For the below question calculating the PVA, why are we assuming the new YTM is the same as the new Immunization rate of 7%?

Thanks!

A portfolio manager has decided to pursue a contingent immunization strategy over a four-year time horizon. He just purchased at par $26 million worth of 6% semiannual coupon, 8-year bonds. Current rates of return for immunized strategies are 6% and the portfolio manager is willing to accept a return of 5%. Given that the required terminal value is $31,678,475, and if the immunized rates rise to 7% immediately,which of the following is most accurate? The dollar safety margin is:

Answer:

We are given the required terminal value of $31,678,475.

Next, we calculate the current value of the bond portfolio: PMT = ($26,000,000)(0.03) = $780,000; N = 16; I/Y = 7/2 = 3.5% ; and FV = $26,000,000; CPT → PV = $24,427,765.

Next, compute the present value of the required terminal value at the new interest rate: FV = $31,678,475; PMT = 0 ; N = 8 ; I /Y = 7/2 = 3.5%; CPT → PV = $24,057,000.

The facts say interest rates have just changed to 7%. That will directly lead to a new PVL and new price of the bond (PVA) that was just purchased at 6% (it was a par bond so now priced at 7% YTM. Both PVL and PVA respond to new interest rate levels (and passage of time if time had passed).

Second Response:

Any of those terms could refer to the level of interest rates. If the level of rates changes then I would expect the discount rate used to determine the PVL has changed and a new PVL would be computed. It almost sounds like you are trying to predetermine the exact phrasing someone or a Q might use. I cannot do that but I would look to see if the facts indicate discount (interest) rates have moved and then compute a new PVL.

Third response:

Any item is discounted at a rate consistent with the remaining term to CF payment or receipt and the riskiness of the item. Yes if the facts are given in such a way to suggest and allow it, L and A might use different discount rates.

I believe you are overthinking this. Follow the basic principal (discounted at a rate consistent with the remaining term to CF payment or receipt and the riskiness of the item) and apply it to the case facts given.

My conclusion:

YTM and Immunization Rates are both affected by the interest rate changes. They could be different but why? The book does not mention and didn’t find the answer yet so could be a level 4 material.

But if we are given two different rates (new YTM and new Immunization rate) like the blue box shown on page 225 of the Kaplan third book, we use two rates.

If the examples only has one new rate no matter they indicate that as the new YTM or new Immunization rate, we use that new rate as both of the YTM and Immunization rate.