Sample Essay On Portfolio Construction

Section 1: Five companies’ stocks selection

Rationale for the five stocks selection and analysis key information about each company’s background
BP p.l.c.
BP P.l.c. operate an integrated gas and oil company. It has three segments of operation: Upstream, Downstream, and Rosneft. The segment of Upstream engages in the exploration of oil and natural gas, development of the field, and production; transportation of midstream, and processing and storage; and trade and marketing of natural gas. The segment of Downstream manufacturers, refines, markets, supplies, transports and trades in petroleum, crude oil and petrochemicals products and services that are related to retail and wholesale customers. The segment of Rosneft engages in the production and exploration of hydrocarbons. It was founded in1889, and its headquarter is in London, the UK (Yahoo finance, 2015c).

Exxon Mobil Corporation

This Corporation produces and explores natural gas and crude oil in the United States, Europe, Asia, Africa, Canada/South America, and Australia/Oceania. It also markets and manufactures commodity petrochemicals, including aromatics, olefins polypropylene and polyethylene plastics, and specialty products; and sells and transport natural gas, crude oil, and petroleum products. The company has approximately 29,870 net and 35,446 gross operated wells. This Corporation is headquartered in Irving, Texas and was founded in 1870 (Yahoo finance, 2015b)

Yahoo! Inc.

Yahoo! Inc. provides display and search advertising services worldwide on Yahoo properties and affiliate sites. The company offers Yahoo Search, Yahoo Mail , Yahoo Answers, Yahoo Groups, Yahoo Messenger, the digital content are offered by the company comprising Yahoo.com, Yahoo Finance, Yahoo Sports and Yahoo Weather, Yahoo Screen, as well as Yahoo News, it provides Flickr, Tumblr Yahoo Bing Network , Yahoo Premium Ads, Yahoo Audience Ads, Yahoo Video. Yahoo Inc. is headquartered in California and was founded in 1994. (Yahoo Finance, 2015g)

Hewlett-Packard

Together with its subsidiaries, Hewlett-Packard Company provides technologies, software, products, services and solutions to small- and medium-sized businesses (SMBs) and individual consumers, as well as to the government, education and health sectors worldwide. The company’s Personal Systems segment, Software segment, Enterprise Group segment, Corporate Investments and Financial Services segment. Founded in 1939 Hewlett-Packard Company is headquartered in Palo Alto, California

IBM

Source: (Yahoo Finance, 2015f)
Calculated mean return and the standard deviations of each company stock
Mean return
The expected return is calculated as the average weight of the possible profits of the assets in the portfolio, weighted by the possible profits of every class of assets. The formula is also written in another way as follows: E(R) = w1R1 + w2Rq + + wnRn
The expected return is not by any means a rate of return that guaranteed. However, it can be used to predict the future`s portfolio value, and also offer a guide from which to calculate the actual return (Vinci, 2010).

Standard deviation

The calculation of dispersion in a given set of data from its mean. The more widely spread apart the data, the bigger the deviation. The square root of the variance is equal to the standard deviation. Standard deviation in finance is used in the annual return rate of an investment to measure the volatility of an investment. Historical volatility is another reference to standard deviation and is used as a gauge for the amount of volatility expected by investors. Standard deviation is used as a statistical calculation that gives light to historical volatility. For example, a stock that is volatile will have a high standard deviation while the stock of stable blue chip will have a lower deviation. A huge dispersion expresses to us how much the fund`s return is deviating from the standard returns that were expected.
c) Calculating the covariance and correlation between the stocks
Variance (σ2)This is a measure of the dispersion of a given set of data points within their mean value. In other words, σ2 is a mathematical expectation of the squared average deviations from a given mean. It is calculated by finding the probability-weighted average of a given squared deviations from the value that is expected. The variability from an average (volatility) is what variance measures. Volatility is, therefore, a measure of risk whose statistic can help find out the risk an investor might take on when buying a certain security. (Vinci, 2010).
CovarianceThis is the measure of how two variables move together. It calculates to see whether the two move in a similar direction (a covariance that is positive) or in the opposite directions (a covariance that is negative). The variables in this article will usually be prices of stock, but they may be anything. In the stock market, the emphasis is strongly placed on decreasing the risk amount taken on for the similar amount of return. When creating a portfolio, an analyst will choose stocks that will work together well. This mainly means that these stocks do not move in the similar direction.
Measuring a stock's covariance begins with looking a list of previous prices. Typically, each day`s closing price is used to measure the return from one day to the next day. This is done for both stocks, and a list is created to start the calculations. In finance, a statistical measure of relation of two securities on how they move. In advanced portfolio management, correlations are used.

Correlation

Correlation is computed into what is referred to as the correlation coefficient, whose range is between -1 and +1. The Perfect correlation that is positive (a correlation co-efficient of +1) implies that as a single security moves, either down or up, the other security will move in the same direction in a lockstep. Perfect negative correlation alternatively means that if a single security moves in any of the direction the security that is perfectly correlated negatively will make a move in the opposite direction. If 0 is the correlation, the securities movements are said to have no correlation; they are completely random.
All pairs have a positive coefficient meaning that their returns move in the same direction. On the other hand, the pair containing HPQ and YHOO have the least correlation while that of XOM and BP has the highest correlation.

Section 2: Portfolio construction

Rationale for the two stocks
The selected stocks were XCOM and IBM that have the least standard deviation indicating that they are less volatile in line with the client's risk-averse nature.

Different combinations of risk and return for portfolios

Portfolio mix that represents the minimum variance portfolio based on the efficient frontier.
The portfolio's return variance is the variance`s function of the component assets components as well as the covariance between each of them. Covariance is a calculation of the degree to which outputs on two assets that are a risky move in tandem. A covariance that is positive means that returns of assets move together. A covariance that is negative means returns moves inversely. There is a close relation of covariance to correlation while the variable between the two is the standard deviation latter factor. The Modern Portfolio Theory says that portfolio variance can, by choosing asset classes with a negative or low covariance be reduced, such as bonds and stocks. To reduce the risk, this type of diversification is used.
Portfolio variance looks in the portfolio at the correlation coefficient or covariance for the securities. Portfolio variance is calculated by multiplying each security squared weight by the variance of its corresponding and add two times the weighted average weight multiplied by all the individual security pair’s covariance. Thus, we get the formula to calculate portfolio variance in a two-asset portfolio simple:(weight(1)^2*variance(1) + weight(2)^2*variance(2) + 2*weight(1)*weight (2) *covar (1& 2)

In another way the formula is stated:

Portfolio Variance= Risk = w2A*σ2(RA) + w2B*σ2(RB) + 2*(wA)*(wB)*Cov(RA, RB)Where: wA and wB  are portfolio weights, σ2(RA) and σ2(RB) are variances and Cov(RA, RB) is the covariance (Bodie, Kane & Marcus, 2008)

The risk and return of the minimum variance portfolio

A portfolio that suits the client’s best; Portfolio A.
Weighting of each stock in the portfolio
Given the two socks returns and risk, they are each allocated an equal weight of 0.5.

Portfolio’s mean return and the standard deviation.

The portfolio has the least risk among those with a return of above 20% as required by the client.
Estimated Sharpe ratio of Portfolio A
Use of Sharpe ratio to you client.
Measure for calculating risk-adjusted return is referred to as Sharpe Ratio, and the ratio of such calculations has become the industry standard. It was developed by William F. Sharpe a Nobel laureate. The ratio is the earned average return in rate per unit excess of the risk-free of total risk or volatility. Subtracting from the mean return risk-free rate, the performance can be isolated which are associated with risk-taking activities. A portfolio engaging in “Zero risk” investment is one intuition of this calculation, such as the U.S. Treasury bills purchase (for which their expected rate of return is risk-free), has a Sharpe ratio of zero. The greater the Sharpe ratio value, the more risk-adjusted return are attractive.
The theory of Modern Portfolio states that there can be a decrease in portfolio risk without sacrificing return by adding assets to a diversified portfolio that have correlations with each other of less than one. Such diversification will serve to increase a portfolio’s Sharpe ratio.
Sharpe ratio = (Mean portfolio return − Risk-free rate)/Portfolio return standard deviation
The Sharpe ratio also can help explain if excess returns of a portfolio are due to a result of too much risk or smart investment decisions. Although higher returns can be enjoyed by one portfolio or fund than its peers, it is a good investment if only an excess of the additional risk is not coming from those higher returns. The greater Sharpe ratio portfolio is, the better has been its risk-adjusted performance. A negative Sharpe ratio indicates that there would be a better perform from a risk-fewer assets than the security being analyzed. (Strong, 2009) he following is the ratio for the portfolio A.
The ratio of 0.64 indicates moderate high risk for the portfolio.

Section 3: Constructing Portfolio B by combining one risk-free asset with the two company stocks selected for Portfolio A.

Weighting of the risk-free asset as well as for each company stock in Portfolio B.
The three assets will have weights of 0.4, 0.4 and 0.2 for BP, HPQ, and 91 government bills given that the bill has a low return. That is because the bill has a low return of 0.02%. (Bank rate, 2015)

Estimated expected return and standard deviation of Portfolio B assuming FTSE 100 as the market portfolio and using Capital Market Line

Calculated mean returns and risks of FTSE 100 and S&P500 respectively.
Comparing Portfolio A’s mean return and risk with those of FTSE100 and S&P500.
Portfolio A Return
Source: (Yahoo finance, 2015d; 2015f)
Portfolio a has better return compared to the FTSE 100 and the S&P 500 although it has relatively high risk as shown by high standard deviation.

Whether the portfolio can beat the markets

In view of the portfolio A’s return and risk in comparison with the market as represented by FSE 100 and S&P 500, the portfolio beats he market in terms of returns but has relatively high risk thus may not be suitable for risk averse clients.

Reference list

Bank rate. 2015. 91-day T-bill auction average disc rate. [Online] Available at <http://www.bankrate.com/rates/interest-rates/91-day-treasury-bill.aspx>[Accessed 11 April 2015]
Bodie, Z., Kane, A. & Marcus, A., 2008. Investments. 8th ed. New York: McGraw-
Hill/Irwin.
Damodaran, A., 2010. Applied Corporate Finance. 3rd ed. Colorado: Wiley.
Strong, R. 2009. Portfolio Construction, Management, and Protection. London: Richard D. Irwin Inc.
Vinci, L. 2010. Investment Analysis and Portfolio Management. New Jersey: Prentice Hall.
Yahoo finance. 2015a. HPQ Competitors. [Online] Available at <http://finance.yahoo.com/q/co?s=HPQ+Competitors >[Accessed 11 April 2015]
Yahoo finance. 2015b. XOM Profile. [Online] Available at <http://finance.yahoo.com/q/pr?s=XOM+Profile>[Accessed 11 April 2015]
Yahoo finance. 2015c. BP Competitors [Online] Available at <http://finance.yahoo.com/q/co?s=BP+Competitors>[Accessed 11 April 2015]
Yahoo finance. 201d. FTSE 100 Historical Prices. [Online] Available at <https://uk.finance.yahoo.com/q/hp?s=^FTSE&a=0&b=3&c=1984&d=3&e=12&f=2015&g=d&z=66&y=528> [Accessed 11 April 2015]
Yahoo finance. 2015e. S&P 500 Historical Prices. [Online] Available at <http://finance.yahoo.com/q/hp?s=^GSPC&a=00&b=3&c=1950&d=01&e=27&f=2015&g=d&z=66&y=462>[Accessed 11 April 2015]
Yahoo finance. 2015f. IBM Profile. [Online] Available at <http://finance.yahoo.com/q/pr?s=IBM+Profile> [Accessed 11 April 2015]
Yahoo finance. 2015g. YHOO Profile. [Online] Available at <http://finance.yahoo.com/q/pr?s=YHOO+Profile>[Accessed 11 April 2015]
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