## Pension Longevity Hedge Case Solution

**Problem Statement**

The rubric of this case illustrates the impact of using the actual pension funds as a baseline for longevity hedge, where various statistical tools are used to determine the risk of loss incur on the actual pension funds and to find out the best possible solution to minimize that risk accordingly. However, the introduction of longevity hedge would consider being a valuable method to minimize the future risk associated with pension liability. Therefre, under the case of involving the hedge, the future liabilities would be minimized by contributing the fixed amount of pensions to the related community. It would also determine the use of hedge effectiveness in order to compare the actual scenario with hedged one. Therefore, it is concluded that such method would be more preferable for analyzing the impact of actual data with the estimated one.

**Analysis**

From the following analysis, it has been identified that the data is collected from the morality Index of England & Wales and is used to determine the risk longevity of the hedged pension funds. Therefore, the analysis indicates the use of different statistical and financial concepts to determine the long-term risk associated with the use of pension data that was considered to pay long-term benefits to the retired professionals.

The data also identifies the distance between the date of birth and the retired date of average employees. However, the death rate illustrates the difference of period between the paid pensions and the death of a human. This shows that how much payments each retired employee received during the selected period. Thus, the first step taken to analyze the risk of pension funds is to determine the average change in the paid amount concluded in each period.

This shows the related change in the rates of pensions given to each employee for the considerable time. Another important factor to determine the risk is to calculate the standard deviation of the two new funds connected with each other. This shows the related fluctuations of the paid pensions as well as it analyzes the risk of volatility. The same process is concluded for the hedged funds, which is calculated by analyzing the survival rate of each employee between the periods of paid funds till death.

The process of survival rate is determined by adding the total number of employees eligible for the pension funds and then multiplied by the exponential rate of survival. Another tool of statistics has been used, named as correlation. It defines the relationships between two selected variables. Therefore, the two variables under the case are hedged and actual pension funds, where the results indicate that there is a negative relationship between these two outcomes, which indicates that hedged funds are more effective to use for long-term as compared to actually paid funds.

The other most important tool for analyzing the risk is the use of an optimal hedged ratio, which defines the related risk associated with the combination of two variables. Therefore, according to the case, it shows that most of the optimal hedge shows negative results, which is directly proportional to the concept of correlation between the variables.

It means that hedged funds have more value than the actual pension funds. On the other hand, in order to extract the impact of risk for both the funds, the use of indexed funds would determine a consolidated value that could be paid for employee overtime. Therefore, the results indicate the fluctuated payments of each period. As far as the confidence interval is 95%, thus the related risk for each fund would consist of 5% of the risk. It is concluded from the following analysis that the hedged effectiveness shows that if an actual pension criteria are followed accordingly, after which the value will be decreased and would not cover pension benefits for long-term.

Another statistical tool to predict the hedged funds for the considerable period is the use of regression analysis, which indicates the projected results based on the current scenario. Therefore, the use of R-square clearly shows that the current trend would be directly proportional to the expected one, which means that the same change would be followed accordingly. Thus, it is concluded that these tools would analyze the impact of pension in the future and can be beneficial for the industry to predict the outcome suitable for the employees’ benefits.

**Recommendation**

From the results, it is concluded that using the statistical models to analyze the impact of longevity of hedge would be more preferable to determine the estimated outcome for reducing the risk. However, the results also indicated the proper use of hedging tools that would be demanded for the industry standards. Therefore, it is recommended that by using the hedge effectiveness tool, the risk factor would be reduced overtime by indicating the fixed amount of pension’s payable for each selected period until the life of maturity. This method would be more useful to analyze the future payments and decrease the volatility overtime, as well as it can provide relevant information about the future risk that would reduce the amount based on the historical estimates....................................

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