I’m reading about immunization and I feel like there’s a key assumption that I missed when it comes to reinvestment risk. I understand the concept of reinvestment risk. If rates fall, any cash flow from the bond will be invested at a lower rate offsetting gains in price.
However, I missed the part in regards to what time frame you reinvest your cash in. For example, on page 43 of Reading 20 in Fixed Income Portfolio Management, there are 2 portfolios. Both portfolios have a horizon date, but also contain bonds that mature after the horizon date. If there’s a twist in interest rates where short rates decrease and long rates increase, in the text, it says “the barbell portfolio experiences the lower reinvestment rates longer than the bullet portfolio does”.
I don’t get that sentence. Why would the barbell portfolio experience lowered reinvestment return? I know short term rates fall, but what’s to prevent the portfolio manager to buy long term bonds and take advantage of the higher long term rates? Additionally, both portfolios have the same horizon date so why would the barbell one experience lower reinvestment rates for a longer period of time?
I must have missed an assumption where the portfolio manager is restricted to only investing in short term rates or something. What did I miss?
I believe it is due to the fact that have a payment(liability) coming up. So in the barbell, you have to consistently invest in shorter and shorter terms as you approach payment @ time T. With a bullet, your so close to time T, you have to reinvest at less time (less loss from reinvestment thus). Remember, principle is going to be used to pay the liability. So if you had time T, and some bonds at T-4, and a bond at T+1, you can’t put all the reinvestment in T+1 because you need to the principle.
Another thing I think is that if you are going to invest in loner term bonds with reinvestment, you are going to overshoot your duration. Remember that the idea is that duration of asset matches duration of liability (roughly, as the text says if you can get a zero coupon bond paying @ that date then you have immunized).
" So if you had time T, and some bonds at T-4, and a bond at T+1, you can’t put all the reinvestment in T+1 because you need to the principle."
Why is that? Can’t you just sell your portfolio to pay off the liability? Let’s say you have a 5 year liability and then you took the reinvestment income and invested in 10 year bonds, you could still sell those 10 year bonds to pay off your 5 year liability. At least that’s my understanding of how the barbell portfolio works. It has short term bonds and long term bonds and a medium term liability. When you hit your time horizon, you liquidate your portfolio to pay your liability.
The duration argument makes sense in which if you reinvest your coupon into long term bonds, that will increase the duration of your portfolio and cause a duration mismatch which you don’t want. BUT, I still don’t understand why the " barbell portfolio experiences lower reinvestment returns…."
What do you mean when you say “you have to reinvest at less time (less loss from reinvestment thus).”
I haven’t done questions on this yet…so take this with a grain of salt. But this is how I’m thinking of it.
"Can’t you just sell your portfolio to pay off the liability? ". What if rates go up? Your price gets hit, won’t be able to cover the liabillity. Since it’s due, you won’t be able to depend on the additonal reinvestment income. Also, becuase it’s higher duration, it *should* be more sensitive to rate changes.
" barbell portfolio experiences lower reinvestment returns…." , “you have to reinvest at less time (less loss from reinvestment thus).”
Say with a bullet, you only have to reinvest one year. YTM was 5%, now you get 3%, difference is only 2% for year. Expected 105, got 102.
Now say with the barbell you are operating in a low interest environment…your inital YTM was 5%, but now you are only getting 4% …that 4% is going to be over multiple years. The difference between 100*(1.05)^5 vs 100*(1.04)^5 will be greater than the above. For 100 dollars, it is a difference of -3 dollars in the bullet, and ~6 dollars in the barbell. Now in the barbell since rates go down, we would expect the price to increase (if you bought longer term bonds), but I think the big idea is the goal of immunization is to control risk, not bet on it.
I may be oversimplifying, but the way I understand it: the portfolio with the longer time horizon will have great reinvestment risk simply because the cash being reinvested at a lower rate will be invested longer than the portfolio with a shorter time horizon. In other words, both portfolios are forced to reinvest at a lower rate, but the longer time horizon will compound the discrepancy.
Can anyone else collaborate or otherwise correct my thought process?