could anyone explain the example on page 41 (CFA reading volume 4):
how can u get the value of portfolio of $541.36 after YTM drop to 3.75%?
thx!!
Its given that the entire $500 million portfolio is invested in 4.75%, 10 year notes at par and the YTM suddenly changes to 3.75%. Plugging in Financial Calculator,
N=20, I/Y=3.75/2 = 1.875%, PMT = $11.875 (considering semi annual payments : 0.0475/2 *500), FV = 500 (par value at maturity)
CPT -> PV -> $541.37
So, as the YTM decreases, the value of portfolio increases leading to a greater cushion spread. This in turn will lead to greater amount which can be allotted to active management over and above immunization.
wow, thanks a lot for the quick reply! really appreciate!!!
I forgot to * 500 for the PMT…
You’re welcome.
so it`s actually the economic surplus decide whether it can continue active mgt or back to full immunization. (and this has to do with the duration of asset vs duration of liability)
has nothing to do with whether the cushion spread is positive or negative?
in that question, if YTM fell to 3%, which make the cushion spread equal to zero. but the economic surplus is even bigger(still positive of course)
It has to do everything with cushion spread actually. If the Target Immunization Rate > Portfolio Required Rate of Return, there will be a positive cushion spread. In this case the dollar safety margin will always be positive and there will be scope of active management. When the two rates are equal, there is no cushion spread. Dollar safety margin is obviously zero in that case and there can’t be any scope of active management.
i think i mixed the YTM with immu rate,they are not the same right?
in the question, what is the immu rate then when the YTM fall to 3%?
Immunization target rate and YTM are entirely different concepts.
Immunization target rate (ITR) of return is the total return one can get on a portfolio provided there is no change in term structure of interest rates.
In an upward sloping yield curve, ITR < YTM - This is because in an upward sloping yield curve, you can reinvest the interim cash flows at a higher rates in future (unlike YTM where the basic assumption is that all coupons can be reinvested only at YTM rate). So, in this case, you can cover your liabilities even if ITR
In a downward sloping yield curve,ITR > YTM - Reason being now when rates are down, the interim cash flows will have to be reinvested at a lower rate (unlike YTM where you can still enjoy the higher constant YTM rates).
In a flat yield curve, ITR = YTM.
Coming to the question, they have assumed ITR = 4.75% throughout.
can we say as long as the Target Immunization Rate > Portfolio Required Rate of Return, there will be a positive cushion spread, and in this case eco surplus is positive, so we can active mgt, no matter what the YTM is rising/declining?
Right.
Wait. I’m confused on what you’re saying now based on his/her question. In the curriculum example, the required rate is 3% and the ITR is 4.75% Obviously active management can begin immediately, but an immediate rise in the YTM to 5.80% erases the dollar safety margin and active management has to stop.
this is also what confused me, in this sense, YTM do have influence. I guess its safe to use eco surplus to judge whether we could active mgt or not
Yes JayWill you are right. Sorry it was a mistake in my last post. Just to rephrase krone’s previous post:
As long as the Target Immunization Rate > Portfolio Required Rate of Return, there will be a positive cushion spread, and in this case eco surplus is positive, so we can active mgt, provided YTM does not change.