R28: Immunization target rate of return & YTM

V4, P29, 2nd paragraph under Determining the Target Return The statements : In general, for an upward-sloping yield curve, the ITRR will be LESS than the YTM because of the LOWER reinvestment return. Conversely, in a downward-sloping yield curve, the ITRR will be GREATER than the YTM because of the HIGHER reinvestment return. ITRR : immunization taeget rate of return, YTM : Yield to maturity Why ? Can anyone explain ? Thanks !

the immunization rate of return covers the shortfall between total assets and liabilities . Assume for a second that liabilities are known in advance. Total assets are higher if the yield curve is upward sloping ( interest on interest is higher at each maturity cycle, adding to assets at each period end). So the shortfall is lower , requiring less ITRR. If, on the other hand, the yield curve is falling , the coupons ( interest ) are being reinvested at lower rates , i.e. interest on interest is declining, so total assets will be lower than the YTM initially suggested it would be. So the shortfall is greater between assets and liabilities charge. We have to make this up by seeking a higher immunization rate of return . Upward sloping Yield Curve = Lower immunization rate of return needed. Downward sloping yield curve = Higher immunization rate of return needed. You need to look no further than than states and corporations pension funds which are facing huge shortfalls because over the past few years they have faced a declining yield curve

Just to clear a simple definition of duration in this chapter: do we assume that duration is both the sensitivity to price for a parallel shift in yields + the timeliness in receiving cash flows or is just the former?

Only confused because a condition of immunization is matching the duration of the portfolio to the investment horizon, therefore implying time as key

also can someone please explain the section on how to immunize general cash flows clearer than the book for me? thanks

janakisri, Thank you very much for your response, but please note : 1. It is not mentioned in the text that this has anything to do with the “shortfall”. 2. The statements in the text said (please read carefully) : upward-sloping yield curve : ITRR < YTM because of the “LOWER” reinvestment return downward-sloping yield curve : ITRR > YTM because of the “HIGHER” reinvestment return ITRR is compared with YTM and your reasons seem to be discrepant with those in the text. Can you clarify again ? Thanks !

ITRR is a target rate to balance a: 1. the decline in portfolio value with increased cash flow when yields change to the higher side 2. or an increase in portfolio value with reduced cash flow when yields drop The expectation is that such a rebalancing will ensure an acceptable target rate of return ( which is the value we initially wanted to offset our liabilities). If we don’t rebalance often duration of portfolio will drift. If we rebalance often duration will remain tight , but trading costs will rise. The happy mix will have a lower cost , but a better control on duration which will ensure future cash flows and portfolio value The ITRR , which is our expectation of return could go either more or less than YTM , which is a measure of IRR of the investment. Our examples in Lvl I & II showed a static cash flow with a single yield curve. When you have a dynamically changing yield curve, rebalancing is the only way to get back in line so YTM ( of the portfolio ) is in line with expected return set initially.

janakisri, In the case where Yields change on the higher side, cashflow from interest on interest increases but at the same time the value of the assets we hold(bond value) will decline. For ITRR to be less than YTM, dollar value of interest on interest is > the dollar value of decline in Asset value. how do we know that the dollar value of interest on interest is > the dollar value of decline in Asset value.

janakisri, We shall focus on : upward-sloping yield curve : ITRR < YTM because of the “LOWER” reinvestment return downward-sloping yield curve : ITRR > YTM because of the “HIGHER” reinvestment return It seems to me that in a upward-sloping yield curve, the reinvestment return will be HIGHER (rather than LOWER) and in a downward-sloping yield curve, the reinvestment return will be LOWER (rather than HIGHER). Also why ITRR < YTM or > YTM ?

This Reading 28 is a poorly written chapter. For example, it uses the word ‘duration’ very loosely. Sometime referring to the % change in portfolio value per 100 bps change in interest rate. Sometime it refers to the time. It also make generalised statements on immunization which do not make sense. The statement highlighted by threadstarter is one of those made by the author of this Reading but with little elaboration. janakisri’s explanation is likely due to his knowledge from elsewhere or just guess work (no offence). Looking at the table contents of the remaining fixed-income chapters that will not be coming back to immunization, it looks like we have to just memorise the contents of R28 and ‘moved’ on. It remains me of the FSA texts in Level 1 in which were very poorly written. Many candidates have to rely on external materials/help to understand FSA.

bell99, I agree with you ! The readings (R28~31) of fixed-income are very poorly written. No clear defintions of many terms and no clear explanations (WHYs) of many statements (they are vague enough to waste my time to try to understand what they mean) ! I am very much confused by them. Many CFA charterholders said they don’t understand these readings well. I can not imagine why CFAI assigned these reading in L3 curriculum and I think CFAI shall have some people to answer our questions raised on this forum !

In another sweeping statements made by the author of Reading 28 page 27 with regard to Classical Single-Period Immunization: “Setting the duration of the portfolio equal to the specified portfolio time horizon assures the offsetting of positive and negative incremental return sources under certain assumptions, including the assumption that the immunizing portfolio has the same present value as the liability being immunized.15 Duration-matching is a minimum condition for immunization.” This is another example of comparing ‘Duration’ to a time horizon when the former is a measure of change of investment value for each change of 100bps in interest rate. Also, the above is a sweeping statement. It doesn’t give any proof. I guess, we just have to memorise it and move on.

On P26~29, they use following terms of “return” without any clear defintion of each. guaranteed rate of return, assured rate of return, assures return, target return, assured rate of return of immunization, target rate of return. Some of these caused my confusion ! Also please look at the definitions on V4, P108 (R30), they are very much different from my understanding in common financial/accounting terms and the statements in Durtion Management and Duration Hedging (P116~120) are vague and inconsistent with those in R41.

One more term of “return” on P26~29 : Immunization target rate of return.

I was having difficulty understanding the immunization for ‘general cash flows’ under LOS28k and I thought I could hear what Greg Filbeck of Schweser video has to say. Well, he COMPLETELY just skip explaining the ‘general cash flow’ part. Great.

I think the explanation is in the last para in Pg 28. I was confusing between a portfolio to be immunized and a bond that we purchase for the purpose of immunization whose YTM is being discussed here . We would be short such a bond to immunize the main portfolio from the effects of rising interest rates. Think about it like this: For immunizing a portfolio , we buy a bond whose value balances any decline in the value of the portfolio at the horizon, plus keeps the total return of the portfolio+bond at an assured rate. Normally the TVM calculation assumes a constant YTM over the horizon and a constant coupon at each period . But if the yield curve is not flat , our bond will pay off a higher reinvestment return when yields are rising , so the minimum YTM required is LESS than the initial YTM would suggest. Similarly if yields are falling , coupon reinvestment of the immunization bond will not keep up with the initial projection using a flat curve TVM calculation so we need to think of a HIGHER YTM on our immunization bond to keep the total return of the bond from declining below acceptable rate. We have to remember that decline in the price of the bond does not keep in step with increase in coupon , because duration changes non-linearly. That is why need the > and < signs , duration needs to be adjusted to keep the total return of the bond above a certain expected rate

janakisri, Please note that it is said in the text : upward-sloping yield curve : “LOWER” reinvestment return => ITRR < YTM downward-sloping yield curve : “HIGHER” reinvestment return => ITRR > YTM And you said : upward-sloping yield curve : "HIGHER reinvestment return => ITRR < YTM downward-sloping yield curve : "“LOWER” reinvestment return => ITRR > YTM

Upward sloping yield curve - it is LOWER reinvestment rate. Why - you had say a 5 year bond originally - now it has become a 4 year bond. The 4 year cash flows (coupons) are now having a higher yield rate to contend with (due to the upward sloping yield curve) - so PV of that Cash flow would be lower that what it was before. This would make the Reinvestment rate lower. YTM was calculated based on original cash flows, original yield curve - and that was a single point in time rate. That YTM would be higher because all the rates were lower than what they are NOW (at the 4 year point).

cpk123, In your example, suppose a 5-year 5% annual bond is selling at par of $100 at T=0 when yield curve is upward sloping and the yields are : 5%(T=0), 6%(T=1), 7%(T=2), 8%(T=3), 9%(T=4), 10%(T=5) The YTM shall be 5% in this case. Shall the investment rate (return) from the coupon payments ($5 at T=1/2/3/4/5) be lower or higher ? And how do you know that ITRR < YTM in this case ?

AMA Your question makes sense , but I think the ITRR rate of return applies to total return needed for immunization. Example: Initial ytm ( when the bond was purchased ): T=0( just before bond is purchased) YTM of 5 year bond =6% T=0+ 1month( Fed announces higher discount rates , yields jump up): YTM of 5 year bond = 6.5% Yield curve has shifted up ( it may even keep going up in next few months). Coupons, when reinvested pay more interest so at the horizon , you have a higher return on reinvestment than initially planned. Your bond 's value to YOU is constant because you intend to hold it until maturity , so it will pay the par value at the horizon. Hence same bond value + higher reinvestment value = higher accumulated value at the horizon , so there is an excess available over your liabiities at the horizon. The portfolio manager knows this will happen in a RISING interest rate scenario, but is interested only in matching liabilities and assets ,so she is likely to seek a LOWER reinvestment rate of return ( not the same as current YTM , just a lower reinvestment rate on the bond she already owns ) thru duration matching : For example she may seek lower coupon rate on the initial bond purchase, more quality , or both. This will balance the asset and liability , and reduce risk at the same time. Please let me know if this makes sense