RA manages several fixed-income portfolios. You decide to propose a mix of the following two portfolios: A portfolio of Treasury notes with an average duration of eight years. A portfolio of short-term Treasury bills and notes with an average duration of two years. The term structure is flat, and the yield on both portfolios is 5%. Please fill in the information below (iiv) and evaluate the portfolio duration (v):

Duration	Two years	Eight years
Investment (millions)	i	ii
Fraction of portfolio	iii	iv
Portfolio duration	v

Rensselaer Advisers You are a vice president Advisers (RA), which manages portfolios for institutional of Rensselaer vestors (primarily corporate pension plans) and wealthy individuals. In mid-2017 about billion under management, invested in a wide range of common and fixed-income por folios. Its management fees average 55 basis points (55%), so RA's total revenue for 2017 will be about .0055 x $1.1 billion $6.05 million You are attempting to land a new client, Madison Mills, a conservative, long-established manufacturer of papermaking felt. Madison has established a defined-benefit pension plan for ts employees. RA would manage the pension assets that Madison has set aside to cover defined benefit obligations for retired employees. Defined benefit means that an employer is committed to pay retirement income according to a formula. For example, annual retirement income could equal 40% of the employee's average salary in the five years prior to retirement. In a defined-benefit plan, retirement income does not depend on the performance of the pension assets. If the assets in the fund are not sufficient to cover pen sion benefits, the company is required to contribute enough additional cash to cover the shortfall Thus the PV of promised retirement benefits is a debt-equivalent obligation of the company Table 26.6 shows Madison's obligations to its already retired employees from 2018 to 2036 Each of these employees receives a fixed dollar amount each month. Total dollar payments decline as the employees die off. The PV of the obligations in Table 26.6 is about $89 million at the cur- rent (2017) 5% long-term interest rate. Table 26.6 also calculates the duration of the obligations at 87 years Madison has set aside $90 million in pension assets to cover the obligations in Table 26.6, so this part of its pension plan is fully funded." The pension assets are now invested in a diversified portfolio of common stocks, corporate bonds, and notes After reviewing Madison's existing portfolio, you schedule a meeting with Hendrik van Wie Madison's CFO, Mr. van Wie stresses Madison's conservative management philosophy and warns against "speculation." He complains about the performance of the previous manager of the pen sion assets. He suggests that you propose a plan of investing in safe assets in a way that minimiz exposure to equity markets and changing interest rates. You promise to pre an illustration of how this goal could be achieved Rensselaer Advisers You are a vice president Advisers (RA), which manages portfolios for institutional of Rensselaer vestors (primarily corporate pension plans) and wealthy individuals. In mid-2017 about billion under management, invested in a wide range of common and fixed-income por folios. Its management fees average 55 basis points (55%), so RA's total revenue for 2017 will be about .0055 x $1.1 billion $6.05 million You are attempting to land a new client, Madison Mills, a conservative, long-established manufacturer of papermaking felt. Madison has established a defined-benefit pension plan for ts employees. RA would manage the pension assets that Madison has set aside to cover defined benefit obligations for retired employees. Defined benefit means that an employer is committed to pay retirement income according to a formula. For example, annual retirement income could equal 40% of the employee's average salary in the five years prior to retirement. In a defined-benefit plan, retirement income does not depend on the performance of the pension assets. If the assets in the fund are not sufficient to cover pen sion benefits, the company is required to contribute enough additional cash to cover the shortfall Thus the PV of promised retirement benefits is a debt-equivalent obligation of the company Table 26.6 shows Madison's obligations to its already retired employees from 2018 to 2036 Each of these employees receives a fixed dollar amount each month. Total dollar payments decline as the employees die off. The PV of the obligations in Table 26.6 is about $89 million at the cur- rent (2017) 5% long-term interest rate. Table 26.6 also calculates the duration of the obligations at 87 years Madison has set aside $90 million in pension assets to cover the obligations in Table 26.6, so this part of its pension plan is fully funded." The pension assets are now invested in a diversified portfolio of common stocks, corporate bonds, and notes After reviewing Madison's existing portfolio, you schedule a meeting with Hendrik van Wie Madison's CFO, Mr. van Wie stresses Madison's conservative management philosophy and warns against "speculation." He complains about the performance of the previous manager of the pen sion assets. He suggests that you propose a plan of investing in safe assets in a way that minimiz exposure to equity markets and changing interest rates. You promise to pre an illustration of how this goal could be achieved