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 = medium-term corporate bond yield

For example, if GDP is $18 trillion, and bonds yield 5 percent, then the intrinsic value of the S&P 500 is 1800.

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 the medium-term 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 = medium-term corporate bond yield

The charts below show the inputs of the PYi formula from 1919 to 2016, ending with the PYi ratio against its median of 0.499.

**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 = medium-term corporate bond yield

PYi median = 0.499, the median PYi ratio from 1919 to 2016

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.

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.

hi peter, why are you using 0.515 as the pyi for all the data table, please help me understand thank you.

Hi Stefan,

I use 0.515 because that is the median value of PYi from 1962 to 2014 (weekly data). For monthly data from 1919 the median is 0.503.

You need to know the median to calculate intrinsic value.

Mr. Brock, is there anway to modify this formula to plot over/undervaluation of the real estate market?

Yes, Andreas, you could substitute median rent for GDP and median price for the S&P 500. The trick is to find enough data to determine a valid median. Good luck and let us know how what you find.

Which series did you use for GDP? (nominal, real, seasonally adjusted, not seasonally adjusted, etc.)

I use nominal GDP, seasonally adjusted at annual rates, and I get my data from the Bureau of Economic Analysis, Table 1.1.5

http://www.bea.gov/iTable/iTable.cfm?ReqID=9&step=1#reqid=9&step=3&isuri=1&903=5

It seems that aaa corporate bond yields have become difficult to find. FRED has discontinued the data as of Oct 11 2016. Have you found another good source?

Not yet. I am still looking. Let me know what you find, including any worthy substitutes.

Instead of continuing with Moody’s, I have substituted BofA Merrill Lynch Corporate 7-10 year yields, starting in 1997 to gain long-term continuity.