Inflation!!! :(

I'm having a lot of trouble while working with inflation indices. For instance, in the example given on page 6 of chapter 11, I understand the first step (ie, calculating the coupon values as per the index of year 1999) but the rest of the solution confuses me every time.

Now I'm having confusion even in questions 1.5 and 1.6. (Dunno how I solved it the first time). :/

 

In the rest of the solution we are trying to calculate the real value of payments on the stock issue date i.e February 2000 but without the time lag.

like payments of interest on Feb 2001 = 3.64 * (index of BASE month 2000/index of the coupon payment 2001)

and so on we continue...

This will give us the real value of payments for the base date 2000, and if we will calculate the interest rate within, we will have our real rate of interest.
Hope this helps.

 

I'm still having problems. Why don't you explain to me the complete solution? Maybe that'll help.

 

I really need some help!

 

It sounds like you don't understand about calculating real values.

Try thinking about it this way:

(under the assumption of positive inflation ie prices are rising), then £100 in 1 year's time will buy less than £100 today.

From that point of view, £100 in 1 year's time is worth less than £100 today.

To work out how much less, we look at the inflation over the year - either as a percentage, or in terms of an index.

So, in the example on page 6 of Chapter 11, we know that in Feb 2001 we would actually receive 3.64. To work out the real value of this payment in Feb 00, we strip out the inflation over the year by multiplying by the 2000 inflation index and dividing by the 2001 inflation index. This gives us 3.50 as the real value.

What this tells us is that the 3.64 when it is received in Feb 01, will buy as much stuff as 3.50 in Feb 00.

So to work out a real value, you take the payment actually received in the future and adjust it for inflation over the time period from the date you're interested in (here Feb 00) and the date of the future cashflow.

 

I still have a few queries:

1. If the formula 3.5 x (2001 index)/(1999 index) gives the coupon payment on February 2002, what does the formula 3.5 x (2001 index)/(2000 index) give me?
   
2. Do the sentences "linked to an inflation index with a
   one-year time lag" and "linked to the previous years' inflation rate" have the same meaning? If no, what is the difference between them? (I know the difference between inflation index and inflation rate).
   
3. Can we solve these questions using the inflation rates?

 

1. 3.5 x (2001 index)/(2000 index) doesn't really give you anything useful for this question. (It would give you the amount of the coupon paid in Feb 01 if there was no time-lag on the inflation-linking. But we do have a time lag in this question.)

2. I'd say those two phrases didn't mean the same thing, although it's hard to tell in the second case, as I'm not sure where you're quoting from, and the rest of the sentence might affect interpretation of this phrase.

"linked to an inflation index with a one-year time lag" is a specific phrase that you would see in questions on index-linked bonds. It tells you that the actual payments received from the bond (coupons and redemption) will be calculated based on inflation index values one year before each of the relevant dates (as illustrated in this question).

"linked to the previous years' inflation rate" is a more general phrase indicating that a payment (say) is dependent on inflation over the last year. It doesn't indicate any time-lag.

3. Yes. eg the coupon payment in Feb 01 could be calculated as 3.5*1.0407 = 3.64.

 

You calculated the coupon payment on Feb 01 using 3.5*1.0407 = 3.64. How do I calculate the Feb 02 coupon payment value?

 

For the Feb 02 coupon payment, you'd need at allow for an extra year of inflation:

3.5*1.0407*1.0391 = 3.7849

This uses the inflation rates at the bottom of the page.

This matches the value of 3.79 calculated in the example using the inflation indices (other than a small amount of rounding).

The other years' coupons could be calculated in a similar way, using the inflation rates, though I think it's easier using the indices.