# Ture or false:

Ture or false: immunization target rate of rtn is less than YTM.

false…YTM is more conservative because assumes constant reinvestment rate so must be more conservative, therefore lower minus 3 or plus 3?

false I think, immunization rate of return is the rate that will allow you to pay the cash flow of future liability… usually immunization rate is higher than minimum acceptable return… huh…

True, if yield curve is upward sloping

Shape of the yield curve determines whether YTM or target investment rate is larger. YTM=Target rate if yield curve is flat. As tanyusha said, upward sloping means it can be less, because when you reinvest, you’ll be reinvesting your first coupons for a long time and will be getting the benefit of the higher long term rates (assuming the curve doesn’t change, of course). It’s the reverse for downward sloping. Hey, I learned something and remembered it! Yeah!

tanyusha and bchadwick, do you really understand this concept? I mean you guys are right with the ans given from CFA. which is great. here is the ans given by CFA: In general for an upward sloping yc, the immu target rate of rtn will be less than YTM because of the lower reinvestment rtn. Conversely a negative or downward sloping yc will result in an immu target rtn greater than ytm because of the higher reinvestment rtn. but don’t you ever find it funny or strange ? did you check the assumption how to determine the target rate ? it is based on no change in interest rate. then where is the need to do immunization… god.

Should this line be In general for an upward sloping yc, the immu target rate of rtn will be less than YTM because of the ****HIGHER**** reinvestment rtn?

I don’t claim to understand this thoroughly, but I think I got the target rate of return bit right at least in a qualitative sense. I assume that is because the target rate of return takes into consideration the implied forward rates built into the yield curve to compute the reinvestment contribution, whereas YTM just uses a constant rate for both principal and reinvested interest. I do intend to review how you calculate target rate though.

I didnt understand it. I had to call my good actuary friend and ask him to explain it to me. He did, now i understand it from mathematical point of view but it still not intuitive. Here is the reason: When curve is upward sloping, you will be reinvesting at the rates lower then YTM, therefore total return will be lower as showing here: rf - forward z - total ret x - YTM 10/(1+x) + 10/(1+x)^2 = (10*(1+rf) + 10)/(1+z)^2 (10(1+x) + 10)/(1+x)^2 = (10*(1+rf) + 10)/(1+z)^2 We know that 10(1+x) + 10 > 10*(1+rf) + 10 since x > rf it follows (1+x)^2 > (1+z)^2 so YTM > Total return

flapechino, I think of it like this. Say your immunization time-horizon is 6 years. Your immunized portfolio(some mix of Treasuries, corporates, MBS, etc) will have a certain YTM that is > the corresponding Treasury yield for 6 years(by definition because you always invest to earn a return that is more than the rfr). If you chose a immunization target rate of return of say 7%, you expect 7% to be your total return at the end of 6 years, when all cash-flows between now and 6 years are reinvested at the prevailing Treasury rates(the expectated values of those rates are forward rates determined by the YC). your portfolio YTM is always > the 6 year Treasury yield. If your YC is upward-sloping, the 6-year yield is in turn higher than all intermediate yields. So the YTM is higher than all intermediate yields that your cash-flows have been reinvested in. Now the cash-flows yield a total return of 7%(immunized target return). So your YTM has to be greater than the immunized target return(7%). Now, if the YC is downward sloping, the 6-year yield will be lower than all intermediate yields as well as the YTM. But, some of those intermediate yields may(theoretically)be higher than your portfolio YTM. So, I think in that situation it will actually depend on the cash-flows whether the YTM > immunized rate of return. Let me know if that helps.

flapechino Wrote: ------------------------------------------------------- > > but don’t you ever find it funny or strange ? > did you check the assumption how to determine the > target rate ? > it is based on no change in interest rate. I think this means “unchanging yield curve,” not just no change in a single interest rate. > then where is the need to do immunization… > god. The immunization needs to be adjusted over time. When the yield curve changes, you’ll need to rebalance the immunization to accommodate things. However, you will have avoided the large losses or surpluses that might happen if asset and liability durations aren’t matched. If convexity is matched, you’ll have even smaller losses/surpluses from yield curve changes (but a lot more work, and potentially transaction costs). In fact, even if the yield curve doesn’t move, you will have to rebalance periodically to make sure your durations match, because they will fall out of alignment. The only exception is if you have perfect cash flow matching, but this tends to be more expensive to set up (i.e. required assets at t=0 are higher). If you understand dynamic hedging with options, you can think of it as a similar process… your durations will be hedged for now, but the moment things change, you’ll need to rebalance/rehedge or you’ll start risking large mismatches between assets and liabilities. Even over time, you’ll have to rebalance (durations change over time for FI portfolios; delta changes with time as options approach maturity). — CSK, I don’t follow your math, but I was always a “use math only when necessary” kind of guy. I think about it this way. * Suppose you have a 10y \$100 bond paying 6%. \$100 is the par value, not actually the price of the bond. * In 6 months, you now have a \$3 coupon payment that needs to be reinvested. It needs to be reinvested so that it matures in 9.5 years, because that’s when you need the money (this is why you bought a 10y bond). * If the yield curve is upward sloping, you’ll be getting a better rate than you would on short term cash… that’s good, so your target return can be lower than the alternative, which is… * If the yield curve is downward sloping, you’ll be getting a worse rate than you would on short term cash… that’s bad… your target return needs to increase to accommodate that (compared to the upward sloping scenario). You might think that you should just decide to take the higher cash rate, but then you start having duration mismatch problems and take on more risk. * So yield curve up sloping means lower target rate needed, yield curve down sloping means higher target rate. Now, how do we know how this compares to YTM?? well, YTM assumes that all coupons are invested at the same constant rate. To get this, the yield curve would have to have the same rate at all maturities… and that means it would be flat. SO… The higher the slope of the yield curve, the lower the target rate needed… The lower the slope of the yield curve, the higher the target rate needed… Target rate = YTM requires a flat yield curve. Therefore upslope implies < YTM downslope implies > YTM. How to remember? Remember two things! 1) Flat curve means Target = YTM. 2) Then, think about what you want to do with that first coupon payment, and remember that it will be invested at the long end of the curve. The more you get from reinvestment, the less you need to make up by having a higher target rate.

thanks guys, i will try to go over your posts and remember them.