AA Credit Analysis November 21 2018 - Dire times.

AA Credit using market cap volatility, solving for Distance to Default

(d2 in Black Scholes)

Now we change to a stochastic analysis of AA spread. First we solve for the volatility of the SP500, specifically the one year realized volatility (240 N):

The asset volatility, or the volatility of the market cap (debt and equity) is derived by a simultaneous equation solving for Vola, or asset volatility with the knowns the market cap V, the equity E and the equity volatility, which in this case is one year realized SP500 volatility.

Vole = [N(d1) X V X Vola] / E

The asset volatility derived is given:

Plotting the Asset Vol of the SP500 in a scatterplot to AA spreads shows the nuance and deeper insight that a stochastic analysis of credit provides.

While the above log of SP500 levels versus log of AA spread suggests that AA spreads might even be wide and may tighten, using SP500 asset vol shows the opposite.:

The asset volitility is used as the sigma, or vol, in a standard Black Scholes formula to find the d2. There is no interest in solving for price, just the d2 as the price is usually an asymtope along the x axis and while correct theorectical is of no use for trading and risk management.

The d2 formula is well known: 

The d2 depicts in units of years (Brownian scaling of time) how far the underlying credit is from default given the current asset volatility, for a certain time period (we use 5 years) and for a certain interest rate or rho (we use 3%). The d2 is often called when using a Merton formula the “distance to default”, or D2D. D2D us plotted over time and while the SP500 has sold off of late, the D2D of the SP500 has crashed and has lost 1/2 the peak value during the low sub 10% volatility period before Feb 2018 this year:

The above D2D is scatter plot as we did with SP500 asset vol against AA spread.

It is obvious that AA spread can explode upwards, doubling towards 150 to 175. Since this is based upon volatility the characteristics of vol changes, long dated vol, to change via regime shifts of jumps up or down should be considered. Volatility does not move in a discrete fashion like SP500 price and likewise credit spreads which we are showing are pricing volatility will move in regime shifts. Few understand this now.

A closeup of the above larger scale scatter is given, which gives greater deatil:

It is very likely that AA credit spreads, unless long dated volatility of the SP500 drops again to levels of 2017, will surge wider. This may surprise as it can happen while the SP500 is trading upwards. It is obvious an ex post Altman or Graham Dodd type of credit analysis does little to anticipate or provide prescience for key credit spread moves.