Lot of confusion here. Rebalancing, page 31, Example 7: 1. A year has elapsed. The future liability date is now 1 year sooner. Why do we have to dial the dollar duration back up to level before? 2. What exactly are we doing with the $1 million cash required? Target Return, page 29, middle of page: 3. Not understanding why target return and portflio’s YTM would differ. For instance, example 5 on page 27, aren’t both figures 7.5%? Thank you, HM
Pg 31: They state that in the problem, hence… Our requirement is to maintain the portfolio dollar duration at the ini- tial level. To do so, we must rebalance our portfolio. but realistically - you are managing the bonds to meet some liabilities. If the rates rise and the bond values drop as a result - you need to now invest more so as to meet the liabilities when they come due. if the rates fall - and you have a higher bond portfolio (you could choose to leave it there) and hence are better off to meet future shortfalls if any. Or else you could take out something, invest it elsewhere. Most of the time the immunization strategy is for “ALM”. Pg 29: Part related to Target Rate of return, Slope position of the Yield Curve and the immunization rate required and its relation to YTM is one of the most confusing aspects. You would need to wait for Search to come back up (or go to the old site) – and there was whole commentary on this topic (elcfa, and others), and see if it makes sense. Takeaway - if Upward sloping yield curve - Target Rate of Return will be < YTM because of lower reinvestment yield. trying to explain this statement: each period after the initial period your yield is higher than the previous year. As the rate rises - the Total Return on the bond reduces - PV of the bond will be lower - even though the coupons themselves are earning more. So the reinvestment return is lower. and hence you would have a target rate of return lower than the YTM you started with. Downward sloping yield curve - Target rate of Return > YTM because of higher reinvestment yield. Each period after initial period - rate is reducing - so PV of the bond on a total return basis is higher (though coupons are reinvested at lower rates, the effect of the bond principal is more). hence the target rate of return would be higher than the YTM of the bond that you started out with.
I see the comment on p31 about the requirement to maintain the duration. Is this a given of the problem only, or is this fundamental to rebalancing? Conceptually, why would the horizon always remain at 5 years? The liability has to be eventually.
Maintaining the duration is the maintenance of time weighted cashflows. (remember one of the various definitions of Duration). Horizon is reducing. Rebalancing is - maintaining the value of the assets (here the bonds) so you can pay the liabilities when they come due (now 4 years later). You do not want to have a shortfall in a rising interest rate environment (since the liabs which might be bonds as well are becoming bigger).
Why on earth would they not use a horizon date that draws closer with time? CFAI took a rather difficult subject and through lack of visual aides and a rather convoluted example, made this as difficult to understand as possible. It reminds me of the pension reading in Level II.
not sure what you are meaning. when you started you had a five year horizon. one year later it is a 4 year horizon. so it is drawing closer with time, in that sense.
Then this gets back to 1) at the top. If the horizon has dropped to 4, why are we increasing the dollar duration back to what it was before?
what is the duration really telling you? (or rather what is the dollar duration doing for you?) it is basically telling you that you have enough stowed away to meet your liabilities. once you liabilities have increased because of the yield curve / term structure of rates rising - you need a higher Dollar duration (when compared to what it was, or at least that much) so you do not have a shortfall. that is the basic idea, and dollar duration gives you a way to measure that number.
Maybe I’m missing a key point. Assuming a flat yield curve, duration of the liability naturally drops as the horizon date approaches. Assuming a not so flat yield curve, the duration also drops, although not at necessarily the same rate. In either case, the duration changes over time. Why then are we trying to match the dollar duration from a year ago (an in this example by adding 35% to the portfolio)? What the F did I miss?
when rates increase - your assets which are also bonds drop in value. so from an ALM perspective your duration has actually reduced - and you need to rebalance your portfolio to be able to do what you were trying to do before (meet the liability schedule). and think if you were a life insurance company, or a DB Pension plan - your Funding Ratio would have dropped - so there is a higher probability of a shortfall. the two parts - one a liability, the other the assets required to meet those liabilities - and here the assets also happen to be a bond portfolio.
Fine, you adjust it for changes in the slope and the movement along that slope, but why go back to square 1 and not someplace else? Duration started at 5 when the debt was due in 5 years. Now its 4 years out, so why are we going back to 5?
we are not going back to 5. you are adjusting for the fact that you need to meet those liabilities in a shorter time frame. you had 5 years before - now you are down to four, so the pressure to meet that is higher. that pressure is what the dollar duration is measuring… at the least - you need to be able to be in the position of where you were at year 5 - in year 4, 3, 2 and 1, and finally 0. so that if there was a shortfall, when you started, you maintain that much and not more than that.
Doesn’t immunization assumes positively Sloping yield curve?
My question is regarding the extensions of classical immunization theory. One of the assumptions of this theory is that the portfolio is valued at a fixed horizon date. I thought this fixed horizon date is the maturity date. If yes, then on Pg 36( 2nd paragraph) it says, the 2nd extension of classical immunization theory applies to overcoming the limitations of fixed horizon. Why is this fixed horizon considered to be a limitation? Doesn’t it just mean that we are valuing our portfolio on the maturity date? It also says that “a lower bound exists on the value of an investment portfolio at any particular time, although this lower bound may be below the value realized if int rates do not change”. What is this lower bound they are talking about? Any inputs on this will be appreciated.
No. Classical Immunization only assumes that interest rates will shift in a small and parallel way. This is the only way duration will be a good approximation of the change in the bond prices due to a change in interest rates. Thus, matching the duration of the assets and liabilities neutralizes the changes in prices. This is at the heart of Asset/Liability Management.
The fixed horizon approach applies only when both the timing and the amount of the liability are known in advance. If you know that there will be a $$$ liability in 7 years, then you can buy enough of a 7-year zero-coupon treasury note to fund the liability. Since you will hold the zero bond until maturity, you will know the value (i.e. par value). Hence, it creates a lower bond value. If you don’t know the timing of the liability with precision or think the timing can change, the approach is to invest in a zero-coupon T-note and in a balanced portfolio (e.g. stocks, real estate, etc). This way your combined positions will have a range of possible values: the zero bond at maturity will provide a lower bond value. I hope this helps.
Thank you CFAFRM. I have a basic question regarding immunization. Here, we match the duration with the investment horizon. Which definition of duration are we considering here? Is it the one which measures price sensitivity for changes in the int rates? Or the definition where duration is a measure of the number of years it takes to recover the PV of coupons and principal. I am unable to understand the concept of immunization. How can the matching of duration with investment horizon neutralize the change in price. I seem to be missing something here. Totally confused.
There are a number of approaches to fund liabilities. The Classical Immunization Approach is one and focuses on matching the interest sensitive of assets and liabilities (duration). Here the assumption of small paralel interest rate shifts is important and as a result, duration plays a critical part. As we previously discussed, an extension of the Classical Immunization is the Fixed Investment Horizon Approach, which is kind of a Cash Flow Matching Strategy. In this approach you select a zero-coupon that matures at the end of the investment horizon when you need to fund the liability. The maturity of the zero is the critical component here, since you already locked in the return and value of the bond (par) at the end of the investment horizon. As a result, Duration doesn’t play a part in this approach, since price sensitivity is not important.
Thanks again CFAFRM! Can you help me out with another question? On pg 27(reading 23) it says “setting the duration of portfolio equal to the specified portfolio time horizon offsets the positive and negative incremental return sources under certain assumptions” How can matching the duration with invt horizon offset positive and negative incremental returns? I’m unable to understand the logic behind this
primary requirement is one of duration matching for any immunization strategy. basically - 1. the duration of the liability = duration of the portfolio used for the immunization. 2. PV of the liability = Value being immunized. these are the two basic requirements. [under certain assumptions - they ask to refer to the Fabozzi book - which means not required to know]?