Immunization & Dollar Safety Margin- V4 Pg 37

[3rdtimesacharm]

-Firm has a 3 year investment horizon over which it must ear 3%
-It can immunize its asset portfolio at 4.75%
-If the manager started with a $500 million portfolio, after 3 year the portfolio needs to grow to $546.72 mil ( $500(1+ .03/2)^2*3
-At time 0, the portfolio can be immunized at 4.75% which implies that the required initial portfolio amount $474.90 mil ($546.72/ (1+.0475/2)^2*3
The manager therefore has an initial dollar safety margin of $25.10 million ( $500 - $474.90)
OK SO FAR SO GOOD:
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If the the manager invests the entire $500 million in 4.75%, 10 yr notes at par, and the YTM immediately drops to 3.75%, what will happen to the dollar safety margin ?
- If YTm suddenly drops to 3.75%, the value of the portfolio will be $541.36 Million
*MY QUESTION1
- The initial asset value required to satisfy the terminal value of $546.72 million (original amount) at 3.75% YTM is $489.06 milion ($546.72/1+.0375/2)^2*3
Dollar Safety Margin has grown to $541.36-$489.06 = $52.3 million, therefore the manager may therefore commit a larger proportion of their assets to active management ** MY QUESTION 2
Q1) How do they calculate the $541.36 ?
Q2) I understand the concept that a larger dollar safety margin means more room to play around to earn excess returns etc, but I dont understand why this happens when YTM decreases( to 3.75%). I see it as , hey your YTM decreased to 3.75% so now you have more room to be risky ( i.e more room for active management) .. I dont get this. ????

 

[mwvt9]

Q1. Use the PV keys on your calculator to get this answer.
Q2. If the YTM went down that means the price of the bonds you were holding went up. That’s good- bigger cushion.

 

[3rdtimesacharm]

Would you be kind enough to show the PV calcs. I am so lost when it comes to Fixed income.
So when people say “Yield goes down” - this refers to when bond prices go up due to decreasing interest rates. I get confused with interest rates and “yields”
So I guess people use “yields” and “YTM” to mean the same thing ?

 

[sbmfj]

mwvt9 Wrote:
——————————————————-
> Q1. Use the PV keys on your calculator to get this
> answer.
>
n = 10 * 2 =20
fv = 100
i = 3.75/2 = 1.875
cpn/pmt = 4.75/2 = 2.375
pv= cpt = 108.275
you bought the bonds at par, therefore at 1000$. you bought 500m worth, so you bought 500 000 ‘issues’, 500 000 * 1082.75 = 541 375 000

 

[Neveruse_95_ev]

I did the calculations this way (same idea, just slightly different approach):
FV = 500
PMT = 11.875
n = 20
i = 1.875
hit “PV” and voila, -541.38 appears
Think of it like the gain in bond value offsets the loss of reinvestment income (i.e. reinvest the coupons at a lower rate), so the manager is set. They only have to grow to $546.72 at maturity. Now the portfolio value’s spitting distance from this ($541 and change) and they’re getting at least one more coupon (= $9.38 on $500 par value).