# Long study day - little confused - General CFs and Immunization - FI

Pg 46 in the text. — FI

When immunizing portfoilio with cash inflows RATHER then the entire amount available at the beginning. Liability obligation in 2 years. Half the CFs available now to pay that off and half available in 1 year. Says we can use a duration of 3 for the first half of funds and a duration of 1 for the other half of fund available 1 year from now.

Therefor the weighted average of the portfolio duration matches the duratio of liabilities.

Is it just essentially (3 + 1)/2 = 2 And liability duration = 2

Couldn’t we have any combiation of stuff? Duration of 1 NOW and a duration of 3 one year from now —> and then then weighted average is still 2. Or am I missing somethihng?

Long study day. Might be just ridiculously tired. Any help is much appreciated.

The funds that you’re getting in one year have a duration of (essentially) 1 year: think of it as a 1-year zero-coupon bond.

You want the dollar duration of the assets to equal the dollar duration of the liabilities, so:

50%(1 year) + 50%(x years) = 100%(2 years)

(x + 1)/2 = 2

x + 1 = 4

x = 3

Therefore, the 50% funds you have today should be invested in a portfolio with a 3-year duration.

Thanks so much. Mind is exhausted.

Great explanation.