Financial Risk Manager Part 2
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An analyst has provided the following information about a specific fund to a pension fund advisor. The advisor's fund is currently managing a surplus of USD 40 million, which is invested in a combination of government and corporate bonds.
Pension Fund Assets Liabilities Amount (USD million) 180 140
The anticipated annual growth rates for assets and liabilities are 6% and 10% respectively. The annual volatilities of these growth rates are 25% for assets and 12% for liabilities.
To evaluate the sufficiency of the fund's surplus, the advisor forecasts the potential surplus amounts at the end of one year. The advisor assumes that both the annual returns on assets and the growth rates of liabilities follow a normal distribution, with a correlation coefficient of 0.68 between them. Given that the surplus volatility is USD 35.76 million, what is the lower limit of the 95% confidence interval for the projected year-end surplus that the advisor can report?
An analyst has provided the following information about a specific fund to a pension fund advisor. The advisor's fund is currently managing a surplus of USD 40 million, which is invested in a combination of government and corporate bonds.
| Pension Fund | Assets | Liabilities | Amount (USD million) |
|---|---|---|---|
| 180 | 140 |
The anticipated annual growth rates for assets and liabilities are 6% and 10% respectively. The annual volatilities of these growth rates are 25% for assets and 12% for liabilities.
To evaluate the sufficiency of the fund's surplus, the advisor forecasts the potential surplus amounts at the end of one year. The advisor assumes that both the annual returns on assets and the growth rates of liabilities follow a normal distribution, with a correlation coefficient of 0.68 between them. Given that the surplus volatility is USD 35.76 million, what is the lower limit of the 95% confidence interval for the projected year-end surplus that the advisor can report?
Explanation:
The lower bound of the 95% confidence interval for the expected end-of-year surplus is calculated using the formula: Expected Surplus minus (95% confidence factor times the Volatility of Surplus). The expected surplus is computed by taking the assets' expected growth rate and subtracting the liabilities' expected growth rate from the current surplus. The formula for expected surplus is , where is the current assets, is the expected annual growth rate of assets, is the current liabilities, and is the expected annual growth rate of liabilities.
In this case, the expected surplus is calculated as follows:
For a 95% confidence interval, the z-value (confidence factor) is 1.96. The volatility of surplus is given as 35.76 million USD. Applying these values to the formula gives us the lower bound of the 95% confidence interval:
Rounded to two decimal places, the lower bound of the 95% confidence interval for the expected end-of-year surplus is approximately -33.2896 million USD, which corresponds to option C: USD -33.3 million.