Portfolio analysis  
(Risk, Return, Sharpe, Beta)  
 
Neither this site, the available materials, nor its contents (including any information concerning   
This is a step-by-step description of some aspects of a portfolio analysis any securities mentioned on this site) constitutes  an advertisement of any securities or     
an offer to sell or a solicitation of an offer to purchase any securities.         
We will create a portfolio of several stocks and try to apply some analysis approaches to it
But that's not all. We will use 2009 weekly data for the portfolio analysis. After that we will change the portfolio depending on the results of analysis to optimize it and then check if our changes helped
to improve the performance vs original portfolio and vs S&P index in 2010
Note: we will analyze weekly data, which implies that we are planning to create a portfolio for one week. If you want to create a portfolio for a month, quarter, year - you need to use monthly, quarterly
and annual data, respectively. Usually investors create portfolios for at least several month. We just use weekly data for convenience (2008 market distorts all the statistics and analysis)
STEP 1 CREATING A PORTFOLIO  
Let's create a simple portfolio consisting of 5 stocks (the number of stocks as well as the stocks themselves are just taken from the head). 
We take Apple (AAPL), Citi (C), General Electric (GE), Exxon Mobil (XOM) and Alcoa (AA). I tried to pick the stocks from different sectors. 
Let's imagine that currently we are at the end of 2009. We will analyze 2009 data, modify our portfolio and see what will happen to it in 2010
Here it is, our portfolio:
Company Ticker Last price (end of 2009), $  Number of shares Position $ Share in portfolio
Apple AAPL 209.04 12 2 508 18.1%
Citi C 3.35 785 2 630 19.0%
General Electric GE 15.44 200 3 088 22.3%
Exxon Mobil XOM 68.66 37 2 540 18.4%
Alcoa AA 16.34 187 3 056 22.1%
Total       13 822 100.0%
STEP 2 CALCULATING PORTFOLIO PARAMETERS Prices ($) Change (%)
AAPL C GE XOM AA S&P AAPL C GE XOM AA S&P Portfolio
Let's look at the expected return and risk for our portfolio 09.01.2009 90.6 6.8 16.0 77.6 10.8 881.7
16.01.2009 82.3 3.5 14.0 78.1 9.4 843.7 -9.1% -48.1% -12.8% 0.7% -12.8% -4.3% -22.8%
We uploaded weekly prices for our stocks and S&P index for 2009 (to the right) and 23.01.2009 88.4 3.5 12.0 78.0 8.3 834.0 7.3% -0.9% -13.8% -0.1% -11.7% -1.2% -4.9%
calculated weekly changes for all instruments and for portfolio (we will need this row later) 30.01.2009 90.1 3.6 12.1 76.5 7.8 816.5 2.0% 2.3% 0.8% -2.0% -6.5% -2.1% -0.5%
06.02.2009 99.7 3.9 11.1 80.3 8.4 868.6 10.6% 10.1% -8.5% 5.0% 7.8% 6.4% 4.2%
Expected return is a average weekly return  13.02.2009 99.2 3.5 11.4 74.6 7.5 815.3 -0.6% -10.7% 3.1% -7.2% -11.0% -6.1% -5.9%
Risk is standard deviation of weekly returns (use STDEV function in excel) 20.02.2009 91.2 2.0 9.4 71.2 6.3 776.6 -8.0% -44.1% -18.0% -4.5% -15.9% -4.7% -19.9%
27.02.2009 89.3 1.5 8.5 67.9 6.2 725.6 -2.1% -23.1% -9.3% -4.7% -1.0% -6.6% -8.2%
So here is the stocks' parameters and S&P index parameters 06.03.2009 85.3 1.0 7.1 64.0 5.2 679.4 -4.5% -31.3% -17.0% -5.7% -16.2% -6.4% -13.6%
13.03.2009 95.9 1.8 9.6 67.2 5.7 762.9 12.5% 72.8% 36.3% 5.0% 9.8% 12.3% 21.9%
  Share in portfolio Expected return (Re) Risk (σ) 20.03.2009 101.6 2.6 9.5 66.1 6.5 783.4 5.9% 47.2% -0.8% -1.7% 14.1% 2.7% 10.2%
Apple 18.1% 1.8% 4.9% 27.03.2009 106.9 2.6 10.8 70.0 7.8 805.6 5.2% 0.0% 13.0% 5.9% 19.3% 2.8% 7.8%
Citi 19.0% 0.4% 19.1% 03.04.2009 116.0 2.9 10.9 70.4 8.2 837.6 8.6% 8.8% 1.5% 0.7% 4.7% 4.0% 4.3%
General Electric 22.3% 0.3% 9.0% 10.04.2009 119.6 3.0 11.3 69.8 8.9 854.0 3.1% 6.7% 3.6% -0.9% 8.3% 2.0% 3.8%
Exxon Mobil 18.4% -0.2% 3.3% 17.04.2009 123.4 3.7 12.4 66.8 9.3 868.3 3.2% 20.1% 9.4% -4.4% 4.6% 1.7% 6.8%
Alcoa 22.1% 1.2% 8.6% 24.04.2009 123.9 3.2 12.1 66.6 9.1 857.9 0.4% -12.6% -2.3% -0.3% -1.3% -1.2% -4.0%
S&P   0.6% 3.6% 01.05.2009 127.2 3.0 12.7 68.0 9.7 880.4 2.7% -6.9% 4.8% 2.2% 6.0% 2.6% 1.3%
08.05.2009 129.2 4.0 14.5 70.8 10.0 923.0 1.5% 35.4% 14.5% 4.1% 3.3% 4.8% 12.9%
Now we will perform operations similar to what we did in Markowitz portfolio calculation 15.05.2009 122.4 3.5 12.9 69.1 9.0 893.2 -5.2% -13.4% -11.5% -2.4% -9.8% -3.2% -9.0%
http://www.financetoys.com/portfolio/markeng.htm 22.05.2009 122.5 3.7 13.1 68.8 8.9 881.6 0.1% 5.5% 1.9% -0.4% -1.9% -1.3% 1.4%
29.05.2009 135.8 3.7 13.5 69.4 9.2 927.8 10.9% 1.4% 2.9% 0.8% 4.1% 5.2% 3.2%
STEP 3 CALCULATING THE RISK AND RETURN FOR PORTFOLIO 05.06.2009 144.7 3.5 13.5 73.0 10.9 935.0 6.5% -7.0% 0.4% 5.2% 18.7% 0.8% 3.2%
12.06.2009 137.0 3.5 13.5 73.8 12.0 935.2 -5.3% 0.3% -0.2% 1.1% 9.6% 0.0% 1.1%
The primal aim of portfolio creation is the diversification of non-systematic risks 19.06.2009 139.5 3.2 12.1 71.1 11.0 912.6 1.8% -8.6% -10.4% -3.7% -8.3% -2.4% -6.4%
26.06.2009 142.4 3.0 11.8 69.1 10.8 920.9 2.1% -4.4% -2.9% -2.8% -2.2% 0.9% -2.3%
Let's find the average risk and return of the portfolio and compare it with the  03.07.2009 140.0 2.9 11.5 68.5 9.9 890.4 -1.7% -5.0% -2.5% -0.8% -8.4% -3.3% -3.6%
respective parameters of S&P index 10.07.2009 138.5 2.6 10.8 65.1 9.3 881.9 -1.1% -10.1% -5.9% -4.9% -5.3% -1.0% -5.7%
17.07.2009 151.8 3.0 11.7 68.5 10.2 945.4 9.6% 16.6% 8.1% 5.2% 9.4% 7.2% 9.6%
The formula for the average portfolio return is  24.07.2009 160.0 2.7 12.0 72.3 11.0 977.6 5.4% -9.6% 3.3% 5.5% 7.8% 3.4% 2.2%
Rp = sum (Re x Ws) 31.07.2009 163.4 3.2 13.4 70.4 11.8 996.5 2.1% 16.1% 11.4% -2.6% 6.7% 1.9% 6.5%
07.08.2009 165.5 3.9 14.7 69.5 13.0 1 005.0 1.3% 21.5% 9.7% -1.3% 10.5% 0.9% 8.5%
I.e. you multiply all the stocks' expected returns on its weights in portfolio and sum up them 14.08.2009 166.8 4.0 13.9 68.2 13.3 986.8 0.8% 4.9% -5.3% -1.8% 2.1% -1.8% 0.1%
21.08.2009 169.2 4.7 14.2 69.9 12.6 1 028.6 1.5% 16.3% 2.1% 2.5% -5.4% 4.2% 4.1%
Rp =  0.7% 28.08.2009 170.1 5.2 14.1 70.1 12.5 1 020.3 0.5% 11.3% -0.9% 0.3% -0.5% -0.8% 2.9%
04.09.2009 170.3 4.9 13.9 69.2 12.2 1 025.7 0.2% -7.3% -1.5% -1.3% -2.6% 0.5% -3.1%
The expected weekly return of the portfolio is higher than S&P index's expected return (0.6%) 11.09.2009 172.2 4.6 14.7 70.0 13.0 1 036.4 1.1% -4.9% 5.8% 1.2% 6.7% 1.0% 1.3%
18.09.2009 185.0 4.3 16.5 70.0 14.1 1 067.1 7.5% -7.6% 12.5% 0.0% 8.2% 3.0% 3.3%
This is good. Potentially our portfolio can outperform index on a weekly basis 25.09.2009 182.4 4.4 16.4 68.7 13.1 1 045.4 -1.4% 2.8% -0.8% -1.8% -7.0% -2.0% -1.4%
02.10.2009 184.9 4.5 15.4 66.6 12.8 1 027.9 1.4% 3.2% -6.2% -3.1% -2.0% -1.7% -1.4%
Let's calculate the risk  09.10.2009 190.5 4.6 16.2 69.3 14.2 1 075.1 3.0% 2.4% 5.3% 4.0% 11.1% 4.6% 5.0%
16.10.2009 188.1 4.6 16.1 73.1 14.0 1 088.6 -1.3% -0.9% -0.6% 5.6% -1.4% 1.3% 0.2%
Here is the formula for portfolio risk calculation: 23.10.2009 203.9 4.5 15.2 73.6 13.7 1 082.9 8.4% -2.8% -5.5% 0.6% -2.2% -0.5% -0.9%
30.10.2009 188.5 4.1 14.3 71.7 12.4 1 042.0 -7.6% -8.3% -6.2% -2.6% -9.5% -3.8% -6.9%
06.11.2009 194.3 4.1 15.3 72.6 12.9 1 077.0 3.1% -0.7% 7.5% 1.3% 3.8% 3.4% 2.9%
13.11.2009 204.5 4.1 15.7 72.5 13.2 1 100.8 5.2% -0.2% 2.2% -0.2% 2.2% 2.2% 1.7%
Where σ is a risk of a stock (calculated as it's standard deviation) 20.11.2009 199.9 4.2 15.6 74.4 13.1 1 094.9 -2.2% 3.7% -0.4% 2.6% -0.4% -0.5% 0.8%
w - is a share of the stock in the portfolio  27.11.2009 200.6 4.1 15.9 74.9 12.7 1 091.1 0.3% -3.3% 2.2% 0.7% -3.6% -0.3% -0.7%
ρ is a correlation of the stocks in the portfolio 04.12.2009 193.3 4.1 16.2 74.3 13.0 1 105.0 -3.6% 0.0% 1.6% -0.8% 2.6% 1.3% 0.0%
11.12.2009 194.7 4.0 15.9 72.8 14.6 1 111.1 0.7% -2.7% -1.7% -1.9% 12.5% 0.6% 0.9%
After you find this, don't forget to get a square root from it  18.12.2009 195.4 3.4 15.6 68.2 14.6 1 108.2 0.4% -13.9% -2.1% -6.3% -0.2% -0.3% -4.7%
25.12.2009 209.0 3.4 15.4 68.7 16.3 1 127.6 7.0% -1.5% -1.0% 0.7% 12.1% 1.7% 3.3%
Let's calculate the risk in several steps
First, we need to calculate the correlations between the stocks 
Use CORREL function in excel to do this
Correlation matrix
  AAPL C GE XOM AA
AAPL 1.000 0.574 0.501 0.463 0.587
C 0.574 1.000 0.729 0.357 0.517
GE 0.501 0.729 1.000 0.449 0.619
XOM 0.463 0.357 0.449 1.000 0.550
AA 0.587 0.517 0.619 0.550 1.000
Now let's draw a couple more matrices to simplify valuation. We do all this just following the formula for portfolio risk calculation shown above
Share matrix (matrix with market share of the stocks in portfolio)
AAPL C GE XOM AA
18.1% 19.0% 22.3% 18.4% 22.1%
18.1% 19.0% 22.3% 18.4% 22.1%
18.1% 19.0% 22.3% 18.4% 22.1%
18.1% 19.0% 22.3% 18.4% 22.1%
18.1% 19.0% 22.3% 18.4% 22.1%
Weights multiplication matrix (to calculate wi x wj from the formula for portfolio risk)
  AAPL C GE XOM AA
AAPL 0.033 0.035 0.041 0.033 0.040
C 0.035 0.036 0.043 0.035 0.042
GE 0.041 0.043 0.050 0.041 0.049
XOM 0.033 0.035 0.041 0.034 0.041
AA 0.033 0.035 0.041 0.034 0.041
Risk matrix
AAPL C GE XOM AA
4.9% 19.1% 9.0% 3.3% 8.6%
4.9% 19.1% 9.0% 3.3% 8.6%
4.9% 19.1% 9.0% 3.3% 8.6%
4.9% 19.1% 9.0% 3.3% 8.6%
4.9% 19.1% 9.0% 3.3% 8.6%
Risk multiplication matrix (to calculate σi x σj from the formula for portfolio risk)
  AAPL C GE XOM AA
AAPL 0.002 0.009 0.004 0.002 0.004
C 0.009 0.037 0.017 0.006 0.016
GE 0.004 0.017 0.008 0.003 0.008
XOM 0.002 0.006 0.003 0.001 0.003
AA 0.004 0.016 0.008 0.003 0.007
Now we multiply three matrices' values: correlation matrix, weights multiplication matrix and risk multiplication matrix
Final multiplication matrix
  AAPL C GE XOM AA
AAPL 0.00008 0.00018 0.00009 0.00002 0.00010
C 0.00018 0.00133 0.00054 0.00008 0.00036
GE 0.00009 0.00054 0.00041 0.00006 0.00024
XOM 0.00002 0.00008 0.00006 0.00004 0.00006
AA 0.00008 0.00030 0.00020 0.00005 0.00030
I made up the matrices' names by myself. Actually, they don't have official names
Now we simply need to sum up all the values from the final matrix to get σ2
σ2 =  0.00547
To get a risk for our portfolio we simply need to get a square root from this figure
σ =  7.4%
Now we see that the risk of our portfolio is higher than for S&P index (3.6%)
But at the same time our portfolio offer better expected return. What should we do in that situation?
Just go to the next step for an answer
STEP 4 SHARPE RATIO (SR)    
Sharpe ratio (SR) is a measure of excess return over a unit of risk
To learn more about Sharpe ratio read this Wikipedia article. It’s good  http://en.wikipedia.org/wiki/Sharpe_ratio
We will calculate Sharpe ratio using the formula
SR = (Re - Rf) / σ
where Re is the expected asset's return
Rf is a risk-free rate
and σ is a standard deviation, or risk of the asset
As a risk free rate we take 10Y US treasuries yield at the end of 2009 and divide it by the number of weeks in a year to get a weekly risk-free return
Rf = 3.807% / 52 = 0.1%
Let's calculate this coefficient for all the stocks in the portfolio, for the portfolio itself and for S&P index. We  already know all the inputs, so it should be easy
  Expected return (Re) Risk (σ) Risk-free rate (Rf) Sharpe ratio (SR)
Apple 1.8% 4.9% 0.1% 0.35
Citi 0.4% 19.1% 0.1% 0.02
General Electric 0.3% 9.0% 0.1% 0.03
Exxon Mobil -0.2% 3.3% 0.1% -0.08
Alcoa 1.2% 8.6% 0.1% 0.13
Portfolio 0.7% 7.4% 0.1% 0.08
S&P index 0.6% 3.6% 0.1% 0.13
Investors should choose the assets with the highest Sharpe ratio as it assumes higher excess return for a unit of risk
In our case Apple would be the best choice
STEP 5 BETA (β)    
Beta describes the relation of the asset's return to the market return
If Beta = 1, the price for the asset changes in the same way as the market index. 
If Beta = 0, there are no relation between the asset and the market
If Beta = -1, the asset's and the market's price go in opposite directions
If Beta > 1, the price of the asset changes more than by 1% for every market movement by 1%
If Beta >1, the price of the asset falls by more than 1% every time market goes up by 1%; and it growth more than by 1% every time the market falls by 1%
Want to know about Beta? Go here  http://en.wikipedia.org/wiki/Beta_coefficient
Beta equals the covariance between the asset's and market's returns divided by market's variance
Ra - return of asset
Rp - return of the market (or of the portfolio)
For covariance use COVAR function in excel and for variance - VAR function
Below is the calculation of Beta for each stock and for portfolio
  Covariance Variance Beta
Apple 0.00128 0.00130 0.99
Citi 0.00484 0.00130 3.71
General Electric 0.00235 0.00130 1.80
Exxon Mobil 0.00081 0.00130 0.62
Alcoa 0.00207 0.00130 1.59
Portfolio 0.00219 0.00130 1.68
 
You might notice that Citi has a Beta equal to 3.71. That's unusual. But if you remember 2009 was the crisis year and banking sector demonstrated the highest volatility
STEP 6 DECISION MAKING    
Let's insert all the parameters we found in a single table
  Share in portfolio Expected return (Re) Risk (σ) Sharpe ratio Beta
Apple 18.1% 1.8% 4.9% 0.35 0.99
Citi 19.0% 0.4% 19.1% 0.02 3.71
General Electric 22.3% 0.3% 9.0% 0.03 1.80
Exxon Mobil 18.4% -0.2% 3.3% -0.08 0.62
Alcoa 22.1% 1.2% 8.6% 0.13 1.59
Portfolio   0.7% 7.4% 0.08 1.68
S&P index   0.6% 3.6% 0.13  
The first thing you might notice is that the Sharpe ratio for our portfolio is lower than for S&P index which means that the latter provide better relation of risk and return. 
At the same time our portfolio has Beta equal to 1.68 which means that if the market grows, our portfolio grows faster
Let's make the following changes:
    decrease the share of a stock with the lowest Sharpe ratio (Exxon Mobil)
    decrease the share of a stock with the lowest Beta (for example, it is because we expect S&P to grow and want to have more stocks which will outpace the index) (also Exxon Mobil)
    increase the share of a stock with a highest Beta (Citi)
    increase the share of a stock with a highest Sharpe ratio (Apple)
We keep Alcoa's and General Electric weights the same
STEP 7 PORTFOLIO TESTING    
Now let's test our portfolios on 2010 data
Here is our old portfolio. 
  Ticker Last price (end of 2009), $  Number of shares Position $ Share in portfolio
Apple AAPL 209.04 12 2 508 18.1%
Citi C 3.35 785 2 630 19.0%
General Electric GE 15.44 200 3 088 22.3%
Exxon Mobil XOM 68.66 37 2 540 18.4%
Alcoa AA 16.34 187 3 056 22.1%
Portfolio       13 822 100.0%
And here is a new portfolio with all the suggested changes (look at the number of shares)
  Ticker Last price (end of 2009), $  Number of shares Position $ Share in portfolio
Apple AAPL 209.04 17 3 554 25.7%
Citi C 3.35 1000 3 350 24.3%
General Electric GE 15.44 200 3 088 22.4%
Exxon Mobil XOM 68.66 11 755 5.5%
Alcoa AA 16.34 187 3 056 22.1%
Portfolio       13 803 100%
We changed the number of shares for Apple, Citi and Exxon Mobil to get approximately the same total position in $
Prices ($) Change (%)
After that let's calculate weekly returns for old and new portfolios (to the right) AAPL C GE XOM AA S&P AAPL C GE XOM AA S&P Old portfolio New portfolio
01.01.2010 210.732 3.31 15.13 68.19 16.12 1122.9
Here is what we get for average weekly return for the old and new portfolios and for 08.01.2010 211.98 3.59 16.6 69.52 17.02 1148 0.6% 8.5% 9.7% 2.0% 5.6% 2.2% 5.5% 5.7%
S&P index 15.01.2010 205.93 3.42 16.44 69.11 15.63 1137.6 -2.9% -4.7% -1.0% -0.6% -8.2% -0.9% -3.6% -3.9%
    OLD  NEW S&P index 22.01.2010 197.75 3.25 16.11 66.1 13.4 1098.7 -4.0% -5.0% -2.0% -4.4% -14.3% -3.4% -5.9% -5.9%
2010 average weekly return 0.458% 0.548% 0.251% 29.01.2010 192.063 3.32 16.08 64.43 12.73 1080.2 -2.9% 2.2% -0.2% -2.5% -5.0% -1.7% -1.6% -1.3%
05.02.2010 195.46 3.22 15.79 64.8 13.18 1064.5 1.8% -3.0% -1.8% 0.6% 3.5% -1.5% 0.0% -0.1%
12.02.2010 200.38 3.18 15.55 64.8 13.28 1081.2 2.5% -1.2% -1.5% 0.0% 0.8% 1.6% 0.0% 0.1%
19.02.2010 201.67 3.42 16.17 65.87 13.53 1112.3 0.6% 7.5% 4.0% 1.7% 1.9% 2.9% 3.2% 3.4%
As we can see our improvements helped. 26.02.2010 204.62 3.4 16.06 65 13.3 1109.6 1.5% -0.6% -0.7% -1.3% -1.7% -0.2% -0.6% -0.3%
Both portfolios outperformed S&P index and the new portfolio demonstrated better  05.03.2010 218.95 3.5 16.35 66.47 13.84 1139.2 7.0% 2.9% 1.8% 2.3% 4.1% 2.7% 3.5% 3.9%
performance than the old one 12.03.2010 226.6 3.97 17.04 66.8 13.6 1147.3 3.5% 13.4% 4.2% 0.5% -1.7% 0.7% 4.1% 5.0%
19.03.2010 222.25 3.9 18.07 67.04 14.26 1153.9 -1.9% -1.8% 6.0% 0.4% 4.9% 0.6% 1.6% 1.3%
 Let’s see the average weekly performance for the stocks 26.03.2010 230.9 4.31 18.34 66.54 14.27 1170.4 3.9% 10.5% 1.5% -0.7% 0.1% 1.4% 3.2% 4.1%
02.04.2010 235.97 4.18 18.33 67.61 14.7 1179.9 2.2% -3.0% -0.1% 1.6% 3.0% 0.8% 0.5% 0.3%
  Change 09.04.2010 241.79 4.55 18.52 68.76 14.39 1195.7 2.5% 8.9% 1.0% 1.7% -2.1% 1.3% 2.5% 3.0%
Apple 0.9% 16.04.2010 247.4 4.56 18.97 67.93 13.91 1189.3 2.3% 0.2% 2.4% -1.2% -3.3% -0.5% 0.3% 0.6%
Citi 0.8% 23.04.2010 270.83 4.86 19.07 69.24 14.11 1216.8 9.5% 6.6% 0.5% 1.9% 1.4% 2.3% 4.0% 4.8%
General Electric 0.4% 30.04.2010 261.09 4.37 18.86 67.77 13.43 1191.9 -3.6% -10.1% -1.1% -2.1% -4.8% -2.0% -4.5% -5.0%
Exxon Mobil 0.2% 07.05.2010 235.86 4 16.88 63.7 12 1142.4 -9.7% -8.5% -10.5% -6.0% -10.6% -4.2% -9.2% -9.5%
Alcoa 0.0% 14.05.2010 253.82 3.98 17.64 63.6 12.36 1136.5 7.6% -0.5% 4.5% -0.2% 3.0% -0.5% 3.0% 3.5%
21.05.2010 242.32 3.75 16.42 60.88 11.35 1085 -4.5% -5.8% -6.9% -4.3% -8.2% -4.5% -5.9% -6.0%
We increased the weights of Apple and Citi and luckily they were the best performers 28.05.2010 256.88 3.96 16.35 60.46 11.64 1085.7 6.0% 5.6% -0.4% -0.7% 2.6% 0.1% 2.7% 3.5%
We decreased the weigh of Exxon Mobil and it was the second worst performing stock 04.06.2010 255.965 3.79 15.71 59.525 10.84 1066.7 -0.4% -4.3% -3.9% -1.5% -6.9% -1.8% -3.3% -3.3%
11.06.2010 253.51 3.88 15.56 61.86 11.36 1096 -1.0% 2.4% -1.0% 3.9% 4.8% 2.7% 1.5% 1.0%
But do not be confused by the results  18.06.2010 274.074 4.01 15.95 63.1 11.11 1124.5 8.1% 3.4% 2.5% 2.0% -2.2% 2.6% 3.1% 3.7%
This approach does not work well all the time…as everything in financial analysis 25.06.2010 266.7 3.94 14.91 59.1 11.23 1078.2 -2.7% -1.7% -6.5% -6.3% 1.1% -4.1% -3.4% -2.9%
02.07.2010 246.94 3.79 13.88 56.57 10 1030.2 -7.4% -3.8% -6.9% -4.3% -11.0% -4.5% -6.5% -6.7%
  09.07.2010 259.62 4.04 14.95 58.78 10.94 1076.7 5.1% 6.6% 7.7% 3.9% 9.4% 4.5% 6.5% 6.6%
These were the simplest tools for portfolio analysis.  16.07.2010 249.9 3.9 14.55 57.96 10.41 1067.5 -3.7% -3.5% -2.7% -1.4% -4.8% -0.9% -3.2% -3.5%
Soon such instruments as intra-portfolio correlation, Sortino ratio,  23.07.2010 259.94 4.02 15.71 59.72 11.05 1103.6 4.0% 3.1% 8.0% 3.0% 6.1% 3.4% 4.8% 4.9%
Alpha etc will also be explained on our website 30.07.2010 257.25 4.1 16.12 59.68 11.17 1108.7 -1.0% 2.0% 2.6% -0.1% 1.1% 0.5% 1.0% 1.0%
06.08.2010 260.091 4.06 16.45 61.97 11.59 1123.6 1.1% -1.0% 2.0% 3.8% 3.8% 1.3% 1.7% 1.2%
13.08.2010 249.1 3.88 15.38 59.91 10.64 1077.5 -4.2% -4.4% -6.5% -3.3% -8.2% -4.1% -5.3% -5.3%
20.08.2010 249.64 3.75 15.03 58.89 10.57 1074.2 0.2% -3.4% -2.3% -1.7% -0.7% -0.3% -1.6% -1.6%
27.08.2010 241.62 3.76 14.71 59.8 10.32 1061.3 -3.2% 0.3% -2.1% 1.5% -2.4% -1.2% -1.3% -1.7%
03.09.2010 258.77 3.91 15.393 61.32 10.88 1101.7 7.1% 4.0% 4.6% 2.5% 5.4% 3.8% 4.8% 5.2%
10.09.2010 263.41 3.91 15.98 61.2 11.17 1113.4 1.8% 0.0% 3.8% -0.2% 2.7% 1.1% 1.6% 1.8%
17.09.2010 275.37 3.95 16.29 60.78 11.172 1127 4.5% 1.0% 1.9% -0.7% 0.0% 1.2% 1.6% 2.1%
24.09.2010 292.32 3.904 16.66 61.75 12.2 1148.6 6.2% -1.2% 2.3% 1.6% 9.2% 1.9% 3.4% 3.5%
01.10.2010 282.52 4.09 16.36 62.54 12.23 1144.6 -3.4% 4.8% -1.8% 1.3% 0.2% -0.4% 0.0% -0.2%
08.10.2010 294.07 4.19 17.12 64.38 12.89 1165.9 4.1% 2.4% 4.6% 2.9% 5.4% 1.9% 3.9% 3.9%
15.10.2010 314.74 3.95 16.3 65.19 13.13 1176.8 7.0% -5.7% -4.8% 1.3% 1.9% 0.9% -0.2% 0.0%
22.10.2010 307.47 4.11 16.055 66.34 12.72 1186.6 -2.3% 4.1% -1.5% 1.8% -3.1% 0.8% -0.3% -0.5%
29.10.2010 300.98 4.17 16.02 66.49 13.14 1187 -2.1% 1.5% -0.2% 0.2% 3.3% 0.0% 0.3% 0.1%
05.11.2010 317.13 4.49 16.73 70 14 1222.6 5.4% 7.7% 4.4% 5.3% 6.5% 3.0% 5.8% 6.0%
12.11.2010 308.03 4.29 16.25 70.99 13.49 1202.4 -2.9% -4.5% -2.9% 1.4% -3.6% -1.7% -2.7% -3.2%
19.11.2010 306.73 4.268 16.22 70.54 13.38 1195.3 -0.4% -0.5% -0.2% -0.6% -0.8% -0.6% -0.5% -0.5%
26.11.2010 315.76 4.11 15.8 69.23 13.17 1183.8 2.9% -3.7% -2.6% -1.9% -1.6% -1.0% -1.2% -0.9%
03.12.2010 317.44 4.45 16.78 71.19 14.23 1223.5 0.5% 8.3% 6.2% 2.8% 8.0% 3.4% 5.0% 4.9%
10.12.2010 320.56 4.77 17.72 72.18 14.25 1243.4 1.0% 7.2% 5.6% 1.4% 0.1% 1.6% 3.2% 3.5%
17.12.2010 320.61 4.7 17.7 72.17 14.56 1246.5 0.0% -1.5% -0.1% 0.0% 2.2% 0.2% 0.0% -0.1%
24.12.2010 323.6 4.68 18.04 73.2 15.34 1253.6 0.9% -0.4% 1.9% 1.4% 5.4% 0.6% 1.7% 1.5%
31.12.2010 322.56 4.73 18.29 73.12 15.39 1262.9 -0.3% 1.1% 1.4% -0.1% 0.3% 0.7% 0.5% 0.5%