A fixed income portfolio manager sets a minimum acceptable rate of return on the bond portfolio at 5% per year over the next 4 years.The portfolio is currently worth $10 million.One year later interest rates are at 6%.What is the portfolio value trigger point at this time that would require him to immunize the portfolio?

Question

Quizplus · Accepted Answer

To calculate the portfolio value trigger point, we need to first calculate the future value of the current portfolio after one year at the new interest rate of 6%.

Future value = Current value x (1 + interest rate)^time 
Future value = $10 million x (1 + 0.06)^1 = $10,600,000

Next, we need to calculate the present value of the minimum acceptable rate of return of 5% over the next 3 years (since one year has already passed), using the formula:

Present value = Future value / (1 + interest rate)^time

Year 1: Present value = $10,600,000 / (1 + 0.05)^1 = $10,095,238.10 
Year 2: Present value = $10,600,000 / (1 + 0.05)^2 = $9,615,968.82 
Year 3: Present value = $10,600,000 / (1 + 0.05)^3 = $9,153,349.44

Adding up the present values, we get the total present value of the minimum acceptable rate of return over the next 3 years:

Total present value = $10,095,238.10 + $9,615,968.82 + $9,153,349.44 = $28,864,556.36

Finally, we need to find the portfolio value trigger point by solving for the portfolio value that would give us a present value of $28,864,556.36 at the current interest rate of 6%:

$28,864,556.36 = Portfolio value / (1 + 0.06)^3 
Portfolio value = $28,864,556.36 x 1.191 = $34,379,098.49

Therefore, the portfolio value trigger point at this time is $10 million + $34,379,098.49 = $44,379,098.49.

The closest option to this value is B) $10,205,625

A Fixed Income Portfolio Manager Sets a Minimum Acceptable Rate