Essay about Portfolio Management

1. Introduction
This report will create an investment portfolio for two different types of individual investors; the one is highly risk averse, the other is more tolerant to risk. The investment portfolio will be consisting of three shares which are belong to the Dow Jones Industrial Average. And the portfolio is based on the year January 2012 to December 2012 daily data of the three shares which is showed in the appendix. The three shares are International Business Machines Corporation (IBM), Visa Inc. (V), and Wal-Mart Stores Inc. (WMT), which are not fall into a same industry. That means the correlation between the three shares is low.
IBM was founded in Armonk, New York in 1911. It is the largest company which is service information technology and project solutions. “Visa is a technology and payments business.” (Visa 2013) It connects over two hundred countries and area’s consumers, companies, financial institutions and governments to help people make electronic payment more convenient. Wal-Mart is the largest retailer in the world. And it was established in USA in 1962. The company provides various kinds of products with low price to customers.
2. Findings
2.1 Daily return and Mean return of single asset
In order to evaluate the three shares, the daily return of the shares should be calculated first. Daily return will help investors to know how much they will get or loss in a day which can make a comparison between the three shares. And the result can help investors make decisions. Daily return = (later adjusted close price – previous adjusted close price)/ previous adjusted close price. Based on the data in Table 1(see appendix), daily adjusted close price of the three shares has showed, therefore daily return can be calculated. For example:
IBM
Date Adj Close Daily Return
2012/1/3 179.73 2012/1/4 178.99 -0.004117
The return on 4 January 2012 = (178.99 – 179.73)/ 179.73 = -0.004117
After that, mean return should be calculated. Mean return will demonstrate the relationship between the portfolio’s risk and return by figures which can help investors to understand (Investopedia 2013). And if the risk is acceptable, investors usually prefer maximum their returns. Mean return equates the average return of all the daily return. Thus, mean returns of the three shares are as follow:
Mean ReturnIBM = 0.000229975
Mean ReturnV = 0.00167138
Mean ReturnWMT = 0.000645017
Although the mean returns of the three shares are all above 0, their returns are quite low. To compare the returns, it can be easily found that Visa stock has the highest return and IBM’s return is the lowest.
2.2 Variance of single asset
Risk is “the uncertainty associated with an investment.” (The Free Dictionary 2013) There are several measurements to measure the risk. Volatility or standard deviation and variance are the most common two measurements.
Volatility or Standard deviation: σ=t=1n(Rt-R)2(n-1)Variance: σ2=t=1n(Rt-R)2(n-1)Actually, variance is used more frequently. Therefore, the three shares’ variances can be solved: σIBM2=0.000103234σV2=0.000174127σWMT2=0.000105782The larger variance, the higher uncertain risk. From the results, it is obviously that Visa stock has the highest variance while IBM’s variance is the lowest which means the risk of Visa is higher than IBM and Wal-Mart.
Table 2: Mean return and variance
IBM VISA WMT
Mean Return 0.000229975 0.00167138 0.000645017
Variance 0.000103234 0.000174127 0.000105782
Combine with the mean returns of the three shares; it is found that Visa has both the highest return and variance. IBM’s variance is the lowest in the three shares, so its return is also the lowest.
2.3 Portfolio theory and expected return
A portfolio consists of several assets. Every asset has certain proportion of total investment which is called weight. A portfolio has its own expected return and risk which are depend on the relationships between the assets and weights. Portfolio

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