Question: On 10/24/12 Blackrock created an emerging
market fund IEMG.
A broker calls his client and says you need to diversify
internationally. Sell some of your
shares in the domestic U.S. fund ITOT and buy IEMG.
What was the mean daily return from the two funds?
What was the standard deviation of returns from the two
funds?
Test the hypothesis that the two funds have identical
returns?
The person takes the broker’s advice and puts $10,000 in
IEMG on the day the fund was created.
How much did the person gain or lose by diverting $10,000 from ITOT to
IEMG?
Analysis: Statistics on the mean and standard
deviation of daily returns for the emerging market fund and the domestic U.S.
fund are presented in the table below.
Mean and Standard
Deviation of Returns for Two ISHARE Funds


Mean

STD


Emerging Market Fund

0.00016

0.00039

Total U.S. Stock Market
Fund

0.00056

0.00028

Sample covers the period starting with the inception of IEMG
on 10/24/2015 to 12/22/15.
The correlation of the emerging market fund and the Domestic
U.S. fund is 0.7517. This is a pretty
high correlation. The potential gain to
U.S. investors from diversifying with emerging markets appears really
small. Future blogs will look at a
larger number of funds and try to find a better way to diversify.
The hypothesis that the mean returns from the two funds are
identical was tested against the twotailed hypothesis that the means
differed. I use a paired ttest in this
situation because on some days the market is much more volatile than other days
and pairing the observations across days controls for this variability.
The pvalue from this test is 0.0028.
The difference between mean returns from the two funds is
significantly different from zero.
Highly significant!
The closing price on the fund’s first day was 45.1
The close adjusted for splits on 12/22/2015 was 39.86
The closing value of a $10,000 investment was $8,838
The loss is around $1,161.
The closing price of the U.S. fund on 10/24/13 was 59.8.
The closing value of the U.S. fund 12/22/2015 was 93.2.
The foregone gain from taking money out of the U.S. market
was $5,585
Of course these numbers don’t include the brokers fee from
selling ITOT and buying IEMG.
A lot of the international funds created by Blackstone have
actually done a lot worse than IEGM.
More on this topic will be placed on my finance blog soon.
If you liked this post you might also like the post comparing S&P 500 to a utility fund.
http://dailymathproblem.blogspot.com/2015/12/statisticaltestsofidenticalfund.html
If you liked this post you might also like the post comparing S&P 500 to a utility fund.
http://dailymathproblem.blogspot.com/2015/12/statisticaltestsofidenticalfund.html
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