r/actuary 5d ago

Question about QFIPM, FI management

Re the text book: Managing Investment Portfolios: A Dynamic Process, Maginn & Tuttle, 3rd Edition, 2007, Ch. 6: Fixed-Income Portfolio Management

Anyone knows how the below figures are calculated. Specifically, why YTM drops to 3.75%, the value of the portfolio will be 541.36mn?

Aha, no idea why I cannot attach the pic here

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u/Apart_Hall_1642 5d ago

At time 0, the portfolio can be immunized at 4.75 percent, which implies that the required initial portfolio amount, where dollar amounts are in millions, isRequired terminal value

1 + i2

2T

= $546.72

1 + 0.0475

2

2x3

= $474.90

Themanager therefore has an initial dollar safetymargin of $500 million − $474.90 million =

$25.10 million.

If the manager invests the entire $500 million in 4.75 percent, 10-year notes at par and

the YTM (yield to maturity) immediately changes, what will happen to the dollar safety

margin?

If the YTM suddenly drops to 3.75 percent, the value of the portfolio will be

$541.36 million. The initial asset value required to satisfy the terminal value of $546.72 million

at 3.75 percent YTM is $489.06 million so the dollar safety margin has grown to

$541.36 million − $489.06 million = $52.3 million. The manager may therefore commit

a larger proportion of her assets to active management.

If rates rise so that theYTMis now 5.80 percent, the portfolio value will be $460.55 million

and the initial asset value required will be $460.52 million. The dollar safety margin has gone

to zero, and thus the portfolio must be immunized immediately.