and not variance values. One notable exception is the formula for correlation. 9) True of false: The sharpe ratio indicates how much risk you take on with each additional unit of return? - False: Sharpe ratio indicates the amount of return in excess of the risk free rate per unit of risk as measured by standard deviation. It is essentially the inverse of CV and is very similar to the safety first ratio. 10) What might you need to be careful of when evaluating the sharpe ratio when the risk free rate is extremely high? If the risk free rate is greater than the risk premium value, then the ratio will be negative. 11) If a distribution is positively skewed, which direction does the tail extend? Postive skew has a tail to the right. The tail points in the direction of the skew. 12) If a distribution is negatively skewed, is it true that the mean > median > mode? No. A negative skewed distribution will have a mean

Pretty close sharp. Check 7, 9, 12, and 15

thanks for the quesitons man i made a dumb mistake about the mean>median>mode thing but i had the right concept in my head (“pulling it” by the mean from side to side) for sharpe i had the right concepts in my head but i guess the semantics of it weren’t very clear (“excess returns per unit of risk” vs. additional return for assuming risk)

I didn’t understand no. 7 … if downside risk semi-variance is less, then overall variance will overshadow and underestimate the downside risk ??

ditto

semi-variance measures only downside risk, so if the sample variance is greater and we use that as a meassure of risk, we are overstating the downside risk, and as an investor is pre-occupied with downside risk, that is the only risk that matters! (Atleast that is the concept of semi-variance, from what I understand) Edit: and I know that explanation was about as clear as mud!!!

for 9, it’s excess return per risk not risk per return

good questions mcf…

Delta is correct on the explanation of semi-variance.

delta9 Wrote: ------------------------------------------------------- > good questions mcf… I concur, thank you mcf

thank delta, clear as mud

thanks delta : ) wasn’t tht muddy