## Published blog Details

Posted by: Uma Shashikant and Deepa Vasudevan on Thu, Jun 6th, 2013

IIBs: Making Sense of the Cut-off Yield and Traded Price

The first inflation-indexed bond (IIB) has been issued on June 4 and we know that cut-off yield was 1.44%. There is a lot of debate whether this is high or low. Link. Link. IIBs also have begun trading in the secondary markets.

In order to understand how an IIB will be traded and valued, we have to understand a simple underlying principle. However spliced, compensation for a bond will have three components - real rate, expected inflation, and a small premium for illiquidity and unexpected changes to inflation. A normal Gsec pays a coupon that includes all these components; an IIB is structured such that the principal is indexed to inflation and only the real rate is paid as coupon. We explained how this works, in an earlier note.

When the IIB was issued on June 4 with a cut-off rate of 1.44%, the corresponding yield of the 10-year Gsec was 7.37%. We can splice the numbers as follows:

(1.0737/1.0144) -1 = 5.85%

(1 + nominal rate)/(1+real rate) = (1+expected inflation)

This equation can be solved for one unknown at all times. To arrive at the real yield payable on an IIB we can say:

(1 + nominal rate)/(1+expected inflation) = (1+real rate)

FIMMDA calls the 5.85% number as LP+IE or liquidity premium plus inflation expectations. The 5.85% number is also called the breakeven inflation, or the expected rate of inflation at which the nominal yield has to be discounted to get the real yield on the IIB.

The auction of the IIB on June 4 revealed a cut-off yield of 1.44% for the IIB, which implied an expected inflation rate of 5.85%. When the bidders in the auction asked for a real yield of 1.44% even when they knew that the yield of an equivalent 10-year Gsec was 7.37%, they were factoring in an inflation expectation of 5.85%. At a real rate of 1.44% they considered both bonds to be equivalent.

The bond traded on June 5, 2013 to close at Rs.100.23. The change in the price of an IIB will only reflect the changes to the real rates required by the market. To compute the implied yield in this price of 100.23, we will ask what would be the real rate players would demand now. We can compute yield implied in this price by discounting the IIB’s coupon rate payable until maturity and equating it to 100.23 (Use the yield function in Excel, plugging in the price at 100.23, coupon at 1.44%). The real rate implied in the price of 100.23 is 1.4153% (which nicely tallies with what CCIL published as end of day price and yield).

This can interpreted in two ways. One: If the IIB were issued on June 5, it would offer a coupon rate of 1.42%. Considering that it instead offers 1.44% as coupon, it is trading at a premium of 0.23p. Two: the implied real yield of 1.42% and the comparative 10-year nominal yield of 7.41% means, the expected inflation (plus liquidity premium) is 5.91%. Compared to 5.85% on June 4, this is higher. A higher inflation expectation translates into a gain for the IIB, which is how it should be.

How should one trade the IIB? Traders will ask whether the IIB adequately compensates for the current expectation for inflation, as reflected in the price of an equivalent nominal par bond. The price will adjust to these expectations, and align (recall the law of one price: both bonds are for the same tenor by the same issuer, though one pays a nominal rate and another the real rate).

If it is expected that inflation would move up, the IE+LP component goes up in the nominal yield of a Gsec. This means, the implied real yield in an IIB falls. That leads to an appreciation in the value of issued IIBs. In other words, when the expectations for inflation are higher than the breakeven rate assumed when the IIB was auctioned, the IIB gains because it has been priced at a higher real yield than at present. Yield and price are inversely related, but while trading and valuing an IIB, it is important to see that its yield moves down when a nominal bond’s yield moves up. That is an opportunity for the investor - the loss in a nominal bond due to an increase in expectation for inflation can be compensated by a gain in an inflation-indexed bond.

For example, the 10-year benchmark bond closed at Rs.105.08 on June 4, and lost 0.23% to close at Rs.104.835 on June 5. In the same period, the IIB issued on June 4 at Rs.100 closed at Rs.100.23, a gain of 0.23%. We may not obtain absolute equivalence in returns from both bonds, due to differences in liquidity and traded volumes. It might be too much to expect IIB with Rs.1000cr of issuance to match the liquidity of the 10-year benchmark whose daily traded volume is Rs.15,000cr.

But the underlying logic for trading and valuation of IIBs is quite simple. The relationship between nominal rates, real rates and inflation is known as this simple equation to most of us:

(1 + nominal rate)/(1+expected inflation) = (1+real rate)

What IIBs will facilitate is a better estimate of expected inflation, by giving us a real rate series from the market. The market will trade expected inflation, reflected in two series of bonds, with two sets of yields - one nominal and the other real.

Suresh Chandra Sharma on Thu, Jun 6th, 2013 8:44:47 pm

very good explanation. Are we expecting more issues of IIB?

Ajit Purohit on Thu, Jun 6th, 2013 7:40:01 pm

Hi, I got the clear information about the iib which is very important and useful to me.

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