The Fed Model is not dead...but really should be.

The Fed Model (not endorsed by the Fed) is one of those rules of thumb that investors use to value stocks, that while being intuitively appealing, is fundamentally flawed.  Recently, one of my MBA students shared another example of its application (which I'll get to in a moment).

First - what is the "Fed Model"?  Simply put, it argues that there is a relationship between the medium term Treasury yield (or some other interest rate) and the earnings yield or forward earnings yield for some basket of stocks (such as the S&P 500).

The idea is this:   Say the 10-year Treasury is yielding 4%, and the forward earnings yield of the S&P 500 is 4%, then stocks are fairly priced. (Note: the earnings yield is the inverse of the Price - earnings ratio).

If, due to inflation, the Treasury yield increases to say 5%, the Fed Model suggests that the earnings yield of the S&P 500 must adjust to 5% also.   This will result in the PE ratio of the S&P 500 falling from 25 (1/0.04) to 20 (1/0.05).   As earnings haven't changed, the price of the S&P 500 must fall from 25 to 20 or 20%.  Ouch!  You can see why investors who subscribe to the Fed Model get so upset about inflation.  In my example, a 1% increase in inflation takes 20% off the stock market.

But, it turns out that this is entirely flawed logic and suffers from my favorite behavioral finance error - "Inflation Illusion".    This is because the Fed Model ignores a key fact.   When inflation increases, the cash flows from a bond don't change.   The bond coupons are fixed.  But, the cash flows from stocks DO change.  Earnings will, on average, increase at roughly the rate of inflation.   The reason is simple - inflation occurs because companies that sell stuff put up prices, which results in higher sales (Sales = Price*Quantity) and are passed down to the bottom line.   As an exercise for the reader - make a simple income statement and increase all the costs and revenues by 1% and see what happens to the Net Income.

So when inflation increases, future earnings of the stocks will increase also.  The stock price will also adjust up to reflect inflation.  The result is that PE ratios and earnings yields stay the same, because both the price and earnings of the stock move in accordance with the higher inflation rate.  This means that the PE of the stock market can stay at 25 even if the Treasury yield is at 5%.   There's no misvaluation, because there is no fundamental reason why the Earnings yield must track the Treasury yield.

You may be wondering - why does the stock price increase in the presence of inflation?

Consider a simple dividend discount model.   Inflation is 0%, dividends grow at 2% a year and the discount rate is 5%.  Dividend today is $1.

Price = 1*(1+0.02)/(0.05-0.02)=34

Now assume 1% inflation.  Inflation increases the discount rate to 6% and the growth rate to 3%.

Price = 1*(1+0.02+0.01)/(0.05+0.01-0.02-0.01) = 34.33

The price change is:  34.33/34 -1 = 1% (rounded because we didn't compound the growth rates).

The takeaway:   When inflation occurs, all else equal, stock prices rise.

So on to that article.  It's here on CNBC and is firewalled , but the gist, according to Ned Davis Research, is that if the current 10-Year Treasury goes from 1.6% to 2%, this will result in a decline of as much as 20% in the Nasdaq index.   Unfortunately, this is exactly the Fed Model.   I've done the calculation, and yes, I get roughly the same number.  If you assume the following:

Nasdaq forward PE = 37, implying an E/P = 2.7%.  An increase of 0.4% in the E/P would result in a new Nasdaq forward PE of 32, and a price decline of about 13%.  

Unfortunately this analysis is entirely flawed.   It assumes Nasdaq earnings don't adjust with inflation.

So, to conclude - the Fed Model is still being peddled by Wall Street Firms, even though they may not call it as such.   But it's still wrong.   For an excellent take down of the model, see Cliff Asness's post at AQR here:  https://www.aqr.com/Insights/Research/Journal-Article/Fight-the-Fed-Model - full article here: https://images.aqr.com/-/media/AQR/Documents/Journal-Articles/JPM-Fight-the-Fed-Model.pdf

How does the weather impact HFT?

Sometimes I come across an academic research paper that is just so interesting I feel compelled to share it with my MBA students.  This is one of those papers.

Here's the basic set up:

High Frequency Traders (HFT) try to make money out of tiny price deviations between stocks traded in Chicago and New York.  Same stock, two trading locations.   If you can see the stock move in New York and can get a trade in in Chicago, you can capture a profit before Chicago figures out what's going on.

There are two ways to do this. 

1. Fiber optic cables.   Very fast

2. Microwaves.  A tiny bit faster.

You also need to know something else about stock trading (and this is an area I did quite a bit of work on in my earlier days) and that is that we can look at the bid-asked spread of a stock and infer from it something called the adverse selection cost of trading the stock.  The adverse selection cost measures uncertainty about the true value of the stock.   For example, if I tell you I have two cars I am selling  - they are identical, except one comes with a warranty the other doesn't - you'll pay more for the warranty car.  In effect the reduced price of the other car reflects an uncertainty cost  - the uncertainty of how good the car actually is.

OK so back to stocks - higher adverse selection cost means that there is more uncertainty about the true value of the stock.  Its true value could be higher, or lower.   High Frequency Traders contribute to this cost as they add risk to the market by being able to exploit mispricing at the expense of other market participants.

So how does this relate to the weather?  Well it turns out that microwaves don't work when it is raining hard or snowing.   So away go some of the HFT traders - just for a short while.   But during that time, the adverse selection component declines!

It's a testament to the ingenuity of the authors to devise an experiment to capture this effect.   And this isn't merely an academic exercise, millions of dollars if not billions are spent in the pursuit of HFT gains.

The paper is here if you are interested.  The intro is well written and quite accessible.  https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2848562.  Not surprisingly, this paper wound up in the very top finance journal.