Question

1. Which of the followings can be used to check whether the data is normally distributed?
   a.   See if the range is approximate 5 times the standard deviation.
   b.   The normal probability plot
   c.   See if roughly 4/5 of the observations lie between 2 standard deviations from the mean.
   d.   See if the mean, median and mode are approximately equal.
   e.   Box-and-Whisker Plot
   f.   See if the interquartile range is approximately 1.33 times the standard deviation.
   g.   Histrogram

2. The expected rate of returns and variance for the Large Cap Fund are 20 and 15 respectively while the expected rate fo returns and variance for the Small Cap Fund are 10 and 5 respectively. The covariance between the two funds is -7.
The total expected rate of returns and variance of the sum of the two funds are, respectively,
Hint: You do not need to use PHStat or any fancy Excel function. Just simple calculation will give you the answers.
(2 decimal places)
(2 decimal places)

3. The expected return of a two-fund portfolio
   a.   will always be higher than the expected return of each of the individual funds if the funds have a negative covariance.
   b.   will always be higher than the expected return of each of the individual funds.
   c.   will always be somewhere in between the expected return of each of the individual funds if the funds have a negative covariance.
   d.   will always be lower than the expected return of each of the individual funds if the funds have a negative covariance.
   e.   will always be lower than the expected return of each of the individual funds.
   f.   will always be somewhere in between the expected return of each of the individual funds.

Answer 1

1. Following can be use to check the normal ditribution.

Note:NO DATA IS PERFECTLY NORMAL.

b. Normal probability plot can be used ,checking if data fall close to identity line.

c.yes,if 4/5 of data falls within 2 SD of mean then data can be said to be APPROXIMATELY normally distributed. AND more precisely if 95% of data falls within 2 SD of mean in perfect NORMAL DISTRIBUTION.

d.yes,NORMAL dist have same mean ,median and mode.

e.yes,you can check normality using BOX and WHISKER PLOT .BOX will be symmetrical with mean and median with center.

f.yes, if IQR=1.33*SD then data is said to be Normally distributed.

g.yes,HISTOGRAM can also be used by checking symmetricity of data.

2.Given: E(x)=20,var(15),E(y)=10,var(y)=5,cov(x,y)=-7

E(x+y)=E(x)+E(y)=20+10=30

var(x+y)=var(x)+var(y)+2*cov(x,y)=15+5+2*(-7)=6

3.b.will always higher than that of individuals,