I need to compare the Standard Deviation and Sharpe Ratios for the
following two portfolios: The asset categories are the same, only the
allocations are different.
Asset Return Std Dev Portfolio 1 Portfolio 2
L Stocks 8 16 $171,000 $160,231
S Stocks 10 21.2 158,000 160,231
ID Stocks 5 18.7 20,000
EM Stocks 12 18.41 153,822
RE Stocks 5.5 11.6 210,000 166,642
LT Treas 4.46 .1 15,000 182,666
Munis 3.8 4.33 194,000 79,408
Total Return: 6.12% 7%
What are the STandard Deviations for each Portfolio?
What is the Sharpe Ratio for each Portfolio? |
Request for Question Clarification by
elmarto-ga
on
18 Jul 2005 15:28 PDT
Hello bluesteel,
It's impossible to calculate the standard deviation of a portfolio
without knowing the correlations among its assets... are we to assume
that there is no correlation at all among them?
Thanks,
elmarto
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Clarification of Question by
bluesteel101-ga
on
18 Jul 2005 15:42 PDT
elmarto -
sorry, forgot that piece. Here is the question a little clearer:
The individual percentages for asset categories is the percentage of
either equities or fixed-income, while the TOTAL percentage is the
piece of the whole portfolio.
The expected total return for Port 1 is 6.12%, and for Port 2 is 7%.
I need to calculate the expected standard deviation for both and then
the Sharpe Ratio for both.
ASSET RETURN STDDEV PORTFOLIO 1 PORTFOLIO 2
Lg-Cap Stocks 8 16 $171,000 ? 30.6% $160,231 ? 25%
Sm-Cap Stocks 10 21.2 $158,000 ? 28.3% $160,231 ? 25%
Int Dev Stocks 5 18.7 $20,000 ? 3.6%
Em Mkt Stocks 12 18.41 $153,822 ? 24%
REITs 5.5 11.6 $210,000 ? 37.5% $166,642 ? 26%
Total Equities $559,000 ? 67.4% $640,926 ? 66.5%
LT Treasuries 4.46 0.1 $15,000 ? 7.2% $182,666 ? 69.7%
Int Municipals 3.8 4.33 $194,000 ? 92.8% $79,408 ? 30.3%
Total Fixed Income $209,000 ? 25.2% $262,074 ? 27.2%
Cash Equiv 1% 0.1 $61,000 ? 7.4% $61,000 ? 6.3%
CORRELATION COEFFICIENTS
Lg S Sm S IntDev EmSt REIT LTTres CashEqui Infl
Lg-Cap Stocks 1.0
Sm-Cap Stocks .79 1.0
Int Dev Stocks .56 .37 1.0
Em Mkt Stocks .43 .30 .84 1.0
REITs -.01 -.11 -.06 -.16 1.0
LT Treas .23 .17 .09 -.05 .51 1.0
Cash Equiv -.02 -.04 -.05 -.08 -.03 .32 1.0
Infl .05 .07 .11 .07 .67 -.11 .37 1.0
Thanks,
bluesteel101
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Clarification of Question by
bluesteel101-ga
on
18 Jul 2005 15:44 PDT
elmarto -
also; the correlation for the munis is the same as for the LT Treasuries.
thx.
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Clarification of Question by
bluesteel101-ga
on
18 Jul 2005 21:06 PDT
and in case you need it, the risk free rate is 4.75%
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Request for Question Clarification by
elmarto-ga
on
19 Jul 2005 05:33 PDT
Hello bluesteel,
Thanks for the clarification. I still have some questions:
1) You say that the correlation for the munis is the same as for the
LT Treasuries... however, what is the correlation between LT
Treasuries and Munis
2) I don't understand the percentage values in the first table.
3) Does "Infl" stand for inflation?
Thank you very much,
elmarto
|
Clarification of Question by
bluesteel101-ga
on
19 Jul 2005 07:29 PDT
elmarto -
Sorry.
The Lt Treasuries has the same correlation as the Munis; so the
Correlation factor between the two is 1.0.
And yes, infl stands for inflation.
The percentages are confusing - sorry. The percentages in the "Total
Equities" (67.4)and "Total Fixed Income" (25.2) and Cash Equivalents
(7.4) equals the 100% of the portfolio. The individual percentages in
each category equal the percentage that asset represents in that
category, i.e. Large Cap + Small Cap + Int Dev + Em MKT + REIT = 100%
of Equities.
Hope this helps.
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Clarification of Question by
bluesteel101-ga
on
19 Jul 2005 22:05 PDT
Okay - I've been able to find the Standard Deviation for the Portfolios.
For Portfolio 1 the Standard Deviation is 8.399
For Portfolio 2 the Standard Deviation is 9.219
I still need the Sharpe Ratios for each.
Thanks.
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Clarification of Question by
bluesteel101-ga
on
19 Jul 2005 22:11 PDT
Sorry, made a mistake on the Standard Deviation.
Portfolio 1: 8.017
Portfolio 2: 7.618
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