Inflation Index

[User_111995]

Hi,

Could someone please explain when to use Q(t)/Q(0) and when to use Q(0)/Q(t) for the inflation index questions?

In CT1 April 2010 Question 2, the question gives an inflation index and asks for the cashflows to be calculated, the answer calculates the cashflows by using Q(t)/Q(0). In CT1 April 2011 Question 3, the question gives a retail price index and asks you to calculate the real rate of return and so in the answers uses Q(0)/Q(t) to get the real cashflows. Despite going over the notes, I can't wrap my head around when to use the correct formula, I'm aware money rates are used when inflation can be ignored and real rates of inflation are used when inflation needs to be taken into account, does the formula above come down to whether its money rates or real rates? In both questions, the cashflows are calculated but are calculated using the 2 different formulas. I know I'm probably missing something quite obvious like a standard rule of thumb that's applied to these questions, but I can't figure out what it is and cannot make sense of when to use what formula. Could someone please break it down and explain it at all?

Thanks in advance

 

[Joe Hook]

The difference here is between cashflows that are index-linked and calculations of the real rate of return. I'll give a small example.

Time RPI
0 100
1 103
2 105

Imagine we've purchased an index-linked bond. This is a bond where cashflows increase in line with inflation, designed to protect the holder against inflation and maintain their purchasing power over time. If it were a two-year bond and coupons were 5% pa paid annually and the bond is redeemed at par then the cashflows would be:

5 * (103/100) + 105 * (105/100) [Q(t)/Q(0)]

When calculating real rates of return we need to strip inflation out. High levels of inflation may lead to higher cashflows but they don't make us fundamentally better off because general prices have risen. So I like to think of real rates of return as asking "how much better off are we really?". When we calculate real rates of return we return all cashflows to the price level at which we bought the bond (ie time 0 prices). So we apply the inverse of the fractions above (Q(O)/Q(t)) and multiply them by the actual cashflows:

96 = 5 * (103/100) * (100/103) + 105 * (105/100) * (100/105)

Now in this case you'll see that the two fractions are cancelling out. In practice that will not be the case. The reason is that we use different bases for calculating the index-linked cashflows and the real rates of return. Imagine I have to work out the inflation increase to apply to a bond's cashflows today. Unfortunately I do not know the current value of the RPI index (or the inflation that's occurred over the last year). There is a time lag in these numbers being produced so I might have to use RPI 3 months ago / RPI 15 months ago for example. When it comes to real rates of return we assume that we have perfect information, ie we can use the values of the index at the date of purchase and the date of any cashflows.

Hope this helps

Joe

 

[User_111995]

Hi Joe,

That's extremely helpful, thank you so much for breaking that down!