Investment Portfolio Project Final Paper and Presentation
Investment Portfolio Project Final Paper and Presentation
In an ideal situation, an investor would like to investment in an asset or portfolio of asset characterized by high returns and low risk. However, the ideal world does not exist and so is the ideal portfolio as opined in the sentence above. This understanding gave birth to several portfolio theories and among these theories is the modern portfolio theory whose key contributors included Harry Markowitz and William Sharpe. In the modern portfolio theory of MPT as it is famously referred to, the theorists emphasize the importance of diversification in the portfolio. The sole objective of portfolio diversification remains to be the diversification of risk. In essence, this theory bears the perspective that it is never enough to look at the expected risk and return of a single investment asset. Rather, investing in more than one asset allows the investor to reap the benefits of portfolio diversification.
In the development of MPT, Markowitz explained that the risk for any given investment asset falls into two categories. The first is the systematic risk. Systematic risk is the risk that is inherent in the market and cannot be diversifies away. This risk is inherent in the interest rates, the risk of inflation, and the risks of a recession. On the other hand, there is the unsystematic risk which is also known as the specific risk in the sense that it is the risk that is particular to any given investment asset. The unsystematic risk can then be diversified away by increasing the number of investment assets or stocks in the portfolio. In a well-diversified portfolio therefore, the systematic risk on each asset contributes little to the portfolio risk. This understanding provided the avenue for Markowitz’s development of MPT and explanation of the efficient frontier, which indicates the combinations of assets that would lead to an efficient portfolio (Investopedia, 2016). William Sharpe advanced the MPT and came up with the capital asset pricing model that helps in the estimation of the beta of a portfolio or of any given asset as well as the implications of the time value of money. Under CAPM, beta represents a measure of risk. The risk can be measured using other indices which include the Sharpe ratio, Jensen’s alpha, and the Treynor ratio. This paper illustrates the application of these measures in portfolio management.
In this analysis, we also assume that the average return of the risk averse portfolio (Rp) as illustrated above is at 13.6346%, the beta of the portfolio (Bp) is at 0.796858, the market return (Rm) equals the return on the DJIA for the year to date at 2.70%, and that the beta of the market equal 1. Additionally, the risk-free rate is assumed to be equal to the t-bill rate on the U.S 91-days T-bill at 0.26%. The data is captured in the following table.
Using the data above, we computed the expected return using CAPM and followed by the standard deviation of the portfolio as shown below.
Using CAPM, the expected return on the portfolio would be computed as follows:
ER=0.26%+0.79686(2.70%-0.26%)
ER=0.26%+0.79686(2.44%)
ER=2.20%
Using the expected return from CAPM as computed above, the standard deviation on the portfolio was computed.
StdDev=13.63%-2.20%
StdDev=11.43
Calculation of Portfolio Performance
Using the values above, the Sharpe Ratio, Treynor Ratio, and the Jensen’s alpha were computed as shown below
S(p)=(13.63%-0.26%)/11.43%
S(p)=1.1696
Treynor Ratio
Treynor Ratio=13.63%-0.26%/0.79686
Treynor Ratio=16.78
Jensen’s Alpha
Jensen's alpha=13.63%-[0.26%+0.79686(2.70%-0.26%)
Jensen's alpha=11.4257%
Analysis of Portfolio Performance
The value of Sharpe ratio was computed as S(p)=1.1696. Sharpe ratio compares the returns to the risk that the investor absorbs. In this case, the investor gets additional returns to the tune of 1.1696% for every additional unit of risk absorbed in the portfolio. The Sharpe ratio indicates that the performance of the portfolio is good since there is a higher return for each additional unit of risk. The higher the Sharpe ratio, the more the return that the investor gets per additional unit of risk. Conversely, the lower the Sharpe ratio the more the risk that the investor absorbs (Investopedia, 2016).
The second ration in the computations above is the Treynor ratio which was found to be Treynor Ratio=16.78. the analysis of this measure indicates that the portfolio outperformed the market. This is because the ratio indicates that the return on the portfolio was higher than the market return. Notably, the Treynor ratio compares the returns with the beta. Consequently, the analysis indicates that the performance of the portfolio was commendable (Morningstar, 2016).
The last measure employed in the analysis of performance in this study was the Jensen’s alpha. This value measures the mean yield above and beyond the forecasted return from CAPM. Jensen’s alpha is similar to the alpha value of the portfolio and in this case, the value was found to be Jensen's alpha=11.4257. Notably, the value of Jensen’s alpha in this case is positive and consequently, it is evident that the portfolio manager beat the market. Consequently, this indicates that the performance of the portfolio is good (Guevara, 2015).
Importance
The three measures computed and presented above are some of the most important tools of modern portfolio theory. They are important in the determination of portfolio performance considering that they test the performance of the portfolio against various measures of risk including the beta, the alpha, and the standard deviation. The use of these measures of risk provides various perspectives on the unsystematic risk of the portfolio and even though these measures generally provide the same results, using the measures provided a more certain result informing the action that the investor or the portfolio manager ought to take with regard to the actions that should be taken with regard to the portfolio (Investopedia, 2016).
The measures provided above indicate that portfolio performance can be measured in a number of ways. One way is by looking into the aspect of the long-term risk of the portfolio. This is because by looking into the long-term risk, it is possible for the portfolio manager to effectively predict the long-term direction of the portfolio. Nonetheless, this does not exempt the portfolio manager from periodic reviews of the portfolio. Additionally, the view on the long-term risk of the portfolio indicates the need for the general planning of the portfolio as well as the indication of the factors that are important in the revision of the portfolio (Investopedia, 2016).
Looking at each of the measures mentioned above, the Sharpe ratio becomes one of the most important measures. This is because to a large extent the Sharpe ratio helps in the measurement of the overall stability of the portfolio. For instance, the Sharpe ratio formula in this case indicates a value of 1.1696. The basic interpretation indicates that in general the portfolio outperformed the market. Further analysis of this value indicates that the portfolio has a 16% edge over the market hence indicating that it is more stable. If the value was lower, then this would indicate the need for more concentration on the volatility of the prices of the securities in the market (Investopedia, 2016).
The other measure which is the Treynor ratio is also important since it looks into the unsystematic risk of the portfolio. Notably, the Treynor ratio focuses majorly on the systematic risk as the major measure. Looking into the systematic risk enables the portfolio manager to determine the portion of risk in the portfolio that may be difficult to diversify and hence the need, or lack thereof, for the revision of the portfolio (Morningstar, 2016).
The last very important measure in this study is the Jensen’s alpha that compares the returns to the unsystematic risk of the portfolio. This approach underscores the importance of portfolio management strategies in the sense that it point directly to the importance of portfolio diversification as well as the benefits of the same. This measure is a good indicator of the impact of portfolio diversification but nonetheless, it does not necessarily mean that it is more important than the other two methods presented above. Notably, it is important to combine the three methods as presented in this paper.
Revisions
Conclusion
In conclusion, this paper looks into the modern portfolio theory, need for portfolio diversification, and the usefulness of three measures of portfolio performance on portfolio management. The three measures assessed in this project include Sharpe, Treynor, and Jensen’s measures. The findings from the three measures do not indicate any need for portfolio revision as the portfolio beats the market. However, there is the need to keep tracking the movements in the economy.
References
Guevara, A. (2015). Jensen’s Alpha. Retrieved from https://www.tradestation.com/education/labs/analysis-concepts/jensens-alpha
Investopedia. (2016). Understanding the Sharpe Ratio. Retrieved from http://www.investopedia.com/articles/07/sharpe_ratio.asp
Morningstar. (2016). Treynor Ratio. Retrieved from http://www.morningstar.com/InvGlossary/treynor-ratio.aspx
