TO quickly calculate the approximate intrinsic value of the S&P 500 today, use this easy-to-remember formula:
BV = intrinsic value of S&P 500 index
y = US GDP in billions of dollars
i = Moody’s Aaa bond yield
For example, if GDP is $14 trillion, and bonds yield 5 percent, then the intrinsic value of the S&P 500 is 1400.
Brock Value increases when GDP rises or interest rates fall. Conversely, when GDP declines or interest rates increase, the intrinsic value of the stock market falls.
For a more precise calculation of intrinsic value, read on as I describe the full process. It’s not complicated.
The PYi Ratio
If you wish to calculate a more precise Brock Value, then you need to know about the PYi ratio. PYi is the ratio of price over GDP, adjusted for interest rates. The PYi ratio is similar in concept to the price/earnings ratio, but instead of earnings, I use GDP. Compared to earnings, GDP is far more consistent and not prone to manipulative accounting. Then I standardize the ratio with Moody’s Aaa corporate bond yield. Unlike government bond yields, which fall when investors get nervous, corporate bond yields rise with risk aversion.
Here is the formula for PYi:
PYi = the valuation metric you’re solving for
p = level of the S&P 500 index
y = US GDP in billions of dollars
i = Moody’s Aaa bond yield
The charts below show the inputs of the PYi formula from 1919 to 2012, ending with the PYi ratio against its median of 0.519.
Fluctuations must be fluctuations around something.
Calculating Intrinsic Value
The PYi ratio’s central tendency opens the door to modelling the intrinsic value of the S&P 500. If you input the median, the PYi formula solved for price gives Brock Value.
BV = intrinsic value of S&P 500 index
y = US GDP in billions of dollars
i = Moody’s Aaa bond yield
PYi median = 0.52, the median PYi ratio from 1919 to 2012*
BV gives a useful picture of intrinsic value. When you compare BV to the S&P 500, discrepancies between price and value are distinct. It’s also easy to see when the relationship between BV and stock prices is close.
*The simplified formula for BV (y over 2i) shown at the beginning of this page uses a median PYi of 0.50 for ease of calculation. BV calculated this way will be understated by about 5 percent.
← The BV StoryValuation Pitfalls →
Your BV is missing a hinge. Interest rates and stock valuation have a non-linear correlation. Interest rates have a stock market maximizing level. For Moody’s Aaa rate it appears to be around 7%. As the yield falls or rises toward 7%, stock market valuations go up. As the yield falls below 7%, stock valuations go down. The current Aaa yield of around 3.95 is bad for stocks.
For the 10 year T-Bond the valuation maximizing yield is about 5.5% and the sub 2% yield is very bearish.
Thanks for the idea. I admit no desire to get into calculus.
But there’s no question rising rates hurt intrinsic value. It should be mentioned that the market multiple is independent of fair value. A lot of investors believe that rising rates compress PEs. But PEs are subject to mood and fashion in addition to discount rates.
That’s why low rates can co-exist with low multiples, as we see today.