 # P/10-Year MA(E) - inflation adjustment

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?

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.

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

Interesting…I never paid attention to P/10-Year MA(E) being forward or historical. now compare it to yardeni model…

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.

BTW I think both of you rock. If this is not relevant now then will deal after June 5th. But if it is relevant, lets just clear it out now… I only vaguely understand the reference to lagged behavior between price and earning in this context, especially when you are translating just earnings in isolation from nominal to real terms, where is the lagged behavior? 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 Can someone translate this earnings stream to first base year?

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.

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/??

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%

deriv108 Wrote: ------------------------------------------------------- > 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). That’s it, this is the bit I was missing!! thanks to you as well. Just to bring closure to this-- If the nominal Price series for the same 5 years was: \$1000, \$1100, \$1300, \$1122, \$1400 Real price(t): \$1000*5/5 \$1100*5/10 \$1300*5/12 \$1122*5/15 \$1400*5/20 Agree?

Agreed.