Free Portfolio Management Essay Sample

Introduction

In this report, we will illustrate the portfolio construction process where each stock or asset will be selected considering the client’s risk-return objective. Since, the client is risk-averse; we will not expose the portfolios to high risk, and will try to construct the portfolio composition with the core fundamentals of the portfolio management, i.e. a highly diversified portfolio where weights of each portfolio will be selected on the basis of maximum return-minimum risk profile.

Section 1

a)Five companies to be considered while optimizing the portfolio are Apple Inc., Starbucks Coffee, Caterpillar Inc., Nike Inc. and General Motors. While selecting the stocks our main objective was to select the stocks from different industries, so that each of them has low correlation between each other, and whichever two stocks we select later on for the client, the portfolio should have benefit of diversification. Important to note, when a portfolio of stocks is diversified across assets that are less than perfectly correlated, the overall risk is less than the weighted average of the risk of individual securities in the portfolio.
Moreover, each of the stock is the leader in its own respective industry. For Instance, Apple Inc. is a renowned global consumer electronic company, and with recent announcement of blockbuster profit of $18 Billion and huge market expansion to Brazil and China, the stock is a must include in the portfolio. (Ciaccia, 2015) As for Starbucks Coffee, the company recently announced its quarter profit and has again surpassed the market expectations. Over the recent month, the stock has earned a sustainable return of 16-17%. Similarly, all the three other companies, Nike Inc,. Caterpillar Inc. and General Motors are also big players in the market.
Hence, while the core objective was to select less than perfectly correlated stocks, we also wanted to avoid any penny stocks as the client has openly declared his risk-aversions. Below is general information relating to each company:
b) Mean Return and Standard Deviation of each for the year period:
c) Covariance matrix for the stocks:
-Correlation Matrix for the stocks:

Section 2)

a)Why Apple and Starbucks were included in the portfolio?
The reason for including the above two stocks in the portfolio was purely based on the principles of portfolio management. As we can see from the return-risk combinations below, only these stocks offered the best combination. As for Apple, although the stock was having the high risk factor of 1.50%, but it justifies the risk position with a high return of 0.17%. Similarly, as for Starbucks Inc. the stock had risk factor of 1.21%, the least amongst all the five stocks we analyzed. However, what was attractive in this stock that despite of least risk level, it offered a high return of 1.21%, in comparison to other stocks which despite of high risk factor than Starbucks, are offering lower return. For instance, Caterpillar Inc. indicated risk factor of 1.26%, but offered a negative return of -0.001%.
Thus, it was a rationale and prudent decision to include Apple and Starbucks in the portfolio as out of all the five stocks we analyzed, they both offered best combination of risk-return profile.
b) Different combination of risk-return profile between the two stocks:
-Efficient Frontier
-Minimum Variance Portfolio
Minimum variance portfolio represents a combination of portfolio of stocks that offers lowest risk levels out of all the group of portfolios on the efficient portfolio. Important to note, it is the minimum variance portfolio that makes maximum use of diversification to achieve the resultant risk level that is lower than the individual risk level of each of the stock it contains.
Referring to the efficient frontier graphed above, we can see that allocation of 45% funds in Apple and 55% in Starbucks leads to minimum variance portfolio where at the risk level of 1.03%, portfolio yields return of 66.95%( on annual basis)
d) Appropriate portfolio mix for the client
Since our client is risk-averse and is seeking benchmark return of 20%, we will recommend him to allocate his funds according the minimum variance portfolio mix as with 45% allocation in Apple, and 55% allocation in Starbucks stock, he will be generating a return of 66.95% on annual basis with risk levels at minimum level at 19.67%(on daily return basis it will be 1.03%) in comparison to other portfolio sets.
Therefore, by selecting a highly diversified portfolio, not only he will achieve his targeted return objective, in fact the final portfolio return will be manifold than his benchmark return.
e)Sharpe Ratio of Portfolio A
Sharpe ratio is one of the prominent measures of calculating risk-adjusted return. The ratio multiple is widely used in many industries to calculate the average rate of return earned in excess of the risk-free rate per unit of volatility or total risk. In other words, by subtracting the risk free rate from the mean return, one can judge the performance of his/her portfolio from investing in risky assets. Thus, higher is the Sharpe ratio, more attractive will be the risk-adjusted return. Below is the formula for calculating the Sharpe ratio of the portfolio:
Sharpe ratio = (Mean portfolio return − Risk-free rate)/Standard deviation of portfolio return

Sharpe Ratio Portfolio A

= (66.95-4)/19.67
= 3.20

Section 3:

a) Now, considering the utmost requirement of keeping the portfolio to minimum risk exposure, we introduced risk-free asset into the portfolio, and named it as Portfolio B. Earlier while construction of Portfolio A, we had found that with investment in minimum variance portfolio on the efficient frontier will be a prudent decision for the client as with minimal risk, his portfolio can earn 66.95%, 3.5 times than his benchmark return of 20%.
However, considering his strict desirability of low risk in his portfolio, we have now included risk-free asset that yield 4% per annum in the portfolio. In order to find the optimal weights of two risky assets i.e. Apple and Starbucks and of the risk-free asset, we used SOLVER function in excel where under the constraints of minimal standard deviation and expected annual return of 20%, we found the following optimal weights for the portfolio:
*Refer to excel sheet for calculations
Thus, with allocation of total funds in 69.88% in risk-free asset, 12.84% in Apple and 17.28% in Starbucks, client will be able to earn 20% annualized return at minimal risk level of 0.28%(5.34% annualized). In this way, both of his risk-return objectives will be accomplished.
b)
-Expected Return of Portfolio B: Weight of Apple Stock* Return of Apple Stock+ Weight of Stabrucks Stock* Return of Apple Stock+ Weight of Risk-free asset* Return of Risk-free asset
= 12.8*0.17+ 17.28*0.12+ 69.88*0.106
= 2.18+ 2.07 + 0.7407
= 5%
Expected Return on Annualized Basis= (1+0.05%)^365-1
= 20%
-Standard Deviation of Portfolio B: Sqrt(wA2 s2A + wB2 s2B + wC2 s2C+ 2 wA wB rAB sA sB+ 2 wA wC rAC sA sC+ 2 wB wC rBC sB sC )
where
wA,wB,wC = Portfolio weights on assets
s2A ,s2B ,s2C = Variances of assets A, B, and C
rAB , rAC , rBC = Correlation in returns between pairs of assets (A&B, A&C, B&C)
= 0.28%
Standard Deviation of Portfolio B(annualized)= 0.28%*sqrt(365)
= 5.34%
c) Comparison of Portfolio A with Market Indices:
Comparing the risk-return profile of Portfolio A where we selected Starbucks and Apple stocks for the client, we believe that we will be able to beat the markets. Important to note, in order to compare the portfolio return with market returns, we selected S&P 500 and FTSE 100 as benchmark index and found that although our portfolio is more risky than both the market index, but the manifold return truly justifies it. For instance, in comparison to S&P 500 which yielded an annualized return of 28.01% with risk factor of 13.78%, portfolio A yielded return of 66.95% with risk factor of 13.78%. Similarly, our portfolio performed really well in comparison to FTSE 100 which yielded merely 6.68% with risk factor of 14.39%.
Thus, our portfolio selection is very much capable of beating the markets. However, the final decision relating to portfolio will be entirely our client’s choice because if he is just looking for 20% return, he can invest the money in S&P 500 index where at lower risk levels he will achieve the target return. However, if he is willing to take additional calculated risk, he may earn return three times than what he will earn from investing in the market index. Moreover, we have also provided him with an option of including risk-free asset in Portfolio B where he can earn his benchmark return at risk level of 5.34% only.

Works Cited

Brown, K. (2011). Portfolio Management. Boston: Custom.
Ciaccia, C. (2015, January 27). Apple Surges Following $74B Revenue Quarter, 74M iPhones Shipped. Retrieved April 14, 2015, from http://www.thestreet.com/story/13025026/1/apple-surges-following-74b-revenue-quarter-74m-iphones-shipped.html
Sharpe Ratio. (n.d.). Retrieved April 11, 2015, from Investopedia: http://www.investopedia.com/terms/s/sharperatio.asp
Historical Prices: Apple Inc. (n.d.). Retrieved April 13, 2015, from Yahoo Finance: https://in.finance.yahoo.com/q/hp?s=AAPL
Historical Prices: Starbucks Inc. (n.d.). Retrieved April 13, 2015, from Yahoo Finance: https://in.finance.yahoo.com/q/hp?s=SBUX
Historical Prices: S&p 500. (n.d.). Retrieved April 13, 2015, from Yahoo Finance: http://finance.yahoo.com/q/hp?s=^GSPC+Historical+Prices
Historical Prices: Caterpillar Inc. (n.d.). Retrieved April 13, 2015, from Yahoo Finance: http://finance.yahoo.com/q/hp?s=CAT+Historical+Prices
Historical Prices: General Motors (n.d.). Retrieved April 13, 2015, from Yahoo Finance: http://finance.yahoo.com/q/hp?s=GM+Historical+Prices
Historical Prices: Nike Inc. (n.d.). Retrieved April 13, 2015, from Yahoo Finance: https://in.finance.yahoo.com/q/hp?s=NKE
Historical Prices: FTSE 100. (n.d.). Retrieved April 13, 2015, from Yahoo Finance: https://in.finance.yahoo.com/q/hp?s=%5EFTSE
Appendix:
Note: All the formulas and calculation outputs are available in the excel file
i)
ii) Portfolio A’s supportive data and efficient frontier:
iii) Portfolio B weight selection
iv) Comparison of Portfolio Awith Market indices