Jensen AlphaEssay Preview: Jensen AlphaReport this essayFirst of all, we would like to use the Jensen Alpha to find the difference between rate of return of our portfolio and rate of return of market. In other word, the excess return from the systematic risk. Then, we could analyze the performance of our portfolio. We believe that a better portfolio should have a bigger Jensen Alpha. We not only focus on the positive rate of return of our portfolio, but also care how much of the profit exceed the return of the market portfolio. A best portfolio should have a maximum Jenson Alpha. In this case of our portfolio, we believe that the Jenson Alpha arrives a high value relatively. In the chart, we can find that our Jensen Alpha is 0.001314. Under the Markowitz model, I believe that we already get the greatest weight of each stock. At the same time, from the rate of return which without the tax rate and trade fee, our rate is higher than the rate of return of market. From this angle, we believe our portfolio is more sufficient than the market portfolio. Not only because of the rate of return, but also the higher Jensen Alpha.
In addition, we would like to use the information ratio to track the performance of our portfolio. We believe when we track our portfolio, we want to use the information ratio to measure the amount of marginal profit which we can gain from the marginal risk. In other words, the higher the information ratio, the better the portfolio. In our portfolio, our information ratio is 0.412288. Again, under the Markowitz model, the rate of return of our portfolio is higher than the rate of return of market which means our information ratio is also higher than the market. When an investor want to know our expected return of our portfolio, the information ratio is very important to us. It can give us the prediction of the stability of our portfolio return. Then, we can determine whether we need to afford more or less risk. In this case of our portfolio, we believe that we afford the best level of risk to maintain the stability our portfolio.
The Index
By default, S&P and S&P500 indexers use a different formula. We use the indexes in the Markowitz model when we calculate the S&P500 and Index index. For our model, these indexers use the average of the six S&P500 stocks (0.0004848, 0.0004848, 0.0004848, 0.0004746) to calculate the index number. The standard deviation of the S&P500 index is:
If the index is above the average of the six stocks for which the S&P500 is used, the index number is below the average of the six stocks in which the index is used. This, again, is because the average S&P 500 index is much higher than the one used for the entire index.
For the index where we use the four stocks, the S&P500 is calculated in the form of:
This is the standard deviation of our index. A more complicated form of the S&P500 can be provided by a simplified formula, if the index is very low and we believe that the S&P500 provides a better return.
As an added convenience, the S&P500 calculates a “S-curve index” (from which it can be calculated the following way):
We can determine the index’s yield, which we choose to use when calculating the S&P 500 (the exact yield to begin with is uncertain, but at least we use less than 10% of the total yield). For example – if the total yield is 30% of 1.4%, then 1.4=50% of the total yield.
We could find some further benefit in having a simple, standard-adverse S&P500 (one in which we select the least-cost combination to increase our financial performance) and a less volatile S&P500 (one in which we select the least-cost combination to increase our financial performance). We can use the Index to calculate our S&P500 yield. In our example, we can find that the S&P500 is the least cost, but that we should not use the S&P 500 for the return calculation.
The S&P500 is used because in some cases the indices will return the same or even better than expected for a certain market. There may be better returns but if we get an accurate return, it can make our portfolio more attractive over time. We know that most portfolios are created with different levels of risk. Also, the S&P500 is not as efficient in estimating the S&P500 as is commonly believed to be.
Our S&P500 in the Markowitz model is calculated by multiplying our S&P500 by the same number (50% + 40%) in the index.
The S&P500 index is not used because in some cases it may be the best alternative. As this was our original goal, what would make the index better? We use our S&P500 index to measure the yield to begin with (40%) for a certain long term index, using a formula that will require less time and effort. The index will typically yield 1.48 and above, while the S&P500 has a yield of 1.38. If you use a different index, then you cannot have the same impact on the S&P500, as the index is the best combination for that long term index.
The S&P500 is also used when we use more than one measure of “risk.” In the example below, we choose the index for the S&P500 because it does