Folowing is an extract from CFAI Reading 27, page 350 “The immunization risk measure M2 is the variance of time to payment around the horizon date, where the weight for a particular time in the variance calculation is the proportion of the instrument’s total present value that the payment received at that time represents. The immunization risk measure may be called the maturity variance: in effect it measures how much a given immunized portfolio differs from the ideal immunized portfolio consisting of a single pure discount instrument with maturity equal to the time horizon.” The concepts employed within this sentence, and many others not cited here do not correspond to anything in my intellectual universe. Acknowledging the humbling limits of my intellectual universe, I would like to ask whether this is a good text or just sophisticated BS that can be understood more easily from another source. I will highly appreciate any advise about more accessible sources on fixed-income porfolio management. Thanks in advance.
How about a simple example… Horizon Date: 1/1/2010 I have two bonds: Bond A is selling at 106 with a 6% coupon with final maturity = 4/1/2012 and cash flows every 4/1 and 10/1. Bond B is a zero selling at 80 with maturity 11/1/2009 We want to compare which of these would be better to immunize the portfolio to that horizon date. It should be pretty obvious that B is better, yes? So there is this immunization risk measure that takes all the times until cash flows and the cash flows that happen at that time. A Time Time difference to horizon Date Cash flow % PV 4/1/2008 -2.75 6 PV(6) at ytm/106 10/1/2008 -2.25 6 PV(6) at ytm/106 … 4/1/2012 2.25 106 PV(106) at ytm/106 So now you would put real numbers in that last column (I’m too lazy). Then you would sum them up. Say the number in row i in that last column is PV(i) and the sum is S. We would then calculate M2 =(-2.75)^2*PV(1)/S + (-2.25)^2*PV(2)/S + … + 2.25^2*PV(last)/S. For Bond B it is much easier - just (2/12)^2*1 Note that for Bond A we have some cash flows that are a long freaking way away from the horizon date so they get big deviations. In particular, if the final maturity is a long way past the horizon date (and the discount rate is reasonable) the bond will get a very high M2 which is bad.
in all honesty, its a bit wordy, but not THAT bad. just look at the degrees of portfolio immunization to understand this more fully. a fully immunized portfolio (cash flow matching) has zero maturity variance. Lowest Risk/Highest Cost Immunization Strategies Cash-Flow Matching Horizon Matching Immunization Contingent Immunization will have the highest maturity variance. Higest Risk/Potentially Lower Cost (stollen straight from stalla) Contingent Immunization
Joey and Jeff, thank you both… Joey, the example is really helpful. There are not clear examples for the calculations in the reading.
ok, the graph i posted some how got messed up when i cut & pasted. Since I can’t edit my post, here is what was intended Lowest Risk/Highest Cost Immunization Strategies Cash-Flow Matching Horizon Matching Immunization Contingent Immunization Higest Risk/Potentially Lower Cost (stollen straight from stalla) Contingent Immunization will have the highest maturity variance.