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¶ … Download stock prices companies - 22 daily closing prices company. You database obtain prices e.g. datastream, yahoo finance . Use prices September 2013 onwards. 2.Present a table companies, dates, prices returns ( %).
The 22 daily closing prices for IBM, Microsoft and Apple reflect the period from October 1 to October 30. In order to calculate the price return for each stock, the previous day closing price has been subtracted from the present day closing price and the result was divided by the present day value. The result has been multiplied by 100, to reflect a percentage price return. The formula below resumes this calculation: (a) The companies with the highest correlation coefficient are IBM and Apple. Let's consider XIBM the weight for IBM stock and XAPPLE the weight for Apple stock. Assuming the correlation coefficient is zero, the two equations for the return and standard deviation are
R% = ((Rt-Rt-1)/Rt) * 100
The table below shows the closing prices for the three selected companies (IBM, Microsoft and Apple), as well as the percentage price returns for each of these companies, for the interval October 1 -- October 30.
IBM
Microsoft
Apple
Close Price
Price Return
Close Price
Price Return
Close Price
Price
(a) Before discussing the results for each stock in part and before drawing a conclusion in terms of which stock dominates the other, it is useful to make some general observations about the three types of stock. IBM, Microsoft and Apple are all considered blue chips, namely stocks with low risk, which yield a regular rate of return through time. In the case of the period in analysis here (October 1-October 30), this is reflected through the fact that the daily fluctuations are generally quite small, usually less than $3. The only stock that has a significant fluctuation in a day is IBM, whose closing price drops on October 17 with almost $12.
In terms of average returns, this translates in the fact that both Microsoft and Apple had moderate average returns in the analyzed period: 0.26% for Microsoft and 0.34% for Apple. IBM had a negative return (-0.18%), primarily explained with the one-day drop that has been mentioned previously (a company-related event triggered that most likely, since the other two companies gained on that day).
In terms of variance, a measure of risk, the low values for all the three stocks reflect the blue chip quality. IBM has the highest risk of the three, probably because of some of the price fluctuations (the one-day drop and a significant gain on October 29). Apple has the highest average return and the lowest variance of the three stocks that are analyzed. Given the theory discussed in class, this makes Apple the dominant investment. Since Apple dominates both Microsoft and IBM, it is thus not dominated by any of the other stock. This means that Apple is the mean-variance efficient investment.
4. Variance-covariance matrix
IBM
Microsoft
Apple
IBM
0.000362242
0.000300194
0.00021607
Microsoft
0.000300194
0.000248773
0.00017906
Apple
0.000216069
0.000179059
0.00012888
Correlations
IBM
Microsoft
Apple
Rp = -0.18* XIBM + 0.34*XAPPLE
p = (0.0192* XIBM2 + 0.0112* XAPPLE2)1/2
Combinations
Weight IBM
Weight Apple
Return (%)
Standard deviation (%)
1
1
0
-0.001789
0.019032664
2
0.8
0.2
-0.000749
0.015394489
3
0.75
0.25
-0.00049
0.014553911
4
0.6
0.4
0.0002899
0.012289349
5
0.5
0.5
0.0008096
0.011080645
6
0.4
0.6
0.0013292
0.010215465
7
0.25
0.75
0.0021087
0.009753738
8
0.2
0.8
0.0023685
0.009847496
9
0
1
0.0034077
0.011352553
(b) The companies with the lowest correlation coefficients are Microsoft and IBM.
Combinations
Weight IBM
Weight Microsoft
Return (%)
Standard deviation (%)
1
1
0
-0.001789
0.019032664
2
0.8
0.2
-0.000916
0.01554947
3
0.75
0.25
-0.000697
0.014809106
4
0.6
0.4
-4.25E-05
0.013046492
5
0.5
0.5
0.0003941
0.012359365
6
0.4
0.6
0.0008306
0.012145664
7
0.25
0.75
0.0014854
0.012750494
8
0.2
0.8
0.0017037
0.013179703
9
0
1
0.0025768
0.015772548
6. For the IBM-Apple combination, the Minimum Variance Portfolio (MVP) is for the N= 7 combination, namely for a standard deviation of 0.009754. The MEF is the line that results from joining N=7, N=8 and N=9.
For the IBM-Microsoft combination, the Minimum Variance Portfolio (MVP) is for the N= 6 combination, namely for a standard deviation of 0.012146. The MEF is the line that results from joining N=6, N=7, N=8 and N=9.
7. (a) The two curves are surprisingly similar, the main difference…
Bibliography
1. Levy, H. And Post, T. (2005), Investments, Prentice Hall [LP]
2. Cuthbertson, K. And Nitzsche, D. (2008) Investments -- Spot and Derivative Markets, Wiley [CN].
3. Elton, E., Gruber, M., Brown, S. And Goetzmann, W. (2010) Modern Portfolio Theory and Investment Analysis, Wiley [EGBG].
4. Fama, E. (1991) Efficient Capital Markets II, Journal of Finance, 46 (5), 1575-1617 [F].
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