 # Linking Pension Liabilities to Assets

Is there a difference between the return on a real rate bond and the real return? (1+nominal) = (1+real)x(1+inflation)… If I just look at this equation, it looks like a nominal bond would adjust for inflation. So you would want to use a nominal bond if the liability is inflation indexed (positive inflation would drive the return higher). I am confused because in the book they say use real rate bonds for liabilities that are inflation indexed, so I am thinking that there is a difference between a real rate bond and a real return (as in the above equation). Is that accurate? Am I missing something here? I appreciate the help.

Think about it this way. Inflation is 3%, and you have a nominal bond with a principal of \$100. In one year, that \$100 is going to be worth less in real terms. On the other hand, if you had a real return bond, you’d have a principal of \$103, so your principal wouldn’t be eroded by inflation effects.

That makes sense. But if inflation is 3% and say the real return is 5%, then the nominal return would be 8% (quick math). So your real return, numerically, is lower than your nominal return…so why wouldn’t you want to use nominal bonds to match liabilties that are indexed to inflation?

the 100->103 happens by itself (with no need to do anything) - if my understanding is right. the 5% return on the real bond takes care of things.

but on the nominal bond - it needs to grow at 8% to cover the inflation effects.

1, Inflation hurts nominal bonds.

2, Real rate bonds or TIPS have a fixed rate, and their principal changes with inflation.

3, TIPS hedges inflation only for itself. (No Derivatives can hedge inflation directly, I think).

I think you’re mixing up yield with coupon.

If your coupon is 4% on a nominal bond, and next year inflation jumps to 8% then your real return is actually negative. On the other hand, if had a real return bond with a coupon of 3% and inflation jumps, then your coupon payments are still 3% because the real return bond principal automatically adjusts for inflation.

I think you guys may already have it covered, but here is my explanation:

The inflation portion in your formula (1+nominal) = (1+real)x(1+inflation) is meant to embed EXPECTED inflation of the market at that time into pricing the nominal bond, but once it’s issued, the coupon and principal does not change in face value terms (interest rates will obviously move the market value).

With TIPS, or Real rate bonds, the real component is what the investing community requires to compensate them for their view of the expected real return, but the principal actually adjusts with inflation on a semi-annual basis, so the face value moves.

So when you issue a bond, lets say a 10 year issue, in an environment where 2% is the annual real rate and inflation expectations are 3% a year, you get a yield of 5% (just adding for simplicity). To clear the market at par obviously this bond is issued at 100. In a year if inflatoin is 8%, your nominal coupon and principal do not change, and you will lose money since interest rates increased. But with the TIPS the principal captures the increase.

Short version, nominal bonds compensate you for EXPECTED inflation. TIPS compensate you for ACTUAL inflation. Hope that helps.

Great, thanks a lot guys. I apprecaite it.