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# Contingent Immunisation (source: CFA Reading 20 pp 36-37) - please explain \$541.36 million

For example, if a firm has a three-year investment horizon over which it must earn 3 percent and it can immunize its asset portfolio at 4.75 percent, the manager can actively manage part or all of the portfolio until it reaches the safety net rate of return of 3 percent. If the portfolio return drops to this safety net level, the portfolio is immunized and the active management is dropped.

The difference between the 4.75 percent and the 3 percent safety net rate of return is called the cushion spread (the difference between the minimum acceptable return and the higher possible immunized rate).

- If the manager started with a \$500 million portfolio, after three years the portfolio needs to grow to \$546.72 (n=6, i=1.5%, PV=\$500 m)
- At T=0, the portfolio can be immunised at 4.75% therefore PV = \$474.90 (n=6, i=2.375%, FV=\$546.72)
- The manager therefore has an initial dollar safety margin 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 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. "

• @RaviVooda did you manage to work this one out?
• IndiaPosts: 268 Portfolio Manager
edited December 2013
@Alta12, its nice that we are going together I was reading this reading today only

To answer your question, it says that "If the manager invests the entire \$500 million in 4.75 percent, 10-year notes at par and the YTM immediately changes, what will happen to the dollar safety margin?
" and yield dropped to 3.75

so it says when it invested FV=500, N=20 (since 10 years), I/Y=4.75/2 , PV=500, PMT=(4.75%/2)*500
so when yield dropped to 3.75 => N=20, I/Y=3.75/2, PMT=(4.75%/2)*500, FV=500, PV=? which comes to 541.376

• Posts: 1,997 Sr Partner
@Ravivooda - you're a step ahead of me, just saw @Alta12's question! Thanks
• IndiaPosts: 268 Portfolio Manager
@Sophie, Thanks.
• @Ravivooda @Sophie Many thanks!!!
• @ravivooda I'm struggling with the EOC questions. Having to reread the chapters again and again. It seems like the grey boxes and EOC do not align as much as LII.
• IndiaPosts: 268 Portfolio Manager
@alta12, I too initially felt the same but later realized that since level 3 is more descriptive, I think we need to remember more to justify/critique in detail. I am writing down notes after every subject to recollect faster during exam times. That in a way is helping revise all concepts immediately. In end I also write any mistakes I make.
• @ravivooda Yes, lots of critique. I'm hoping to go over some of the troublesome chapters over Christmas. It seems like you and I are the only ones that have started the readings? 8-X