Elimination of interest rate risk is the end objective of immunization … suppose we hold a Bond liability and we want to immunize it. we will buy such number of assets in which the price risk and reinvestment risk offset each other …Now if the interest rates go down …the bond liability will increse in value so there is additional Price risk … simulteneously the Reinvestment income falls… so additional reinvestment risk … I am just not able to understand how both the risks offset each other… Is it that the assets go up in vaulue and this is the price risk … and offset with reinvestment risk ??? Please throw some light on precisely how immunization works preferably with an example…
zidane2 Wrote: ------------------------------------------------------- > we will > buy such number of assets in which the price risk > and reinvestment risk offset each other I would say that "We buy such number of assets in which the interest rate sensitive/exposure/duration matches with our liability.
type “bond immunization” into Google for about 703,000 examples.
When you immunize you match MV + Duration, this doesnt’; take into account convexity or reinvestment risk, which both the measure of Duration and convexity is based upon a measurement of yield and yield has a mathemathical assumption in regard to reinvestment risk, which is a risk if it is not met and the hedge will be ineffective.
zidane2 Wrote: ------------------------------------------------------- > Elimination of interest rate risk is the end > objective of immunization … suppose we hold a > Bond liability and we want to immunize it. we will > buy such number of assets in which the price risk > and reinvestment risk offset each other …Now > if the interest rates go down …the bond > liability will increse in value so there is > additional Price risk … simulteneously the > Reinvestment income falls… I think the asset you are holding increases in price (to match the increased PV of the liability). So it is not a price “risk” here. > so additional > reinvestment risk … I am just not able to > understand how both the risks offset each other… > Is it that the assets go up in vaulue and this is > the price risk … and offset with reinvestment > risk ??? yes. - sticky
Think about it like this, if a bond innately is a match with the liabilities based upon duration and MV, but due to the cashflow pattern, relative the liability the cashflows come in sooner and rates drop then this will change things up so there is reinvestment risk.
If you immunize “perfectly” there is no reinvestment risk, the cashflows from your FI portfolio perfectly match the cashflows of the liability. The interest rate risk is also eliminated since the price change on your portfolio matches the change in liabilities when interest rates change. Duration and convexity come into play when you can’t perfectly immunize. Then you’re exposed to all kinds of residual risk, as JP mentions.
zidane2, remember that when you immunize your ‘asset’ is a fixed income portfolio. so if you do it right such that the duration of the liability = duration of the asset (FI portfolio), the price increase in the liability should be offset by the price increase in your asset (FI portfolio).
thanks for the help … at the start what we hold are liabilities that we want to immunize… now we buy assets matching the duration and the Present value of the liabilities… with same Duration and the PV… the portfolio is hedged from any interest risk…am i right ?? when rates fall ,liabilities increase in value ( price risk is associated with liabilities here)and so do assets …i m clear uptill this point … the aim of immunization is to match the Price risk and the reinvestment risk …I am confused as to how we match these 2 risks – when rates fall we lose on both ends … liabilities go up and reinvestment income also falls… Are we matching price risk of ASSETS and the reinvestment risk ??? then it is fine…
There is no price risk or reinvestment risk if you can match the cashflows on the assets (i.e. coupons and maturity values) with the cashflows on the liability side (i.e. a payment to somebody else). Reinvestment risk only comes into play when you find yourself with a pocket full of cash, and no liabilities to pay off. The aim of immunization is to match the price risk and ELIMINATE the reinvestment risk, by never having any money to reinvest.
thanks … so if the duration of assets > duration of the liabilities ,and rates rise … liabilities and assets go down , but assets would fall more than the liabilities so there would be a price LOSS… this loss is to be offset from the increased reinvestment income (rates have gone up)… am i right ??
If your liability is one-off, meaning you’ve to pay it at the end of the investment horizon, the perfect immunization would be to buy a zero-coupon bond of the similar maturity. That would take care of the reinvestment risk as there won’t be any interim cash flows. If we compare a zero coupon bond and a coupon bond. a zero coupon bond bears greater interest rate risk than a coupon bond, why is that? Because a coupon bond has interim cash flows, which would partly offset the price increase or decrease, and would make the bond behave like a zero coupon bond having maturity equal to the duration of that coupon bond, and both will be bearing same interest risk (almost, if we don’t take into account the convexity). So, if you want to immunize the liability through a coupon bond portfolio, then set the target duration of your coupon bond portfolio to the maturing liability. Your portfolio will act like a zero-coupon bond having maturity equal to target duration, thus eliminating the reinvestment risk, because that reinvestment risk will be offset by price risk of [maturity - duration] portion of that bond or bond portfolio. This is how I understand it, though not through CFAI curriculum; that confuses me as well.
I am confused aswell … please can anyone who knows how immunization exactly works… explain it here …as to how the whole portfolio works when the rates rise or fall and how r we hedged ?
Price risk I think you are referring to is interest rate risk. Match PV and Duration, for single liability this should be fine, but you might still have reinvestment risk. For multiple match PV and duration and bracket the liabilities, for instance if you have all liabilities within a range (3-9 years( you bracket them with 2 and 10 year bonds, this doesnt’ elimitate reinvestment risk either and neither fully eliminate the effects of convexity.
Duration is a measurement that helps FI managers immunize, but it is not the be all and end all of immunization. You can duration match your liabilities to your assets, but that doesn’t mean you have cash flow matched (the only way to ensure no reinvestment risk). Also duration measures the interest sensitivity of your FI assets with today’s yield curve, it doesn’t consider changes in yields, yield curve twists, and convexity. So just because you’re duration matched doesn’t mean you still don’t have some interest rate risk. I think this is what JP is saying. As for Zidane’s question, if asset duration > liab duration, and rates rise, correct, you’ll have a net loss. But you don’t make up for it on reinvestment because you don’t have enough assets to pay liabilities at any given time (coupons are coming in slower than your obligations to pay), so you’re not reinvesting!