P/10-Year MA(E) - inflation adjustment price, where, period, 163

sabre

Book 3 page 163 Example 13:

When converting time period t "nominal stock price" to "real stock price" the formula uses CPI(t) where as for converting the earnings it used CPI(t+1).

Why?

NakedPuts2011

Got it. Year 2009 is the base year, so.

Real stock price index(2009) = Nominal stock price index(2009).

Actually, the base year can be any year, because it shows in the numerator and denominator. Set base year t=0 is more intuitive to me.

Real stock price index(t) = Nominal stock price index(t) * CPI(2009) / CPI(t)
Real earnings(t) = Nominal earnings(t) * CPI(2009) / CPI(t+1)

The trick is that the Nominal stock price (t) is the price in January in year t, while the earning is for year t(known at year end).

Thanks for raising the Q.



Edited 1 time(s). Last edit at Wednesday, May 18, 2011 at 11:35AM by deriv108.

strikethree

For example-- if following was earnings series for 5 years:
$100, $150, $175, $180, $200

and CPI for same years was:
5, 10, 12, 15, 20

Real earnings(t):

$100*5/10,
$150*5/12,
$175*5/15,
$180*5/20,
$200*5/??

cityboy

Basically when translating to a base year all you are doing is finding a discount factor (rate) to remove the nominal CPI growth over so many years.

For example:

earnings in year 1 are X1 and the CPI is 100. CPI in year 2 is 105 - that's 5% growth from year 1 to year 2 or X1*105/100 =X2. (this could also be written like X1*1.05 = X2) we are just growing the earnings at the expected inflation rate.

If we wanted to find out what the real price is in X2 we just need to solve for X2:

X2 / (105/100) or X2 * 100/105 = Real X1

If you add another year to this and prices are X3 and the CPI is at 120 then:

X3 * 100/120 = Real X1
-----------------------------------------------------------------------
This is why it is a discount factor:

The inflation over the 2 years is: 120/100 - 1 = .20 or 20%

or similarly:
year 1 to yr 2 inflation = (105 - 100)/100 - 1= .05

year 2 to yr 3 inflation = (120 - 105)/105 - 1= .1429


total inflation compounded over yr 1 to 3 = (1.05)*(1.1429) - 1 = .20

and the average annual inflation is 1.2^1/2 = .0954 or 9.54% <--- which would be your annual discount rate for year 3 so the equation would become 120/1.0954^2 = 100 if you were to calculate in this way.

This last part is stricly for further information, and is really just a way to go into further detail on how the equation works. it's a way to modify the CPI adjustment equation to make it look like the DDM, if it doesn't make sense then don't worry, just use the stuff above the hash line.



Edited 1 time(s). Last edit at Wednesday, May 18, 2011 at 11:56AM by FinNinja.

bkballa

You buy based on current price. You are rewarded in terms of the forward earnings. So price lags earnings , and you must appropriately create the lag in the adjustment , i.e. it is a forward price/earnings measure

Windjam

Interesting.....I never paid attention to P/10-Year MA(E) being forward or historical.

now compare it to yardeni model......

NakedPuts00

I have difficulty in understanding the formula:

Real stock price index(t) = Nominal stock price index(t) * CPI(2009) / CPI(t)

If t=2009, then

Real stock price index(2009) = Nominal stock price index(2009)?

...not looking intuitive. Can you elaborate on it? Thanks.



Edited 1 time(s). Last edit at Wednesday, May 18, 2011 at 11:12AM by deriv108.

bpdulog

P/10-year MA(E). The numerator is the value of the price index, and the denominator is the average of the previous ten years’ reported earnings. Both are adjusted for inflation using the consumer price index.

I would just know how to explain it and what the benefits are.