How did your stocks perform over the past five years? How volatile were your stocks?
The performance of the stock over the last five years is good since all the companies indicated a positive average return with the PBR having the highest average return of 20.357%. This return percentage is a clear indication that the company is at a position to pay up its dividends and other dues efficiently. The BSX Company has the lowest average returns of 0.5%. which clearly indicates to an investor that the company will not yield much that would be able to pay its dividends. In terms of volatility, the volatility of the returns are relatively low because the standard deviation of the companies ranges from -0.0011 to 0.009504. This is a clear indication of high investment potential because of lower risks where performance of the investments is concerned.
2) How did the market do over the past 5 years? How volatile was the market?
The market performance was good as indicated by the average prices of the stocks in the companies. All the companies indicated a positive return on investment and hence stands a very good chance for attraction of potential investors. The highest average stock price was 98.44 for the AABL Company. This in itself shows that the company has good reputation and good management strategies too. Again it shows that the company is able to pay good dividends to ist shareholders. The lowest priced stock had an average price of 12.53 for the BSX Company. This is a considerably low return as compared to that of the AABPL and hence it show that the company management still needs more elaborate structure of management in order to ensure better income. However the volatility of the market prices is very high as indicated by the highest standard deviation of around 3.2345 and the lowest having 0.02131. This in effect calls for various hedging techniques to curb the volatility of the market prices. The volatility rates shown indicates that the market return does not vary into a wide range and hence this builds the investor confidence and hence the investor is at a position to predict his/her future investment
Calculate the correlation matrix between all the stocks over the past five-years. Are any of the correlations high (above .6) or low (below 0.1)? What does this tell you?
The correlation matrix table
AABL MSFT QQQ BPR FB F INTC GE BSX BAC
AABL 1.000 0.538 -0.069 -0.243 0.095 0.090 -0.343 0.011 0.044 -0.258
MSFT 0.538 1.000 -0.026 -0.100 -0.018 -0.019 -0.062 0.197 -0.060 -0.219
QQQ -0.069 -0.026 1.000 0.262 -0.083 0.007 -0.210 0.005 0.331 -0.054
PBR -0.243 -0.100 0.262 1.000 0.090 -0.013 -0.041 -0.176 0.116 0.283
FB 0.095 -0.018 -0.083 0.090 1.000 0.073 -0.098 -0.339 -0.444 -0.064
F 0.090 -0.019 0.007 -0.013 0.073 1.000 -0.238 -0.344 -0.524 -0.135
INTC -0.343 -0.062 -0.210 -0.041 -0.098 -0.238 1.000 -0.262 -0.279 -0.052
GE 0.011 0.197 0.005 -0.176 -0.339 -0.344 -0.262 1.000 0.076 0.001
BSX 0.044 -0.060 0.331 0.116 -0.444 -0.524 -0.279 0.076 1.000 0.124
BAC -0.258 -0.219 -0.054 0.283 -0.064 -0.135 -0.052 0.001 0.124 1.000
From the correlation matrix table above, there correlation between the AABL and the MSFT is high at 53.8% this simply indicates that the return performance of the two companies highly influence each other in a positive way such that if one is high, the other one would be high too. Again the correlation between the BAC and the BSX is at 0.1% which is very low showing that there performance on return has minimal influence each other.
Find your Optimal Risky Portfolio using five years of historical information. What are the optimal portfolio weights?
The optimal portfolio weights
PBR = 33.2%
FB = 5.3%
BSX = 0.83%
BAC = 14.2%
Graph the minimum variance frontier.
Minimum Variance Frontier (MVF)
Do your portfolio weights seem reasonable? Would you feel comfortable recommending this investment portfolio to a client?
The portfolio weighs are not reasonable because they all have positive values and this 0simply means that diversification is not viable here because during diversification, the if risk occurs it will affect all the investments in the same way and hence there will be no fall back because as the one investments go down the others will also go down since they positively correlated and their variance stems to the same positive direction. The graph clearly shows that all the companies have deviation in terms of risk therefore as the risk one company increases, the risk of the other company also increases accordingly, to this effect a portfolio manager should take keen concern of this since it poses a threat of the whole portfolio going into a loss in the event of occurrence of loss.
Why does it make sense to use historical information (returns, standard deviations and co variances) as inputs to portfolio theory? Also give at least one argument against using historical information.
It is important to use historical information because the return characteristics of the portfolio do not change much across the periods as depicted by almost stable volatility of the returns. It is also a believable fact that if the characteristics do not change overtime, the longer the data availability and hence the more accurate the mean results would be. To illustrate this, the formula of standard error of mean of a sequence of independent variable random variance divided by the sample size which 10 in this case. Under the assumption of stationary, the expected returns and the returns uncorrelated through the five years, more historical data has improved the estimate of the expected return included in the mean variance model.
What is your optimal portfolio if you do not allow short sales? Use historical inputs. Are the weights more reasonable? Would you restrict short sales? Why or why not? Graph the Minimum Variance Frontier in this case. How does it compare to #5? Why?
The Minimum Variance Frontier with short sales
The waits are proving to be more reasonable because the waits are both negatively and positively correlated and this brings a more formidable adventure for investment. Hence I would not restrict short sales in this event since it brings more diversification and hence reduces the risks involved.
Looking at the graph it clearly indicates that there are some investments that are having an inverse relationship in terms of investment that from one company to the other. This call for an anticipation of a real diversification in terms of investment in the portfolio, at this point in time the portfolio manager can invest in the various companies with easy since in the event of one company going down, another company will be at a position to stand out and bring more returns to counter the loss incurred by another company.
There is a considerable improvement in the use of the short sales because there emerge the other returns that depict negative correlation of the in the portfolio hence there is room for diversification. The short sales therefore are better to invest in compared to the first instance as they have lesser risks. The diversity opening depicted when in the short sales is attributed to the fact that at the short sales, the returns are high and the risks are far much low owing to the fact that they are short term investment strategy.
You are an investor with an ‘ethical agenda.’ Eliminate two stocks from your portfolio. Explain why you found these companies to be ‘bad’ or ‘objectionable.’ What is the optimal portfolio now? Use historical information. How does this portfolio compare? What is the cost to you as an investor?
The INTC and BPR should be removed for they are bad and objectionable from the portfolio because they are quite risky to invest in owing to the fact that they depict high standard deviation. The cost impact on this is that they will reduce the return to the portfolio. These companies were found to be objectionable in the sense that their risk as depicted by the standard deviation was high. Again when remove from the calculation of the portfolio risk, there is a considerable general decrease in the portfolio risk. This in itself proves that the companies should be removed.